My cousin, his wife, and their nine-year-old twin girls love farm fresh eggs. They drove out to the farm so many times for eggs, that we finally just gave them their own hens. We put three big chickens in a cardboard box, closed the lid, and all they needed to do when they got home was to build a chicken coop.
City ordinances in their town allow backyard hens, and the only requirement for the chicken coop is that it be no more than five feet tall.
When designing your own chicken coop, the best plan is to keep it simple. All that chickens really need is a roof to protect them from rain and sun, and some kind of fencing to keep the chickens where you want them.
My cousin's twin girls are creative, intelligent, and absolutely adorable. They named their hens Chick-Chick, Cluck-Cluck, and Janet.
When they got home, the girls engineered a very clever solution to house their hens: they converted their trampoline into a chicken coop!
First, they neatly attached wire fencing around the posts to keep the hens inside. The jumping part of the trampoline served as an excellent roof. They made a simple nest box with a door in the back to reach in and collect the eggs. For a roosting perch, they used a fallen oak branch, perfect for the hens to climb on. And for bedding, they used their own raked-up leaves.
The coop is light enough for my cousin to easily move around the yard, so the hens have continual access to fresh grass. Or, they can leave the coop on the garden to prepare the soil for the next planting. The coop is neat and tasteful, and the neighbors have no idea there are chickens underneath. And best of all, the twins can still play on their trampoline, with the hens nesting peacefully below.
For most people, the challenge of the chicken coop is the main obstacle to keeping backyard hens. But chicken coops are easy. If you don't have a trampoline, you can search the internet for endless examples of inexpensive chicken coop ideas.
If you have a more upscale taste in chickens, Neiman Marcus sells a luxury chicken coop for the low, low price of $100,000. Or, Williams-Sonoma can ship you a chicken coop on wheels for only $1,500. The trendiest chicken coops in Texas compete in the Austin Funky Chicken Coop Contest, and you can vote for your favorite.
Still, I think the chicken trampoline wins the prize for ingenuity, functionability, and hilarity. The next time I visit, I won't be surprised to see the twins, and the hens, all jumping on the trampoline together, everyone having a great time, and I don't think it will hurt the eggs one bit.
« A Gardening Class this Sunday, plus Much More!
Thanks Agi! I am lucky to have such clever friends and family!
Hi Pam! I LOVE that idea! Please feel free to share a picture of your coop! You can post a picture right here in the comments. Chickens make easy and nice pets, plus, they make eggs! Thank you Pam!
Brilliant idea! Turning a trampoline into a chicken coop. Having fun and looking after the chicks at the same time. Clever girls!
I am surprised that it does not scare the chickens when you play on it!
It is funny what chickens can get used to! Laughing and shouting children don't bother the chickens, as long as the chickens have a good roof over their heads and can feel like they are hiding.
I kept chickens under a trampoline as a child. I thought I was the only one.
It's such a clever idea!


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Home > Technical > Bio-Tech > Choose This Day: Life Or Death
Choose This Day: Life or Death
by Mary Gehl
The stakes have been raised in the ethical question: "Does it take a life to save a life?" The choice is ours—especially when one of those lives has no choice.
In the wake of the biotech nightmares of which we have learned so much, a ray of sanity is beginning to beam brightly. A movement, which began at the beginning of the new millennium to provide "pro-life" alternatives to products and vaccines developed with aborted fetal cell line material, is gaining momentum. It is a wake-up call for us all. A passage in Deuteronomy defines our ultimate choice:
I call heaven and earth to record this day against you, that I have set before you life and death, blessing and cursing: therefore choose life, that both you and thy seed may live.
For many years, heated accusations have been hurled by pro-life (anti-abortion) groups toward pharmaceutical companies regarding the development of relatively common vaccines using tissue taken from aborted fetuses. The "pro-choice" (pro-abortion) and scientific community returned rounds of denials. Neither side provided clear documentation in support of its opinions.
Vaccinations have been a topic of public debate since an 1853 law required universal vaccination against smallpox in England and Wales, with fines levied on those who did not comply. Similar laws were enacted in the United States and countries throughout the world in the years that followed.
Vaccinations work by presenting a substance, usually a protein, from the surface of a cell or bacterium that stimulates the production of an antibody, or immune response, into the recipient.
The vaccine development processes require a medium or "cell culture" to grow in. The virus or bacteria invades the culture cells, feeds off the cell, matures, and multiplies. The cell cultures are typically a single type of cell that multiplies itself in a predictable manner. These cell cultures can be sustained in a laboratory setting for years and are referred to as "cell lines."
In the history of vaccine development, the original cells that start these cell lines have been taken from a wide variety of sources from monkey embryo and kidney cells, to chicken and rabbit embryos. However, in 1962, aborted human babies were added to the "source list."
Aborted Fetal Cell Lines
The two fetal cell lines that have been used heavily in vaccine development have been named for the laboratory facilities where they were developed. The first one is WI-38, developed at the Wistar Institute in Philadelphia, Pennsylvania, USA by Dr. Leonard Hayflick in 1962. The cell line began with lung cells from an aborted healthy female fetus at the end of the third month of pregnancy. According to his article published in the scientific journal, Experimental Cell Research , Dr. Hayflick identified three cell lines, WI-26, WI-38, WI-44, developed from aborted babies.
In 1985, cell line PER.C6 was developed by Dr. Alex Van Der Eb and is currently being used in the research to develop vaccines to treat Ebola and HIV. According to Dr. Van Der Eb's testimony to the Food and Drug Administration's Vaccines and Related Biological Products Advisory Committee:
So I isolated retina [cells] from a fetus, from a healthy fetus as far as could be seen, of 18 weeks old.
The Percivia PER.C6 Development Center in Cambridge, Massachusetts, USA marketing documents of PER.C6 circumvent the entire truth of the background of the cell line:
The history of PER.C6®cells is an exceptional example of the market's adaptation to a changing environment both through technology improvements and regulatory stringency. The PER.C6® cell line was derived from a single healthy human retinal cell and recombinant DNA technology allows it to replicate indefinitely. Today, PER.C6® cells provide high yields, industrial level production and human-like glycoforms on expressed proteins.
As a society, consideration is given to the morality and cost of failing to prevent widespread outbreaks of disease. There is a centuries-old civic responsibility associated with vaccines and controlling diseases.
However, the creation of life-sustaining vaccinations prepared from the cells of an aborted human being has caused many to stop and consider the question—"at what cost?"
The moral perspective of those who are utterly opposed to the use of these vaccines is straightforward and justifiable.
Of growing concern is the fact that while the vaccines themselves do not contain fetal cells, it is presumed that there is residual biological matter from the fetal cells that has been assimilated into the vaccine.
For some, the entire matter is becoming eerily reminiscent of the 1973 American science fiction film, Soylent Green , in which dead humans were handily reprocessed into food capsules.
In fact, vaccines are not the only products using aborted fetal tissue.
In 1999 foremost biochemist, Lubert Stryer, founded Senomyx. Senomyx is an American biotechnology company that develops additives to amplify certain flavors and smells in foods. Their marketing information claims the company has reverse engineered the receptors in humans that react for taste and aroma. They are capitalizing on these discoveries to produce chemicals that will make food taste better.
Keep in mind, these chemicals are used in processed foods. According to their website:1
Senomyx is discovering and developing innovative flavor ingredients for the food, beverage, and ingredient supply industries using our unique proprietary technologies. We believe that our novel flavors, flavor enhancers, and bitter blockers will enable our collaborators to improve the nutritional profile of their products and/or achieve a competitive advantage maintaining or enhancing taste.
Unfortunately, Senomyx uses a cell line identified as HEK-293 that stands for "human embryonic kidney" cells. This too is an aborted fetal cell line cultured by Dr. Alex Van Der Eb in his laboratory in Leiden, The Netherlands, in the early 1970s.
While Senomyx boasts several food and beverage company contracts, their agreement with PepsiCo sprang into the public eye in October 2011 when a pro-life organization filed a shareholder resolution with the Securities and Exchange Commission (SEC) and PepsiCo to protest the use of an aborted fetal cell line in the research and development of flavor enhancers for their beverages.
In August 2010, PepsiCo entered into a $30 million four-year agreement with Senomyx for the development of artificial high-potency sweeteners. The public outcry grew to include over two dozen pro-life organizations globally with sanctioned product boycotts in the U.S., Britain, Australia, Spain, Germany, Ireland, Scotland, and Poland.
In February 2012, the SEC decided against the shareholder filing, ruling that PepsiCo's agreement with Senomyx falls under "ordinary business operations" for the beverage company. Jeff Dahncke, senior director of communications for PepsiCo, said the following "to correct the misperceptions and erroneous information" that had appeared in media reports about the controversy:
PepsiCo does not conduct or fund research, including research performed by third parties, which utilizes any human tissue or cell lines derived from embryos or fetuses as clearly stated in the company's "Statement on Responsible Research"2 on our website.3 Any research funded by PepsiCo and conducted by Senomyx for PepsiCo must abide by this responsible research statement.
So how does PepsiCo find it so easy to deny the documented link to an aborted fetal cell line? According to one pro-life spokesperson, "It is all a matter of contorted semantics." The aborted fetal cell line used by Senomyx is from a lab that cultivated it out of cells from a baby aborted in the 1970s. Neither PepsiCo nor Senomyx "took these cells directly from the fetus."
Yet, after months of pro-life opposition, PepsiCo just recently indicated it has altered its contract with Senomyx. PepsiCo's VP of Global Public Policy, Paul Boykas stated that:
Senomyx will not use HEK cells or any other tissues or cell lines derived from human embryos or fetuses for research performed on behalf of PepsiCo. We took the matter very seriously. We have an official Statement on Responsible Research and we intend to live by that policy.
That policy precludes any research by PepsiCo—or third parties they fund—from using human tissue or cell lines derived from embryos or babies who were aborted.
Debi Vinnedge of the pro-life group Children of God for Life, who spearheaded the boycott efforts, said the PepsiCo decision meant an immediate end to the boycott that began in May 2011—good news to both PepsiCo and their customers who have abstained from drinking Pepsi in protest. She announced:
We are absolutely thrilled with PepsiCo's decision. They have listened to their customers and have made both a wise and profound statement of corporate integrity that deserves the utmost respect, admiration and support of the public.
The Business of Abortion
But in reality, the matter of "contorted semantics" can be applied to the entire abortion industry today. There is a federal law (42 U.S.C. § 289g-2 : US Code - Section 289G-2: Prohibitions regarding human fetal tissue) that is supposed to ban the practice of selling aborted fetus body parts:
(a) Purchase of tissue: It shall be unlawful for any person to knowingly acquire, receive, or otherwise transfer any human fetal tissue for valuable consideration if the transfer affects interstate commerce.
However, a gaping loophole has been used to create the wholesale harvesting of more than fetal cells:
(d) Definitions: (3) The term "valuable consideration" does not include reasonable payments associated with the transportation, implantation, processing, preservation, quality control, or storage of human fetal tissue.
Another clarification of terms is valuable. "Embryonic" stem cells are taken from the inner cell mass of an embryo from four days to several weeks after fertilization. After that time, the stem cells are considered to be "adult."
When "adult" cells are utilized, the fact that the fetus was aborted is often obscured in the lack of adequate documentation.
Federal and some state laws permit fetal tissue research, but there are definite gaps in the oversight of the source of the fetus. Additionally, the loophole in the federal regulations has been exploited.
One example is the Brain and Tissue Bank for Developmental Disorders, hosted by the University of Maryland School of Medicine. According to the Bank's "Catalog of Available Tissue," it stores tissue from hundreds of fetuses, including those with chromosomal disorders, anencephaly, and many with no disorders at all, marked as "control" tissue spanning ages 10 to 30 weeks.
When contacted as to the source of the tissue, Bank director, H. Ronald Zielke, assumed the researchers acquired fetal remains directly from "some service that does terminations." This would include those with whom the Bank had "private agreements."
Another top supplier of fetal tissue is the Birth Defects Research Laboratory at the University of Washington in Seattle, Washington, USA. According to the lab's grant records, it received $579,091 from the National Institute of Health (NIH) in 2010. To date, the lab retrieved the "products" of 22,000 pregnancies.
Astonishingly, a description the lab provided in its most recent grant application bemoaned that an increase in nonsurgical abortion methods has "created new obstacles to obtaining sufficient amounts of high quality tissue. To overcome these problems and meet increasing demand, the Laboratory has developed new relationships with both local and distant clinics."
Sanity Enters the Marketplace
In contrast to the University of Washington stands Theresa Deisher, Ph.D. In 2008, Dr. Deisher became the President and founder of Sound Choice Pharmaceutical Institute, also in Seattle. Additionally, in 2008, she formed AVM Biotechnology that is "dedicated to the discovery, development, and commercialization of safe, effective, and affordable pro-life therapeutics."
The stakes have been raised in the ethical question: "Does it take a life to save a life?"
The choice is ours—especially when one of those lives has no choice.
June 2012 Personal Update NewsJournal.
http://codes.lp.findlaw.com/uscode/42/6A/III/H/289g-2
http://www.cogforlife.org
http://www.avmbiotech.com
http://www.soundchoice.org/
http://www.dsm.com/en_US/downloads/dpp/PER.C6_Brochure.pdf
http://www.senomyx.com
http://www.lifenews.com/2012/04/30/pepsi-stops-using-aborted-fetal-cell-lines-to-test-flavors/
http://www.senomyx.com/
http://www.pepsico.com/Company/Corporate-Governance/Policies.html
http://www.pepsico.com

redpajama_set_name: RedPajamaCommonCrawl


text:
Novaci több romániai település neve:
 Novaci, Giurgiu megye
 Novaci, Gorj megye

valamint egy település neve Macedóniában:
 Novaci, Pelagonia régió

redpajama_set_name: RedPajamaWikipedia


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Cleveland Cavaliers vs Minnesota Timberwolves 1/14/2023 Odds, Free Picks and Tips
The Cleveland Cavaliers will go against the Minnesota Timberwolves in NBA action in Target Center, Minnesota, on Saturday, January 14, 2023, at 8:00 PM ET. The Cleveland Cavaliers are now four matches behind the Boston Celtics for the top spot in the Eastern Conference standings. They are generating 111.7 points per game on offense, and their field goal percentage is 48.1%. This represents the eighth-highest team shooting percentage and the 26th-most points scored per game. The Cavaliers have the 10th-highest adjusted offensive rating in the NBA, with a rating of 114.3. On the offensive end of the court, Donovan Mitchell is still in the top with 29.2 points per game on 48.9% field goal shooting.
The Cavaliers were quite difficult to defeat defensively. They are now allowing 106.9 points per game while making their rivals shoot only 46.3% of the time. This is the seventh-lowest shooting percentage surrendered and the fewest points allowed per game. The Cavaliers have the second-lowest adjusted defensive rating in the NBA with a rating of 109.4. Cleveland also demonstrated that they would challenge shots that are taken close to the rim, but they had trouble challenging jumpers taken from outside the paint. The league's 27th-lowest three-point shooting percentage permitted is 36.7%, which their opponents shot from beyond the arc against them.
The total went OVER in 9 of Cleveland's last 12 matches.
The Cleveland Cavaliers are 5-2 SU in their last 7 matches.
The Cavaliers are 1-5 ATS in their last 6 games with Minnesota.
The Minnesota Timberwolves are 8.5 matches behind the Grizzlies and the Nuggets in the Western Conference rankings, where they are now in 10th place. They are scoring 114.8 points per game on offense, and their field goal percentage is 49.1%. The T-Wolves have the 19th-highest normalized offensive rating in the NBA with a rating of 112.9. Anthony Edwards continues to be the offensive standout, scoring 23.6 points per game on 45.6% of his field goal attempts.
The T-Wolves' rivals score 115.5 ppg against them, and they are shooting 46.2% from the field. This represents the 19th most points allowed each game but the sixth-lowest field goal percentage permitted. Minnesota has the 22nd-lowest modified defense rating in the NBA with a rating of 114.1. They proved that they'll block every shot that comes close to the basket, but their perimeter defense did not improve.
The Minnesota Timberwolves are 4-2 ATS in their last 6 matches.
The total went OVER in 8 of Minnesota's previous 11 meetings.
The Timberwolves are 5-1 SU in their last 6 matches.
Cleveland Cavaliers vs Minnesota Timberwolves. The NBA pick for this game is the Cleveland Cavaliers. The Cavaliers are giving up the fewest points per game and have the second-lowest modified defensive rating. It will be very challenging for Minnesota to score enough points to cover this spread since they will contest shots near the rim. The Timberwolves' adjusted offensive rating is only the 19th-highest, and they had trouble making 3-point shots. They won't consistently make baskets, and Cleveland will gradually gain an advantage. They have the eighth-highest team shooting percentage and the tenth-highest adjusted offensive rating. This game will move more slowly as they keep scoring. The Timberwolves are surrendering the 19th most points while ranking 22nd in adjusted defensive rating. They won't consistently make stops, and the Cavaliers will gradually gain ground. Cleveland will win to a predicted score of 116-111.
NBA Starting Time: 8:00 PM (EDT)
Location: Target Center, Minnesota
TV: BSN
NBA Odds: Cleveland Cavaliers -4
NBA Totals: 224.5


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Ivo Babuška (* 22. března 1926, Praha) je česko-americký matematik a stavební inženýr. Narodil se v rodině architekta a stavitele Milana Babušky. Proslavil se aplikovanou numerickou matematikou. Za svůj přínos v oblasti mechaniky byl odměněn Humboldtovou cenou, udělovanou na Humboldtově univerzitě v SRN. Získal několik čestných doktorátů z různých univerzit světa.

Život
Ivo Babuška v letech 1941 až 1945 absolvoval Vyšší průmyslovou školu stavební v Praze (Betlémská ulice). V r. 1945 vykonal doplňkovou maturitu na malostranské reálce a následně se zapsal na Vysokou školu inženýrského stavitelství ČVUT v Praze (směr konstruktivně dopravní).

Babuška vystudoval fakultu, která byla předchůdkyní Stavební fakulty ČVUT. V červnu 1949 se stal stavebním inženýrem (úspěšně zakončil druhou státní zkoušku).

Ivo Babuška pracoval krátce na Ústavu ocelových konstrukcí u prof. F. Faltuse.

Jeho zájmy o obory matematiky, které poskytovaly nástroje pro řešení praktických úloh stavební mechaniky, ho však v roce 1949 přivedly do Ústavu pro matematiku České akademie věd a umění, dnešního Matematického ústavu AV ČR, kde později až do roku 1968 působil jako ředitel.

V roce 1968 odjel legálně na roční vědecký pobyt do USA, kde již zůstal s celou rodinou (emigrace). Po mnoho let pak pracoval na Marylandské univerzitě v College Parku. Ve Spojených státech pokračoval intenzivně v aplikacích metody konečných prvků do praxe, a zůstal jim věrný dodnes. Od roku 1990, po pádu totalitního komunismu a otevření hranic Československa, jezdí opět do Prahy pravidelně. Dosud působí v Institute for Computational Engineering and Sciences, University of Texas, Austin.

Práce
První významný projekt, k jehož řešení Ivo Babuška v letech 1953–1956 přispěl, bylo posouzení mechanického napětí způsobeného uvolňováním tepla při tuhnutí betonu při výstavbě přehradní hráze Orlík. V průběhu řešení tohoto problému vznikla řada disertačních prací celé jedné generace českých numerických matematiků, např. prof. Karla Rektoryse. Počítače v Československu tehdy nebyly, a tak všechny výpočty tehdy prováděla skupina výpočtářek Jarmila Vitásková, Růžena Pachtová a Jana Grünerová na elektromechanických kalkulačkách. Na ČVUT vyučoval aplikovanou matematiku.

Badatelské zaměření Iva Babušky se týká především aposteriorních odhadů chyby přibližného řešení a s tím spojené adaptivní metody konečných prvků, zasloužil se o rozvoj mechaniky kontinua. Vychoval desítky doktorandů, z nichž mnoho se už také proslavilo ve výpočtové matematice v USA nebo v Evropě. Ivo Babuška se proslavil svým dotazem  (volně přeloženo "Víte, že se nakonec budete muset pod ten projekt podepsat?"), který kladl v diskusi všem řečníkům na všech konferencích, které se týkaly aplikací matematiky.

V roce 1956 založil časopis Aplikace matematiky (nyní Applications of Mathematics), který dodnes vydává Matematický ústav AV ČR. Spolu s profesorem Jaroslavem Kurzweilem založil v roce 1962 tradici vědeckých konferencí EQUADIFF. Ty se konají každé čtyři roky po řadě v Praze, Bratislavě a Brně.

Ve Spojených státech dlouhá léta organizoval dvakrát ročně neformální konferenci Finite Element Circus, kterou jeho pokračovatelé pořádají nadále. V roce 1994 založil nadaci – cenu pro mladé vědecké pracovníky, kterou uděluje Česká společnost pro mechaniku společně s Jednotou českých matematiků a fyziků. Cena nese Babuškovo jméno a uděluje se, s přispěním jeho vlastních prostředků, každoročně.

Profesor Ivo Babuška publikoval více než 300 vědeckých publikací z oblasti matematiky, čísel a mechaniky, zejména v době svého exilu. Několik z jeho knih bylo přeloženo do různých jazyků. Je členem více než 15 mezinárodních redakcí. Náleží mu řada ocenění, mezi něž patří např. cena Humbolt Award Spolkové republiky Německa, udílená matematikům, z českých ocenění např. čestná oborová medaile Bernarda Bolzana za zásluhy v matematických vědách, kterou mu udělila AV ČR. Byl též zvolen čestným zahraničním členem Učené společnosti ČR.

Ocenění díla

 V roce 1968 obdržel Státní cenu Klementa Gottwalda za vědecké práce o stabilitě a optimalizaci v numerické matematice.
 V roce 1992 mu byla udělena Medaile pražské Karlovy univerzity.
 V roce 1993 mu byla udělena Medaile České společnosti pro mechaniku.
 V roce 1994 získal Birkhoffovu cenu americké matematické společnosti.
 V roce 1994 mu byl udělen čestný titul Doctor of Science (Hon DSc), University of Westminster, London.
 V roce 1996 pak udělen čestný titul Doctor of Sciences Honouris Causa na Brunel University, United Kingdom.
 V roce 1997 pak Doctor of Sciences Honoris Causa Univerzity Karlovy v Praze.
 V roce 2000 Honorary Doctorate, Helsinská technická univerzita.
 V roce 2007 mu byl udělen čestný titul doktora technických věd (dr. h. c.) Českého vysokého učení technického v Praze
 Babuškovo jméno nese od roku 2003 asteroid 36060.
 U příležitosti 80. narozenin obdržel v Praze dne 29. května 2006 od Akademie věd ČR nejvyšší české akademické vyznamenání, čestnou medaili De scientia et humanitate optime meritis.

Odkazy

Reference

Související články
 Eduard Čech
 Jaroslav Kurzweil
 Karel Rektorys

Externí odkazy

 Ivo Babuška člen ICES
 Ivo Babuška na Univerzitě v Texasu
 Profil na stránkách University of Texas at Austin

Američtí matematici
Čeští matematici
Matematici působící v Česku
Čeští stavební inženýři
Matematici 20. století
Matematici 21. století
Držitelé čestných doktorátů
Držitelé čestných doktorátů ČVUT
Čeští emigranti a exulanti
Laureáti Státní ceny Klementa Gottwalda
Nositelé Ceny Neuron
Absolventi Fakulty stavební ČVUT
Narození v roce 1926
Narození 22. března
Narození v Praze
Žijící lidé
Muži


SHEfinds / Style / Organic Beauty: Where to Start?
Organic Beauty: Where to Start?
We all know the benefits of using organic beauty products — less toxins and irritants being absorbed into the body, the better you feel, the better your health. With the mass numbers of organic this and natural that, how is one supposed to weed through the labels to find what's really and truly a verifiable organic beauty product?
Step One: Know that the term "natural" has no scientific bearing whatsoever. Do you know what most of the ingredients are on the label? If not, chances are you're looking at something as toxic as the rest of the products on the shelf.
Step Two: Steer towards products labeled 100% Organic or Certified Organic. These are the only products legally allowed to carry the USDA Organic Seal. You can rest assured these products have been made safely, free from pesticides, sewage sludge, chemical fertilizers, etc. "Made with Organic" is usually a safe bet, but know these may only have about 70% organic materials. Anything less than that may have organic products listed on the ingredients label, but the product could contain as little as 1% organics.
Step Three: Know the bad ingredients, like methyl/proplylparaben (a preservative), sodium laureth/lauryl sulfate (a skin irritant that should be avoided by those with sensitive skin), phthalates and formaldehyde. You can find a full list of bad-for-you ingredients at the Environmental Working Group's cosmetic database, Skin Deep. Another great resource is Paula Begoun's ingredient directory that explains what things are in plain speak.


Cookies and GDPR compliance, perhaps you haven't thought about how regulation changes could impact the way you market? Find out everything you need to know about how GDPR will affect the way you use web analytics tools like cookies in your business.
Cookies have become a familiar fixture for most web users. Web analytics tools allow businesses to track visitor engagement on their website and follow up with marketing activity. Useful for your marketing team? Certainly. GDPR compliant? Well, that's where the waters get a little muddy.
What do the guidelines say about Cookies and GDPR compliance?
Not all cookies are used in a way that could identify users, but the majority are. This means cookies used for analytics, advertising and functional services such as surveys and chat tools are at risk of non-compliance under GDPR. A risk that comes with a hefty penalty.
Why are Cookies potentially non-compliant with GDPR?
Cookies often contain pseudonymous identifiers (e.g. strings of numbers or letters) to give them uniqueness. Under GDPR it is this uniqueness that qualifies them as personal data. So, any cookie that is capable of identifying an individual, or treating them as unique without explicitly identifying them means your business is processing personal data.
Implied Consent is no longer enough: Previously, most businesses have relied on the idea of 'implied consent'. I.e. Visitors have offered an email address or phone number, they have visited your website and taken some kind of action. Under GDPR this is no longer enough. Consent must be given via an affirmative action, such as clicking an opt-in box or setting preferences. Crucially, opt-in to one type of contact does not qualify your business to assume consent for all types of contact.
It must be as easy to withdraw consent as it is to give it: Even after you have gained consent to process an individual's personal data it must be easy for them to change their preference. If you ask for consent via and opt-in-box, for example, and opt-out must be equally visible.
Soft Opt-In is not sufficient: We are all familiar with the 'by using this site, you accept cookies' message that pops up on websites. We all probably use just such a message on our own websites. However, under GDPR if there's no valid consent option it does not count as consent at all. You must make it possible to accept and reject cookies.
To cut a long story short, using cookies in the established way is going to become increasingly hard. Cookies are not banned under GDPR. However, if you can't prove consent on an individual basis you're at risk of non-compliance.
If you can prove that your business has a lawful ground to collect and process the data in question then you can continue to do so. However, since most businesses rely on implied or opt-out consent it will be increasingly hard to prove lawful consent under the strengthened requirements of GDPR.
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text:
\section{Introduction}
In the past decades, a number of optimization techniques have been proposed for solving machine learning problems~\citep{sra2012optimization}. However, real-world optimization problems often suffer from the issue of data ambiguity that can be generated by natural data noise,   potential adversarial attackers~\citep{DBLP:journals/pr/BiggioR18}, or the constant changes of the underlying distribution (e.g., continual learning~\citep{ring1998child}).  As a consequence, our obtained dataset usually cannot be fully trusted. Instead it is actually a perturbation of the true distribution. The recent studies have shown that even small perturbation can seriously destroy the final optimization result and could also yield unexpected error for the applications like classification and pattern recognition~\cite{goodfellow2018making,DBLP:journals/corr/SzegedyZSBEGF13}.

The ``\textbf{distributionally robust optimization} (\textsf{DRO})'' is an elegant model for solving the issue of ambiguous data. The idea follows from the intuition of   game  theory~\citep{rahimian2019distributionally}. Roughly speaking, the \textsf{DRO} aims to find a solution that is robust against the worst-case perturbation within a range of possible distributions.
Given an empirical distribution $\mathbb{ P}_n=\frac{1}{n}\sum\limits_{i=1}^n\delta_{\xi_i}$ where $\delta_{\xi_i}$ is the Dirac point mass at the $i$-th data sample $\xi_i$, the \textbf{worst-case empirical risk} at the hypothesis $\theta$ is defined as $R^{\mathbb{P}_n}(\theta) = \sup\limits_{\mathbb{Q}\in \mathcal{U}(\mathbb{P}_n)} \mathbb{E}^\mathbb{Q}[\ell(\theta,\xi)]$.
Here $\mathcal{U}(\mathbb{P}_n)$ is the ambiguity set consisting of all possible  distributions of interest, and $\ell(\cdot,\cdot)$ is the non-negative loss function. The DRO model has shown its promising advantage for enhancing the robustness for many practical machine learning problems, such as logistic regression~\citep{shafieezadeh2015distributionally}, support vector machine~\citep{lee2015distributionally},
convex regression~\citep{blanchet2019multivariate}, neural networks~\citep{sagawa2019distributionally, DBLP:conf/iclr/SinhaND18}, etc.

In this paper,  we consider one of the most representative \textsf{DRO} models that is defined by using optimal transportation ~\citep{villani2009optimal}.  \textbf{Wasserstein distance} is a popular measure for representing the difference between two distributions; it indicates the minimum cost for transporting one distribution to the other.
For $p\geq 1$, the $p$-th order Wasserstein distance between two probability distributions $\mathbb{P}$ and $\mathbb{P'}$ supported on $\Xi$ is
\begin{eqnarray}
W_p(\mathbb{P},\mathbb{P'})=\left(\inf _{\pi \in \Pi\left(\mathbb{P}, \mathbb{P}^{\prime}\right)} \int_{\Xi\times\Xi} \mathtt{d}^p(\xi,\xi^{\prime})\pi\left(\mathrm{d} \xi, \mathrm{d} \xi^{\prime}\right)\right)^{\frac{1}{p}},\label{for-wasdist}
\end{eqnarray}
where $\mathtt{d}(\cdot,\cdot)$ is a metric on $\Xi$, and $\Pi(\mathbb{P},\mathbb{P}^{\prime})$ is the set of all joint probability distributions on $\Xi\times\Xi$ with the  marginals $\mathbb{P}$ and $\mathbb{P}'$.
By using the above Wasserstein distance~(\ref{for-wasdist}), we can define the ambiguity set   $\mathcal{U}(\mathbb{P}_n)$ to be the $p$-th order \textbf{Wasserstein  ball} $\mathbb{B}_{\sigma,p}(\mathbb{P}_n)$, which covers all the distributions that have the $p$-th order Wasserstein distance at most $\sigma>0$ to the given empirical distribution $\mathbb{P}_n$.  The use of Wasserstein ball is a discrepancy-based approach for choosing the ambiguity set \cite[section 5]{rahimian2019distributionally}.
Also let
\begin{eqnarray}
\label{eq:worst-case}
R^{\mathbb{P}_n}_{\sigma,p}(\theta)= \sup\limits_{\mathbb{Q}\in \mathbb{B}_{\sigma,p}(\mathbb{P}_n)} \mathbb{E}^\mathbb{Q}[\ell(\theta,\xi)]
\end{eqnarray}
denote the corresponding worst-case empirical risk. The \textbf{Wasserstein distributionally robust optimization} (\textsf{WDRO}) problem~\cite{kuhn2019wasserstein} is to find the minimizer
\begin{eqnarray}
\label{eq:WDRO}
\theta_*=\mathop{\arg\min}\limits_{\theta\in\Theta}R^{\mathbb{P}_n}_{\sigma,p}(\theta)=\mathop{\arg\min}\limits_{\theta\in\Theta}\sup\limits_{\mathbb{Q}\in \mathbb{B}_{\sigma,p}(\mathbb{P}_n)} \mathbb{E}^\mathbb{Q}[\ell(\theta,\xi)],
\end{eqnarray}
where $\Theta$ is the feasible region in the hypothesis space. It is easy to see that the \textsf{WDRO} is a minimax optimization problem.

Compared with other robust optimization models, the \textsf{WDRO} model enjoys several significant benefits from the Wasserstein metric, especially for the applications in machine learning~\citep{xu2009robustness,shafieezadeh2019regularization,blanchet2019robust,DBLP:journals/corr/abs-1712-06050}. The Wasserstein ball  captures much richer information than the divergence-based discrepancies for the problems like pattern recognition and image retrieval~\citep{rubner2000earth,ling2007efficient,gao2016distributionally}. It has also been proved that the \textsf{WDRO} model yields  theoretical quality guarantees for the ``out-of-sample'' robustness~\citep{articleDRO}.

However, due to the intractability of the the inner maximization problem (\ref{eq:worst-case}), it is challenging to directly solve the minimax optimization problem (\ref{eq:WDRO}). As shown in the work of~\citet{articleDRO}, the \textsf{WDRO} problem  (\ref{eq:WDRO}) usually has tractable reformulations~\citep{shafieezadeh2015distributionally,mohajerin2018data,postek2016computationally,lee2015distributionally,hanasusanto2018conic,blanchet2019quantifying}. Although these reformulations  are polynomial-time solvable, the off-the-shelf solvers can be costly for large-scale data. Another approach  is to directly solve the minimization problem and the maximization problem alternatively~\citep{pflug2014problem} under a finite-support assumption. \citet{gao2016distributionally} proposed a routine to compute the finite structure of the worst-case distribution in theory. Nevertheless it still takes a high computational complexity if the Wasserstein ball has a large support size.
Several fast \textsf{WDRO} training algorithms for some specific machine learning tasks, e.g., SVM  and logistic regression by \citet{li2019first,li2020fast}, have been developed recently; but it is unclear whether their methods can be generalized to solve other problems.

Therefore, it is urgent to develop efficient algorithmic techniques for reducing the computational complexity of the \textsf{WDRO} problems.  \textbf{Coreset} is a popular tool for compressing large datasets, which  was initially introduced by Agarwal et al. in computational geometry~\citep{DBLP:journals/jacm/AgarwalHV04}. Intuitively, the coreset is an approximation of the original input data, but has a much smaller size. Thus any existing algorithm can run on the coreset instead and the computational complexity can be largely reduced. The coresets techniques have been widely applied for many optimization problems such as clustering and  regression (we refer the reader to the recent surveys on coresets~~\citep{DBLP:journals/ki/MunteanuS18,DBLP:journals/widm/Feldman20}).
Therefore a natural idea is to consider applying the coreset technique to deal with large-scale \textsf{WDRO} problems.
Below we introduce the formal definition of the coreset for \textsf{WDRO} problems.

\begin{definition}[$\epsilon$-coreset]
\label{def:coreset}
Let $\epsilon$ be any given small number in $(0,1)$. An $\epsilon$-coreset for the \textsf{WDRO} problem (\ref{eq:WDRO}) is a sparse nonnegative mass vector $W=[w_1,\dots,w_n]$, such that the total mass $\sum_{i=1}^nw_i=1$ and the induced distribution $\tilde{\mathbb{P}}_n=\sum\limits_{i=1}^nw_i\delta_{\xi_i}$ satisfies
\begin{eqnarray}
R^{\mathbb{\tilde P}_n}_{\sigma,p}(\theta)\in (1\pm\epsilon) R^{\mathbb{P}_n}_{\sigma,p}(\theta), \forall \theta\in \Theta,
\end{eqnarray}
where $R_{\sigma,p}^{\mathbb{\tilde P}_n}(\theta)\coloneqq\sup\limits_{\mathbb{Q}\in \mathbb{B}_{\sigma,p}(\tilde{\mathbb{P}}_n)} \mathbb{E}^\mathbb{Q}[\ell(\theta,\xi)]$ is the worst-case empirical risk of the coreset.
\end{definition}

It is worth to emphasize that the above coreset for \textsf{WDRO} is fundamentally different from the conventional  coresets~\citep{DBLP:journals/widm/Feldman20}. The main challenge for constructing the coreset of \textsf{WDRO} is from the ``\textbf{uncertainty}'' issue, that is, we have to consider all the possible distributions in the Wasserstein ball $\mathbb{B}_{\sigma,p}(\tilde{\mathbb{P}}_n)$; and more importantly, when the parameter vector $\theta$ varies, the distribution that achieves the worst-case empirical risk also changes inside $\mathbb{B}_{\sigma,p}(\tilde{\mathbb{P}}_n)$.

\subsection{Our Contribution}
In this paper, we propose a novel framework to  construct the $\epsilon$-coresets for general \textsf{WDRO} problems. To the best of our knowledge, this is the first coreset algorithm for Wasserstein distributionally robust optimization problems. Our main contributions are twofold.

 \textbf{-From coresets to dual coresets.} As mentioned before, it is challenging to directly construct the coresets for the \textsf{WDRO} problems. Our key observation is inspired by the strong duality property of the \textsf{WDRO} model ~\citep{articleDRO,blanchet2019quantifying,gao2016distributionally}.  We introduce the ``dual coreset'' for the dual formulation of the \textsf{WDRO} problems. We can neatly circumvent  the ``uncertainty'' issue in Definition~\ref{def:coreset}   through  the dual form.  Also, we prove that the dual coreset  can yield a theoretically quality-guaranteed coreset as Definition~\ref{def:coreset}.

\textbf{-How to compute the dual coresets.} Further, we provide a unified framework to construct the dual coresets efficiently. The sensitive-sampling based coreset framework usually needs to compute the ``pseudo-dimension'' of the objective function and the ``sensitivities'' of the data items, which can be very difficult to obtain~~\cite{DBLP:journals/widm/Feldman20} (the pseudo-dimension measures how complicated the objective function is, and the sensitivity of each data item indicates its importance to the whole input data set). Therefore we consider to apply the spatial partition approach that was initiated by Chen~\citep{chen2009coresets}; roughly speaking, we partition the space into a logarithmic number of regions, and take a uniform sample from each region. This partition approach needs to compute the exact value of the  Moreau-Yosida regularization~\citep{parikh2014proximal},  which is a key part in the dual formulation of \textsf{WDRO} (the formal definition is shown in Proposition~\ref{pro:duality}). However, this value is often  hard to obtain for general $\Xi$ and general $\ell(\cdot,\cdot)$. For instance, suppose $\Xi$ admits a conic representation and the learning model is SVM, then computing the Moreau-Yosida regularization is equivalent to solving a convex conic programming ~\citep[corollary 3.12]{shafieezadeh2019regularization}. For some machine learning problems, it is usually relatively easier to estimate the bounds of the Moreau-Yosida regularization\cite[Theorem 3.30]{shafieezadeh2019regularization}.
Based on this observation, we generalize the spatial partition idea and propose a more practical ``grid sampling'' framework. By using this framework, we only need to estimate the upper and lower bounds of the Moreau-Yosida regularization instead of the exact value. We also prove that a broad range of objective functions can be handled under this framework.

\subsection{Other Related Works}

A number of coreset-based techniques have been studied before for solving robust optimization problems. For example, \citet{DBLP:conf/nips/MirzasoleimanCL20} designed an algorithm to generate coreset to approximate the Jacobian of a neural network so as to train against noisy labels. The outlier-resistant coresets were also studied for computing the robust center-based clustering problems~\citep{DBLP:conf/stoc/FeldmanL11,DBLP:conf/soda/FeldmanS12,DBLP:conf/focs/HuangJLW18,DBLP:conf/esa/DingYW19}.
For the general continuous and bounded optimization problems~\cite{understandingML}, \citet{DBLP:conf/nips/WangGD21} proposed a dynamic framework to compute the coresets resisting against outliers. Several other techniques also have been proposed for dealing with large-scale \textsf{DRO} problems, such as the PCA based dimension reduction methods~\citep{DBLP:journals/siamjo/ChengCNPSW18,cheramin2020computationally} and the stochastic gradient optimization methods~\citep{DBLP:conf/nips/LevyCDS20,DBLP:conf/nips/NamkoongD16}.

\section{Preliminaries}
\label{sec:pre}

We assume the input-output space $\Xi=\mathbb{X}\times\mathbb{Y}$ with $\mathbb{X}\subseteq\mathbb{R}^m$ and $\mathbb{Y}\subseteq\mathbb{R}$, and let $\mathcal{P}(\Xi)$ denote the set of Borel probability distributions supported on $\Xi$. For $1\leq i\leq n$, each data sample is a random vector $\xi_i=(x_i, y_i)$ drawn from some underlying distribution $\mathbb{P}\in \mathcal{P}(\Xi)$.
The empirical distribution $\mathbb{P}_n=\frac{1}{n}\sum_{i=1}^n\delta_{\xi_i}$ is induced by the dataset $\{\xi_1,\dots,\xi_n\}$, where $\delta_{\xi_i}$ is the Dirac point mass at  $\xi_i$. We endow $\Xi$ with the feature-label metric $\mathtt{d}(\xi_i,\xi_j)=\|x_i-x_j\|+\frac{\gamma}{2}|y_i-y_j|$, where $\|\cdot\|$ stands for an arbitrary norm of $\mathbb{R}^m$ and the positive parameter ``$\gamma$'' quantifies the transportation cost on the label. This distance function is used for defining the Wasserstein distance (\ref{for-wasdist}). We assume that $(\Xi,\mathtt{d})$ is a complete metric space.

In the rest of this paper, we consider the \textsf{WDRO} problems satisfying the following two assumptions. The first assumption is on the smoothness and boundedness of $\theta$. Similar assumptions have been widely adopted in the machine learning field~\citep{DBLP:conf/icml/Zinkevich03,DBLP:conf/nips/WangGD21}.

\begin{assumption}[Smoothness and Boundedness of $\theta$~\cite{understandingML}]
\label{ass:snb}
~
\begin{enumerate}
    \item[(\romannumeral1)] ({\em{Boundedness}}) The feasible region  $\Theta$ of the parameter space for the \textsf{WDRO} problem (\ref{eq:WDRO}) is within a closed Euclidean ball $\mathbb{B}(\theta_{\mathtt{anc}},l_{\mathtt{p}})$ centered at some ``anchor'' point $\theta_{\mathtt{anc}}\in \mathbb{R}^d$ with radius $l_{\mathtt{p}}>0$;
    \item[(\romannumeral2)] ({\em{Lipschitz Smoothness}}\footnote{The methods proposed in this paper can be easily extended to other types of smoothness, e.g., gradient Lipschitz continuity.}) There exists a constant $L>0$, such that for any $\xi\in\Xi$ and any $\theta_1,\theta_2\in \mathbb{B}(\theta_{\mathtt{anc}},l_{\mathtt{p}})$, we have
$
|\ell\left(\theta_{1}, \xi\right)-\ell\left(\theta_{2}, \xi\right)| \leq L\left\|\theta_{1}-\theta_{2}\right\|_2.
$
\end{enumerate}
\end{assumption}
 The second assumption states that the loss function $\ell(\theta,\xi)$ is continuous and has a bounded growth rate on data $\xi$. The detailed growth rate functions are discussed in Section \ref{sec:app}.
\begin{assumption}[Continuity and Bounded Growth Rate of $\xi$]
\label{ass:bgr}
~
\begin{enumerate}
    \item[(\romannumeral1)]({\em{Continuity}}) The loss function $\ell(\theta,\cdot)$ is continuous for any $\theta\in\Theta$;
    \item [(\romannumeral2)]({\em{Bounded Growth Rate}}) There exists some positive continuous growth rate function $\mathtt{C}(\theta)$ and $\xi_0\in\Xi$ such that
$$\ell(\theta,\xi)\leq \mathtt{C}(\theta)\left(1+\mathtt{d}^p\left(\xi,\xi_0\right)\right)$$ for any $\theta\in\Theta$ and any $\xi\in\Xi$.
\end{enumerate}
\end{assumption}

Now we state the strong duality for the \textsf{WDRO}, which is an important property to guarantee the correctness of our dual coreset method.

\begin{proposition}[Strong duality~~\citep{articleDRO,blanchet2019quantifying,gao2016distributionally}]
\label{pro:duality}
For any upper semi-continuous $\ell(\theta,\cdot)$, any $\theta$ and any nominal distribution $\mathbb{P}$ with finite $p$-th moment, the worst-case risk satisfies
\begin{eqnarray}
\label{eq:dual-worst-risk}
R^\mathbb{P}_{\sigma, p}(\theta)=\inf _{\lambda \geq 0}\{ \lambda \sigma^{p}+H^\mathbb{P}(\theta,\lambda)\},
\end{eqnarray}

where $H^\mathbb{P}(\theta,\lambda)\coloneqq \mathbb{E}^{\mathbb{P}}\left[h(\theta,\lambda,\xi)\right]$ and $h(\theta,\lambda,\xi)=\sup\limits_{\zeta \in \Xi}\{ \ell(\theta,\zeta)-\lambda \mathtt{d}^p(\zeta,\xi)\}$ is the Moreau-Yosida regularization \citep{parikh2014proximal}. We use $\lambda^{\mathbb{P}}_*(\theta)$ to denote the $\lambda$ attaining the infimum in (\ref{eq:dual-worst-risk}).
\end{proposition}
\begin{remark}
\label{rmk-exist}
By the definition of $h$, for any given $\theta\in\Theta$, we can deduce that there always exists some $\lambda^\mathbb{P}_*(\theta)<\infty$ attaining the infimum of (\ref{eq:dual-worst-risk}).
\end{remark}

For the sake of convenience, we abbreviate  $R_{\sigma,p}(\theta)=R^{\mathbb{P}_n}_{\sigma,p}(\theta)$, $H(\theta,\lambda)=H^{\mathbb{P}_n}(\theta,\lambda)$,   $\lambda_*(\theta)=\lambda^{\mathbb{P}_n}_*(\theta)$, and  $h_i(\theta,\lambda)=h(\theta,\lambda,\xi_i)$.
We define the asymptotic growth rate function
$$\kappa(\theta)\coloneqq\limsup _{\mathtt{d}\left(\xi, \xi_0\right) \rightarrow \infty} \frac{\ell(\theta,\xi)-\ell\left(\theta,\xi_0\right)}{\mathtt{d}^{p}\left(\xi, \xi_0\right)}
$$
so as to conclude the continuity of $h_i(\cdot,\cdot)$ in the following two claims. Here $\xi_0$ is the point in Assumption \ref{ass:bgr} (\romannumeral2).
\begin{claim}[Continuity of $h_i$ on $\theta$]
\label{cla:beta-continuous}
For each $i\in\{1,\dots,n\}$ and any fixed $\lambda\geq0$, we have
$$|h_i(\theta,\lambda)-h_i(\theta,\lambda')|\leq L\|\theta-\theta'\|_2,$$
for any $\theta,\theta'\in \Theta$  with $\kappa(\theta),\kappa(\theta')\leq \lambda$.
\end{claim}

\begin{claim}[Continuity of $h_i$ on $\lambda$]
\label{cla:lambda-continuous}
For each $i\in\{1,\dots,n\}$ and any fixed $\theta\in\mathbb{R}^d$, we have
$$|h_i(\theta,\lambda)-h_i(\theta,\lambda')|\leq \max\{r_i^p(\theta,\lambda),r_i^p(\theta,\lambda')\}|\lambda-\lambda'|, ~\forall \lambda,\lambda'\geq \kappa(\theta),$$
 where $r_i(\theta,\lambda)\coloneqq\min\limits_{\zeta\in\Xi}\{\mathtt{d}(\zeta,\xi_i)\mid \ell(\theta,\zeta)-\lambda \mathtt{d}^p(\zeta,\xi_i)=h_i(\theta,\lambda)\}$ is the closest distance between $\xi_i$ and all the $\zeta$s that attain the supremum of $\ell(\theta,\zeta)-\lambda\mathtt{d}^p(\zeta,\xi_i)$ in $\Xi$.
\end{claim}
\begin{remark}
\label{rem:interval}
The reason that we let $\lambda\geq\kappa(\theta)$ in the above claims is that each $h_i(\theta,\lambda)$ goes to infinity if $\lambda<\kappa(\theta)$. Without loss of generality\footnote{It is possible that $h_i(\theta,\kappa(\theta))=\infty$, e.g., $\ell(\theta,\xi)$ is the loss function of ordinary linear regression. In this case, the argument in this paper still holds with  slight modification. }, we suppose $h_i(\theta,\kappa(\theta))<\infty$ in this paper.
\end{remark}

\section{From Coresets to Dual Coresets}
\label{sec-relation}
In this section, we provide the concept of ``dual coreset'' and prove that it is sufficient to guarantee the correctness with respect to the \textsf{WDRO} coreset. First, we present the definition of the  dual coreset  via directly combining Proposition \ref{pro:duality} and Definition \ref{def:coreset}. Suppose $I$ is an interval depending on $\theta$ (we will discuss this assumption in  detail later).

\begin{definition}[Dual $\epsilon$-Coreset]
\label{def:dualcoreset}
A dual $\epsilon$-coreset for the \textsf{WDRO} problem (\ref{eq:WDRO}) is a sparse non-negative mass vector $W=[w_1,\dots,w_n]$ such that the total mass $\sum\limits_{i=1}^nw_i=1$ and
\begin{eqnarray}
\label{eq:dualcoreset}
\tilde H(\theta,\lambda)\coloneqq\sum\limits_{i=1}^n w_ih_i(\theta,\lambda)\in (1\pm \epsilon) H(\theta,\lambda)
\end{eqnarray}
for any $\theta\in \Theta$ and $\lambda\in I$.
\end{definition}

\begin{remark}
 Note that we require the approximation guarantee holds not only for any $\theta\in\Theta$, but also for any $\lambda\in I$ in the above definition. This is also a key difference to the traditional coresets.
\end{remark}

By the discussion in Remark \ref{rem:interval}, we know $I\subset [\kappa(\theta),\infty)$. If we directly let $I=[\kappa(\theta),\infty)$, the   dual coreset of Definition~\ref{def:dualcoreset} requires to approximate the queries from all $\lambda\geq\kappa(\theta)$, which is too \textbf{strong}  and can be even troublesome for the coreset construction. Below we show that a bounded $I$ is sufficient for guaranteeing a dual coreset to be a qualified \textsf{WDRO} coreset.

Given a non-negative mass vector $W=[w_1,\cdots,w_n]$, the corresponding weighted empirical distribution is $\mathbb{\tilde P}_n=\sum_{i=1}^nw_i\delta_{\xi_i}$.
Recall that we define a parameter $\lambda^{\mathbb{P}}_*(\theta)$ for duality in Proposition~\ref{pro:duality}.
Together with Assumption \ref{ass:bgr}, we show the boundedness of the $\lambda^{\mathbb{\tilde P}_n}_*(\theta)$ (abbreviated as $\tilde \lambda_*(\theta)$ for convenience) for  $\mathbb{\tilde P}_n$. Let $[n]=\{1, 2,\cdots, n\}$. The following result is a key to relax the requirement for the dual coreset in Definition~\ref{def:dualcoreset}.

\begin{lemma}[Boundedness of $\tilde\lambda_*$]
\label{lem:boundedness}
Given the empirical distribution $\mathbb{P}_n=\frac{1}{n}\sum\limits_{i=1}^n\delta_{\xi_i}$, we define the value $\rho=\max\limits_{i\in[n]}\{\mathtt{d}(\xi_i,\xi_0)\}$ that is the largest distance from the data samples to $\xi_0$. Here $\xi_0$ is defined in Assumption \ref{ass:bgr} (\romannumeral2). For any  $\theta\in\Theta$  and any mass vector $W$,  the  $\tilde \lambda_*(\theta)$ of the corresponding weighted empirical distribution  $\mathbb{\tilde P}_n$ is \textbf{no larger than}
\begin{eqnarray}
\label{eq:boundedness}
  \mathtt{C}(\theta)\cdot\left(2^{p-1}+\frac{1+2^{p-1}\rho^p}{\sigma^p}\right), \quad
\end{eqnarray}
where $\mathtt{C}(\theta)$ is defined in Assumption \ref{ass:bgr} (\romannumeral2). We use $\tau(\theta)$ to denote this upper bound  $\mathtt{C}(\theta)\left(2^{p-1}+\frac{1+2^{p-1}\rho^p}{\sigma^p}\right)$.
\end{lemma}

\begin{remark}
\textbf{(\romannumeral1)} In practice, we usually normalize the dataset before training a machine learning model, which implies that $\rho$ is not large.
\textbf{(\romannumeral2)} It is worth noting that the above lemma can help us to  compute an upper bound for $\lambda_*(\theta)$. For example, if letting $W=[\frac{1}{n},\dots,\frac{1}{n}]$, (\ref{eq:boundedness}) directly yields an upper bound.
\end{remark}

The following theorem shows that the query region $I=[\kappa(\theta),\tau(\theta)]$  is  sufficient  for obtaining a coreset of the \textsf{WDRO} problem (\ref{eq:WDRO}).

\begin{theorem}[Sufficiency of the bounded query region]
\label{the-dualsuff}
If we let query region $I=[\kappa(\theta),\tau(\theta)]$ in Definition \ref{def:dualcoreset}, the dual $\epsilon$-coreset defined in such way also satisfies the coreset of Definition \ref{def:coreset}.
\end{theorem}
Therefore in the rest of this paper, we let $I=[\kappa(\theta),\tau(\theta)]$ in Definition \ref{def:dualcoreset}. Theorem~\ref{the-dualsuff} also implies the following corollary. So we can only focus on solving the dual  \textsf{WDRO} problem (\ref{eq:WDRO}) on the obtained dual $\epsilon$-coreset.
\begin{corollary}
Given $\alpha\geq 1$, we suppose the parameter vector $\theta_0$ yields an $\alpha$-approximation obtained on the dual $\epsilon$-coreset. Then $\theta_0$ is also an $(\alpha\cdot\frac{1+\epsilon}{1-\epsilon})$-approximation of the original \textsf{WDRO} (\ref{eq:WDRO}).
\end{corollary}
To end this section, similar to $\mathbb{B}(\theta_{\mathtt{anc}},l_{\mathtt{p}})$ in Assumption \ref{ass:bgr} (\romannumeral1), we define an interval $[\lambda_{\mathtt{anc}}-l_{\mathtt{d}},\lambda_{\mathtt{anc}}+l_{\mathtt{d}}]$ centered at some ``anchor'' point $\lambda_{\mathtt{anc}}>0$ with radius $l_{\mathtt{d}}>0$. To ensure that $[\kappa(\theta),\tau(\theta)]$ is within the interval $[\lambda_{\mathtt{anc}}-l_{\mathtt{d}},\lambda_{\mathtt{anc}}+l_{\mathtt{d}}]$ for all $\theta\in\Theta$, we let $\lambda_{\mathtt{anc}}\coloneqq\max\limits_{\theta\in\Theta}\{\kappa(\theta_{\mathtt{anc}}),\frac{\tau(\theta)}{2}\}$  and $l_{\mathtt{d}}\coloneqq\lambda_{\mathtt{anc}}$.

\section{The Construction of Dual Coresets}
\label{sec:coreset}
Following the results of Section~\ref{sec-relation}, we show how to compute a qualified dual coreset in this section.
Suppose we can evaluate the lower and upper bounds for each $h_i(\cdot,\cdot)$ with respect to  a given couple  $(\lambda_{\mathtt{anc}},\theta_{\mathtt{anc}})$, namely, we have
$$a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})\leq h_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}}) \leq b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$$
for $1\leq i\leq n$.
We defer the details for obtaining such upper and lower bounds for each application to Section~\ref{sec:app}.

\begin{algorithm}[tb]
	\caption{Dual $\epsilon$-Coreset Construction}
	\label{alg:dualcoreset}
	\begin{algorithmic}
		\STATE {\bfseries Input:}  The empirical distribution $\mathbb{P}_n=\frac{1}{n}\sum_{i=1}^n\delta_{\xi_i}$,
		the Lipschitz constant $L$, the ``anchors'' $\theta_{\mathtt{anc}}$ and $\lambda_{\mathtt{anc}}$, and corresponding radii $l_{\mathtt{p}}$ and $l_{\mathtt{d}}$;
		the parameter $\epsilon\in(0,1)$; lower bound oracle $a_i(\cdot,\cdot)$ and upper bound oracle $b_i(\cdot,\cdot)$ for $i\in[n]$.

		\begin{enumerate}
		\item Compute  $A=\frac{1}{n}\sum_{i=1}^na_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ and  $B=\frac{1}{n}\sum_{i=1}^nb_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$.
		\item Let $N=\lceil\log n\rceil$; initialize $W=[0, 0, \cdots, 0]\in \mathbb{R}^n$.
		\item The dataset $\{\xi_1,\dots,\xi_n\}$ is partitioned into $(N+1)^2$ cells $\{C_{ij}| 0\leq i,j\leq N\}$ as (\ref{eq:grid}).
		\item For each $C_{ij}\ne\emptyset$, $0\leq i,j\leq N$:
		\begin{enumerate}
		\item  take a sample $Q_{ij}$ from $ C_{ij}$ uniformly at random, where the size $|Q_{ij}|$ depends on the parameters $\epsilon$, $l_{\mathtt{p}}$, $l_{\mathtt{d}}$ and $L$ (the exact value will be discussed in our following analysis in Section~\ref{sec:analysis});
		\item  for each sample $\xi_k\in Q_{ij}$,  assign the mass of quantity $w_k=\frac{|C_{ij}|}{n|Q_{ij}|}$;
		\end{enumerate}
		\end{enumerate}

		\STATE {\bfseries Output:} the mass vector $W=[w_1, w_2, \cdots, w_n]$ as the dual $\epsilon$-coreset.
	\end{algorithmic}
\end{algorithm}

\subsection{The Construction Algorithm}
\label{sec:contruction}
We show the dual $\epsilon$-coreset construction procedure in Algorithm~\ref{alg:dualcoreset}, where the high-level idea is based on the following grid sampling.

\textbf{Grid sampling.} Let $N=\lceil \log n \rceil$. Given the anchor $(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$, we can conduct the partitions over the dataset based on the lower bounds $a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ and upper bounds $b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ separately.  Let $A = \frac{1}{n}\sum_{i=1}^{n} a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ and $B = \frac{1}{n}\sum_{i=1}^{n} b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$. Then we have the following partitions.
\begin{eqnarray}
\label{eq:lowerlayer1}
A_0&=&\big\{\xi_i\mid a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}}) \le A\big\}, \label{for-layer1}\\
A_j&=&\big\{\xi_i\mid 2^{j-1}A < a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}}) \le
2^{j}A\big\}, 1 \le j \le N.\label{eq:lowerlayer2}
 \end{eqnarray}
\begin{eqnarray}
\label{eq:upperlayer1}
B_0&=&\big\{\xi_i\mid b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}}) \le B\big\}, \label{for-layer1}\\
B_j&=&\big\{\xi_i\mid 2^{j-1}B < b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}}) \le
2^{j}B\big\}, 1 \le j \le N.\label{eq:upperlayer2}
 \end{eqnarray}

We denote the lower bound and upper bound partitions as $\mathcal{A} = \{A_0, \cdots,A_N\}$ and $\mathcal{B} = \{B_0,\cdots,B_N\}$ respectively. Then, we compute the intersections over  $\mathcal{A}$ and $\mathcal{B}$ to generate the ``grid'':
\begin{eqnarray}
\label{eq:grid}
\mathcal{C} = \{ C_{ij}|C_{ij} =A_i \cap B_j, 0\leq i,j\leq N\}.
\end{eqnarray}
It is easy to see that $\mathcal{C}$ is a collection of disjoint ``cells''  and $\bigcup\limits_{i,j} C_{ij} = P$.  For each $\xi_k\in C_{ij}$, we have
\begin{eqnarray}
\label{eq:cell}
\mu_i\cdot 2^{i-1}A\leq h_k(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})\leq 2^jB
\end{eqnarray}
 where  $\mu_i=0$ if $i=0$ and $\mu_i=1$ otherwise.
Through the grid partition $\mathcal{C}$, we can  take a set of samples $Q_{ij}$ from $ C_{ij}$ uniformly at random, and assign the weight $\frac{|C_{ij}|}{n|Q_{ij}|}$  to each sample.
\begin{remark}
\label{rem:upper}
\textbf{(\romannumeral1)} The grid sampling is a variance reduction technique in the Monte-Carlo methods~\citep{gobet2016monte}, since the grid partition is also a stratification for $h_k(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ as shown in (\ref{eq:cell}).
If we consider only the upper bounds $b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ or the lower bounds $a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$, the obtained  partition is not a valid stratification for $h_k(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$.
\textbf{(\romannumeral2)} If we can obtain the exact value of $h_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$, i.e.,  $a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})=b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})=h_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$, then the grid partition is exactly the spatial partition that was studied before~\cite{chen2009coresets,DBLP:conf/nips/WangGD21}.
\end{remark}

\subsection{Theoretical Analysis}
\label{sec:analysis}
In this section we analyze the  complexity of Algorithm \ref{alg:dualcoreset} in theory. Recall that we define  $r_i(\theta,\lambda)=\min\limits_{\zeta\in\Xi}\{\mathtt{d}(\zeta,\xi_i)\colon\ell(\theta,\zeta)-\lambda \mathtt{d}^p(\zeta,\xi_i)=h_i(\theta,\lambda)\}$ in Claim~\ref{cla:lambda-continuous}.
The following theorem provides an asymptotic sample complexity of Algorithm \ref{alg:dualcoreset}. To state the theorem clearly, we define two notations $R\coloneqq\max\limits_{i\in[n]\atop \theta\in\Theta}\{r^p_i(\kappa(\theta),\theta)\}$ and $H\coloneqq\min\limits_{\theta\in\Theta\atop \lambda\in[\lambda_{\mathtt{anc}}-l_{\mathtt{d}},\lambda_{\mathtt{anc}}+l_{\mathtt{d}}]}H(\theta,\lambda)$.

\begin{theorem}
\label{the:wdrocoreset}
Set $|Q_{ij}|=\tilde{O}\left(\left(B\cdot\frac{B+L l_{\mathtt{p}}+Rl_{\mathtt{d}}}{AH}\right)^{2} \cdot \frac{d}{\epsilon^{2}}\right)$\footnote{$\tilde O(g)\coloneqq O(g\cdot\mathtt{polylog}(\frac{nLl_{\mathtt{p}} Rl_{\mathtt{d}}}{\epsilon H}))$} in the Algorithm \ref{alg:dualcoreset}. Then the returned $W$ is a qualified dual $\epsilon$-coreset with probability at least $1-\frac{1}{n}$. The construction time is $O(n\cdot \mathtt{time}_{ab})$ where  $\mathtt{time}_{ab}$ is the time complexity for computing the lower bound $a_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ and the upper bound $b_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$ for each $h_i(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})$.
\end{theorem}
\begin{remark}
Note that the value $H\geq \min_{\theta\in\Theta}\mathbb{E}^{\mathbb{P}_n}\ell(\theta,\xi)$, which should not be too small in practice since the loss function  $\ell(\cdot,\cdot)$ usually contains positive penalty terms. The value of $R$ will be discussed in Section~\ref{sec:app}.
\end{remark}
We show the sketched proof of Theorem \ref{the:wdrocoreset} below.
Based on the continuity of $h_i(\cdot,\cdot)$ and the Hoeffding's inequality~\citep{hoeffding1994probability}, for a fixed couple $(\theta,\lambda)$, we provide an upper bound on the sample complexity first. The bound ensures that the estimation for each cell $C_{ij}$ has a bounded deviation with  high probability.
\begin{lemma}
\label{lem:eachcell}
Let $\delta$ be a given positive number. We fix a couple $(\theta,\lambda)\in\mathbb{B}(\theta_{\mathtt{anc}},l_{\mathtt{p}})\times[\kappa(\theta),\tau(\theta)]$ and take a uniform sample $Q_{ij}$ from $C_{ij}$ with the sample size
\begin{eqnarray}
\label{eq:samplesize}
|Q_{ij}|=O\left((2^jB-\mu_i\cdot2^{i-1}A+2Ll_{\mathtt{p}}+2 Rl_{\mathtt{d}})^2\delta^{-2}\log\frac{1}{\eta}\right).
\end{eqnarray}
Then, we have the probability
\begin{eqnarray}
\label{eq:concentration}
\mathtt{Prob}\left[\left|\frac{1}{|Q_{ij}|}\sum\limits_{\xi_k\in Q_{ij}}h_k(\theta,\lambda)-\frac{1}{|C_{ij}|}\sum\limits_{\xi_k\in C_{ij}}h_k(\theta,\lambda)\right|\geq \delta\right]\leq \eta.
\end{eqnarray}
\end{lemma}
We aggregate the deviations from all the cells to obtain the overall estimation error for the coreset.
 To guarantee the approximation quality of  (\ref{eq:dualcoreset}), we need to design a sufficiently small value of the deviation $\delta$ for each cell $C_{ij}$ under our grid partition framework.

\begin{lemma}
\label{lem:delta}
In Lemma \ref{lem:eachcell}, we set the deviation  $\delta=\epsilon_1 (2^{j-1}+2^{i-1})A$ ~for $0\leq i,j\leq N$. Then we have
\begin{eqnarray}
\label{eq:fixapproximation}
\mathtt{Prob}\left[|\tilde H(\theta,\lambda)-H(\theta,\lambda)|\leq 3\epsilon_1 H(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})\right]\geq 1-(N+1)^2\eta.
\end{eqnarray}
\end{lemma}
To generalize the result of Lemma~\ref{lem:delta} to the whole feasible region $\mathbb{B}(\theta_{\mathtt{anc}},l_{\mathtt{p}})\times[0,2l_{\mathtt{d}}]$, we apply the discretization idea.
Imagine to generate the axis-parallel grid with side length $\frac{\epsilon_3 l_{\mathtt{p}}}{\sqrt{d}}\times\epsilon_2l_{\mathtt{d}}$ inside   $\mathbb{B}(\theta_{\mathtt{anc}},l_{\mathtt{p}})\times[0,2l_{\mathtt{d}}]$; the parameters $\epsilon_2$ and $\epsilon_3$ are two small numbers that will be determined in our following analysis. For each grid cell we arbitrarily take a $(\theta,\lambda)$ as its representative point.
Let $G$ be the set of
the selected representative points; it is easy to see  the cardinality $|G|=\frac{1}{\epsilon_2}\cdot O(\frac{1}{\epsilon_3^d}) $. Through taking the union bound over all $(\theta,\lambda)\in G$ for  (\ref{eq:fixapproximation}), we obtain the following Lemma \ref{lem:allbeta}.
\begin{lemma}
\label{lem:allbeta}
With probability at least $1-(N+1)^2|G|\eta$, we have
\begin{eqnarray}
\label{eq:representative}
|\tilde H(\theta,\lambda)-H(\theta,\lambda)|\leq 3\epsilon_1 H(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc}})~ \text{for all}~ (\theta,\lambda)\in G.
\end{eqnarray}
 \end{lemma}
By using the above lemmas, we are ready to prove Theorem \ref{the:wdrocoreset}.

\begin{proof}(\textbf{of Theorem \ref{the:wdrocoreset}})
For any $(\theta,\lambda)\in \mathbb{B}(\lambda_{\mathtt{anc}},l_{\mathtt{d}})\times[\kappa(\theta),\tau(\theta)]$, we let $(\theta',\lambda')\in G$ be the representative point of the cell containing $(\theta,\lambda)$. Then we have $\|\theta-\theta'\|_2\leq \epsilon_3l_{\mathtt{p}}$ and $|\lambda'-\lambda|\leq \epsilon_2 l_{\mathtt{d}}$.  Without loss of generality, we assume $\lambda'\geq\lambda$. By using the triangle inequality,  we have
\begin{equation}
\begin{aligned}
& |h_k(\theta,\lambda)-h_k(\theta',\lambda')|\\
\leq & |h_k(\theta',\lambda')-h_k(\theta,\lambda')|+|h_k(\theta,\lambda)-h_k(\theta,\lambda')|\\
\leq & L\epsilon_3l_{\mathtt{p}}+ R\epsilon_2 l_{\mathtt{d}}. \quad\quad\text{(By Claim \ref{cla:lambda-continuous}, Claim \ref{cla:beta-continuous} and $\lambda'\geq\lambda\geq\kappa(\theta)$)}
\end{aligned}
\end{equation}
The above inequality implies
\begin{eqnarray}
\label{eq:1}
|H(\theta,\lambda)-H(\theta',\lambda')|\leq R\epsilon_2 l_{\mathtt{d}}+L\epsilon_3l_{\mathtt{p}}
\end{eqnarray}
and
\begin{eqnarray}
\label{eq:2}
|\tilde H(\theta,\lambda)-\tilde H(\theta',\lambda')|\leq R\epsilon_2 l_{\mathtt{d}}+L\epsilon_3l_{\mathtt{p}}.
\end{eqnarray}
Overall we have $|\tilde{H}(\theta,\lambda)-H(\theta,\lambda)|$
\begin{equation}
\begin{aligned}
\leq &\left|\tilde{H}(\theta,\lambda)-\tilde{H}\left(\theta',\lambda'\right)\right|+\left|\tilde{H}\left(\theta',\lambda'\right)-H\left(\theta',\lambda'\right)\right|
+\left|H\left(\theta',\lambda'\right)-H\left(\theta,\lambda\right)\right| \\
\leq & 3 \epsilon_{1} H\left(\theta_{\mathtt{anc}},\lambda_{\mathtt{anc} }\right)+2 \times\left( R\epsilon_2 l_{\mathtt{d}}+L\epsilon_3l_{\mathtt{p}}\right) \quad (\text{By Lemma} ~\ref{lem:allbeta}, (\ref{eq:1}) ~\text{and}~ (\ref{eq:2}))
\end{aligned}
\end{equation}
By setting $\epsilon_1=\frac{H\epsilon}{9B}$, $\epsilon_2=\frac{ H\epsilon }{6l_{\mathtt{d}} R}$, $\epsilon_3=\frac{H\epsilon }{6Ll_{\mathtt{p}}}$ and $\eta=\frac{1}{n(N+1)^2|G|}$ and substituting them into $(\ref{eq:samplesize})$, we obtain the sample complexity as stated in Theorem \ref{the:wdrocoreset}.
\end{proof}

\section{Applications}
\label{sec:app}
In this section, we show several \textsf{WDRO} problems that their complexities can be reduced by using
our dual coreset method.

 \subsection{Binary Classification}
  For the binary classification, $\mathbb{Y}=\{-1,1\}$ and the loss function $\ell(\theta,\xi)=L(y\cdot\theta^\top x)$ where $L(\cdot)$ is a non-negative and non-increasing function. Let $\|\cdot\|_*$ be the dual norm of $\|\cdot\|$ on $\mathbb{R}^m$.
We consider the \textbf{Support Vector Machine (SVM)} and \textbf{logistic regression} problems.
The SVM takes the hinge loss $L(z)=\max\{0,1-z\}$ and the logistic regression takes the logloss $L(z)=\log(1+\exp(-z))$.
If $\mathbb{X}=\mathbb{R}^m$ and $p=1$, by the result of \citet[Theorem 3.11]{shafieezadeh2019regularization}, for both of these two problems we have:
\begin{itemize}
    \item $R\leq\gamma$, $\kappa(\theta)=\mathtt{C}(\theta)=\|\theta\|_*$;
    \item $a_i(\theta,\lambda)=b_i(\theta,\lambda)=h_i(\theta,\lambda)=\max\{L(y_i\cdot\theta^\top x_i),L(-y_i\cdot\theta^\top x_i)-\lambda\gamma\}$ for any $\lambda\geq\kappa(\theta)$.
\end{itemize}

If $\mathbb{X}=[0,l]^m$ is a $m$-dimensional hypercube with side length $l>0$, $h_i(\theta,\lambda)$ in fact is the optimal objective value of a convex constrained programming problem. Therefore we \textbf{cannot} obtain the exact value of $h_i(\theta,\lambda)$ easily. To remedy this issue, we can invoke the upper and lower bounds of $h_i(\theta,\lambda)$ and conduct the grid sampling to efficiently construct the coreset.

 \subsection{Regression}
 \label{sec:huber}
 For the regression problem, $\mathbb{Y}=\mathbb{R}$ and the loss function $\ell(\theta,\xi)=L(\theta^\top x-y)$, where $L(\cdot)$  is a non-negative function. Let $\|\cdot\|_*$ be the dual norm of $\|\cdot\|$ on $\mathbb{R}^{m+1}$.
 We consider the \textbf{robust regression} problem that takes the Huber loss $L(z)=\frac{1}{2}z^2$ if $|z|\leq\delta$ and $L(z)=\delta\left(|z|-\frac{1}{2}\delta\right)$ otherwise for some $\delta\geq 0$. If $p=1$ and $\mathbb{X}=\mathbb{R}^m$, by the result of  \citet[Theorem 3.1]{shafieezadeh2019regularization}, we have
\begin{itemize}
    \item $R=0, \kappa(\theta)=\mathtt{C}(\theta)=\delta\|(\theta,-1)\|_*$;
    \item $a_i(\theta,\lambda)=b_i(\theta,\lambda)=h_i(\theta,\lambda)=L(\theta^\top x_i-y_i)$ for any $\lambda\geq\kappa(\theta)$.
\end{itemize}

\section{Experiments}
\label{sec-exp}
Our experiments were conducted on a server equipped with 2.4GHZ Intel CPUs and 256GB main memory. The algorithms are implemented in Python. We use the MOSEK~\citep{mosek} to solve the tractable reformulations of \textsf{WDRO}s. Our code is available at \url{https://github.com/h305142/WDRO_coreset}.

\textbf{Compared methods.}
We compare our dual coreset method \textsc{DualCore} with the uniform sampling approach \textsc{UniSamp}, the importance sampling approach \textsc{ImpSamp} \citep{tukan2020coresets}, the layer sampling approach \textsc{LayerSamp} \citep{huang2021novel}, and the approach that directly runs on whole training set \textsc{Whole}.

\textbf{Datasets.}
We test the algorithms for the SVM and  logistic regression problems on two real datasets:
\textsc{Mnist}\citep{lecun2010mnist} and \textsc{Letter}\citep{chang2011libsvm}.
To simulate the scenarios  with contaminated datasets, we perform   poisoning attacks to the training set of \textsc{Letter}. Specifically,  we use the \textsc{Min-Max} attack from \citep{DBLP:journals/corr/abs-1811-00741} and \textsc{Alfa} attack from \citep{DBLP:journals/ijon/XiaoBNXER15}. We add the standard Gaussian noise $\mathcal{N}(0,1)$ to the training set of \textsc{Mnist} and randomly flip $10\%$ of the labels.
The dual coreset algorithm for the robust regression problem is evaluated on the real dataset \textsc{Appliances Energy}\citep{candanedo2017data}.

\textbf{Results.}
Let $s$ and $n$ be the coreset size and the training set size, respectively. We set $c\coloneqq\frac{s}{n}$ to indicate the compression rate and fix the parameter $\gamma=7$ for all the instances (recall that $\gamma$ is used for defining the feature-label metric $\mathtt{d}(\xi_i,\xi_j)=\|x_i-x_j\|+\frac{\gamma}{2}|y_i-y_j|$). The experiments of  each instance were repeated by $50$ independent trials. We report the obtained worst-case risk $R_{\sigma,p}^{\mathbb{P}_n}(\theta_*)$ for each  method in table \ref{tab-lr}, \ref{tab-svm} and \ref{tab-huber}.

\begin{table}[!ht]
    \centering
    \begin{tabular}{l|l|l|l|l}
    \toprule[2pt]
        \textbf{$c$} & \textsc{UniSamp} & \textsc{ImpSamp} & \textsc{LayerSamp} & \textsc{DualCore} \\ \hline
        1\% & 0.72518$\pm$0.1268 & 0.70484$\pm$0.0915 & 0.70988$\pm$0.084 & \textbf{0.68933$\pm$0.0587} \\
        2\% & 0.64630$\pm$0.0344 & 0.65798$\pm$0.0447 & 0.63911$\pm$0.0305 & \textbf{0.63708$\pm$0.0257} \\
        3\% & 0.62709$\pm$0.0216 & 0.63015$\pm$0.0333 & \textbf{0.62381$\pm$0.0199} & 0.62546$\pm$0.0225 \\
        4\% & 0.62047$\pm$0.0176 & 0.6235$\pm$0.0183 & 0.61616$\pm$0.0143 & \textbf{0.61292$\pm$0.0149} \\
        5\% & 0.61338$\pm$0.0164 & 0.61524$\pm$0.0137 & 0.61013$\pm$0.0096 & \textbf{0.60986$\pm$0.0097} \\
        6\% & 0.60823$\pm$0.0084 & 0.61284$\pm$0.0131 & 0.60749$\pm$0.0119 & \textbf{0.60556$\pm$0.0092} \\
        7\% & 0.60716$\pm$0.0082 & 0.61198$\pm$0.0113 & 0.6059$\pm$0.0083 & \textbf{0.60381$\pm$0.0073} \\
        8\% & 0.60640$\pm$0.007 & 0.60936$\pm$0.0108 & 0.60376$\pm$0.0078 & \textbf{0.60238$\pm$0.0062} \\
        9\% & 0.60395$\pm$0.0066 & 0.60677$\pm$0.0086 & 0.60235$\pm$0.007 & \textbf{0.60056$\pm$0.0046} \\
        10\% & 0.60220$\pm$0.0069 & 0.60574$\pm$0.009 & \textbf{0.60007$\pm$0.0041} & 0.60113$\pm$0.0071 \\ \bottomrule[2pt]
    \end{tabular}
    \caption{Worst-case risk of logistic regression on \textsc{Letter}, \textsc{Whole}=0.59267, $\sigma=0.3$}
    \label{tab-lr}
\end{table}

\begin{table}[!ht]
    \centering
    \begin{tabular}{l|l|l|l|l}
    \toprule[2pt]
        $c$ & \textsc{UniSamp} & \textsc{ImpSamp} & \textsc{LayerSamp} & \textsc{DualCore} \\ \hline
        1\% & 0.68707$\pm$0.1094 & \textbf{0.66576$\pm$0.103} & 0.70577$\pm$0.1278 & 0.67866$\pm$0.1173 \\
        2\% & 0.59376$\pm$0.0565 & 0.60895$\pm$0.0683 & \textbf{0.58967$\pm$0.0529} & 0.59850$\pm$0.0548 \\
        3\% & 0.56860$\pm$0.036 & 0.57346$\pm$0.0453 & 0.56705$\pm$0.0377 & \textbf{0.56689$\pm$0.0347} \\
        4\% & 0.54429$\pm$0.0308 & 0.55050$\pm$0.0409 & 0.54366$\pm$0.0336 & \textbf{0.53634$\pm$0.0207} \\
        5\% & 0.53218$\pm$0.0234 & 0.54212$\pm$0.0295 & \textbf{0.52981$\pm$0.0182} & 0.53217$\pm$0.019 \\
        6\% & 0.5346$\pm$0.0248 & 0.53835$\pm$0.0288 & \textbf{0.52496$\pm$0.0177} & 0.52835$\pm$0.0184 \\
        7\% & 0.52784$\pm$0.0225 & 0.53388$\pm$0.0275 & 0.52039$\pm$0.015 & \textbf{0.52025$\pm$0.0147} \\
        8\% & 0.52246$\pm$0.019 & 0.51993$\pm$0.0119 & 0.51918$\pm$0.0126 & \textbf{0.51845$\pm$0.0116} \\
        9\% & 0.52025$\pm$0.0153 & 0.52402$\pm$0.0206 & 0.51289$\pm$0.0094 & \textbf{0.51196$\pm$0.0054} \\
        10\% & 0.51458$\pm$0.0083 & 0.51768$\pm$0.0166 & 0.51578$\pm$0.013 & \textbf{0.51066$\pm$0.0065} \\ \bottomrule[2pt]
    \end{tabular}
    \caption{Worst-case risk of SVM on \textsc{Letter}, \textsc{Whole}=0.49734, $\sigma=0.1$}
    \label{tab-svm}
\end{table}

\begin{table}[!ht]
    \centering
    \begin{tabular}{l|l|l|l}
    \toprule[2pt]
        $c$ & \textsc{UniSamp} & \textsc{ImpSamp} & \textsc{DualCore} \\ \hline
        1\% & 28.57655$\pm$0.0005 & 28.57649$\pm$0.0004 & \textbf{28.57627$\pm$0.0002} \\
        2\% & 28.57619$\pm$0.0001 & 28.57617$\pm$0.0001 & \textbf{28.57607$\pm$0.0001} \\
        3\% & 28.57609$\pm$0.0001 & 28.5761$\pm$0.0001 & \textbf{28.57598$\pm$0.0001} \\
        4\% & 28.57600$\pm$0.0001 & 28.57601$\pm$0.0001 & \textbf{28.57593$\pm$0.0001} \\
        5\% & 28.57595$\pm$0 & 28.57598$\pm$0.0001 & \textbf{28.57588$\pm$0} \\
        6\% & 28.57593$\pm$0 & 28.57594$\pm$0.0001 & \textbf{28.57587$\pm$0} \\
        7\% & 28.57591$\pm$0 & 28.57592$\pm$0.0001 & \textbf{28.57585$\pm$0} \\
        8\% & 28.57589$\pm$0 & 28.57589$\pm$0 & \textbf{28.57584$\pm$0} \\
        9\% & 28.57589$\pm$0 & 28.57589$\pm$0 & \textbf{28.57583$\pm$0} \\
        10\% & 28.57588$\pm$0 & 28.57588$\pm$0 & \textbf{28.57582$\pm$0} \\ \bottomrule[2pt]
    \end{tabular}
    \caption{Worst-case risk of Huber regression on \textsc{Appliances Energy}, \textsc{Whole}=28.57578, $\sigma=100$.
     \textsc{LayerSamp} coinsides with \textsc{DualCore} for Huber regression. This is because $h(\theta,\lambda,\xi_i)=\ell(\theta,\xi_i)$ for Huber regression (See Section \ref{sec:huber}).}
    \label{tab-huber}
\end{table}

\section{Conclusion}
 In this paper, we consider reducing the high computational complexity of \textsf{WDRO} via the coreset method. We relate the coreset to its dual coreset by using the strong duality property of \textsf{WDRO}, and propose a novel grid sampling approach for the construction. To the best of our knowledge, our work is the first systematically study on the coreset of \textsf{WDRO} problems in theory.  We also implement our proposed coreset algorithm and conduct the experiments to evaluate its performance for several \textsf{WDRO} problems (including the applications mentioned in Section \ref{sec:app}). Following our work, there also exist several important problems deserving to study in future. For example, it is interesting to consider the coresets construction for other robust optimization models (e.g., adversarial training~\cite{goodfellow2018making}).

\section{Acknowledgements}
 The research of this work was supported in part by National Key R$\&$D program of China through grant 2021YFA1000900 and the Provincial NSF of Anhui through grant 2208085MF163. We also want to thank the anonymous reviewers for their helpful comments.

redpajama_set_name: RedPajamaArXiv


text:
Home/Dunamis Seeds of Destiny SOD/SOD TODAY: Seeds of Destiny 21st January 2023
SOD TODAY: Seeds of Destiny 21st January 2023
SOD Devotional for Saturday 21 January 2023 by Pastor Paul Enenche
Read and Digest Today's Dunamis Seeds of Destiny Daily Devotional Message written by Pastor Paul Enenche. May the Lord bless you as study.
TOPIC: MIRACLES OF THE GLORY
SCRIPTURE: And it came to pass, when Moses came down from mount Sinai with the two tables of testimony in Moses' hand, when he came down from the mount, that Moses wist not that the skin of his face shone while he talked with him. Exodus 34:29.
THOUGHT FOR THE DAY: The glory is the secret of vibrancy of health, buoyancy of strength, clarity of mind and sharpness of sight.
The glory of God has been confirmed to be a major secret of outstanding existence on earth. Moses was one man who experienced the glory of God, and he lived an outstanding life.
It is important to know that before Moses left the earth, the glory produced some physical miracles in his life.
Now, what miracles did the glory produce in the life of Moses?
1. Vibrancy of health (Deuteronomy 34:7).
Moses could have been a permanent victim of weakness or health breakdown considering his difficult assignment and hectic schedules, but he never broke down once because of the glory of God on his life.
2. Buoyancy of strength (Deuteronomy 34:7).
Moses' natural strength did not reduce. There are people that are healthy but not strong. They may not have malaria, typhoid, High Blood Pressure, or ulcer but they don't have energy; they are not strong. Moses had vibrancy of health and buoyancy of strength.
3. Clarity of mind (Deuteronomy 34:7).
At the age of one hundred and twenty years, his mind was still clear, he was still receiving Word from God, documenting and declaring them.
Beloved, you are too young to suffer mental confusion.
4. Sharpness of sight (Deuteronomy 34:7).
The eyesight of Moses was not dim. Moses could see as clear as he ever saw. You need sharpness of sight to fulfil destiny.
I decree that short-sightedness, glaucoma and cataract, astigmatism, retinal detachment and anything that has put your eyes under pressure dies now in Jesus' Name.
The glory is the secret of vibrancy of heath, buoyancy of strength, clarity of mind and sharpness of sight.
I decree that you shall experience the Glory of God in Jesus' Name.
Remember this: The glory is the secret of vibrancy of heath, buoyancy of strength, clarity of mind and sharpness of sight.
SOD DEVOTIONAL 21 JANUARY 2023 ASSIGNMENTS:
1. Make up your mind to prioritize and experience the Glory of God.
2. Spend more time with God at the place of prayer and the Word to experience His Glory.
PRAYER: Father, I ask for the grace to spend more time with You to experience Your Glory in my life, Lord, in Jesus' Name.
FOR FURTHER UNDERSTANDING, GET THIS MESSAGE: MIRACLES OF THE GLORY.
QUOTE: And it was when the pattern was followed that the glory fell. So, the glory of God follows the pattern of God. Culled from "MAKING FULL PROOF OF MINISTRY" by Dr Paul Enenche.
DAILY READING: Leviticus 11-14
AMAZING FACT: The longest word in the Bible is "Mahershalalhashbaz (Isaiah 8:3). While it took over 1,000 years to write the Old Testament, the New Testament was written within a period of 50-75 years.
PROPHETIC DECLARATION/WORD: I decree the invasion of the glory in your life to produce the needed result in Jesus Name.
Read Other Daily Devotional on TVSeries
Streams of JOY Sunday Live 22nd January 2023
SOD TODAY: Seeds of Destiny 22nd January 2023
Seeds of Destiny 29th January 2023 (SOD Today Devotional)
SOD: Seeds of Destiny 28th January 2023 Today
SOD TODAY: Seeds of Destiny 27th January 2023


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About iCAIR
iCAIR®: International Consortium for Anti-Infective Research
iCAIR® is establishing its position as an expert preclinical development platform for new anti-infective drugs
iCAIR® contributes to filling the empty pipelines in anti-infective drug development to address the current global threat of antimicrobial resistance and new infectious diseases.
As a close-knit research alliance, iCAIR® is working on the development of anti-infective therapies that take new treatment options all the way from the identification of potentially beneficial substances to the preclinical proof of concept. In selected lighthouse projects, iCAIR® is establishing and demonstrating its position as an expert preclinical development platform for new anti-infective drugs. One objective of these projects is to target new treatments to combat the pathogens Pseudomonas aeruginosa, Aspergillus fumigatus, Neisseria meningitidis, different respiratory viruses such as the human parainfluenza and influenza viruses, RSV, and coronaviruses, and develop these treatments to the point of preclinical proof of concept.
The development platform established in the iCAIR® project will be made available to external partners in addition to its use in proprietary projects. This is geared towards contract research in the pharmaceutical industry as well as small and medium-sized enterprises and publicly funded projects. iCAIR® thereby enables them to develop their early-stage compounds to the stage of preclinical proof of concept ready to go into regulatory development for market approval or, depending on the business model, out-licensing to big pharmaceutical players. Either way, iCAIR® contributes to filling the empty pipelines in anti-infective drug development to address the current global threat of antimicrobial resistance and new infectious diseases.
iCAIR aims to develop treatments against Pseudomonas aeruginosa, Aspergillus fumigatus, Neisseria meningitidis, respiratory viruses such as the human parainfluenza and influenza viruses, RSV, and coronaviruses, and develop these treatments to the point of preclinical proof of concept.
The "Valley of death" in drug development
Overview of expertise in the iCAIR® consortium
Four strong iCAIR® partners – Institute for Glycomics, Hannover Medical School, Helmholtz Centre for Infection Research, and Fraunhofer ITEM – set out to collaborate in infection research: they have joined forces to develop novel anti-infective drugs – from target identification via hit-to-lead to proof-of-concept studies.
iCAIR® consortium
Our goals will be achieved by synergizing the partners' unique expertise:
Drug target identification
Molecular characterization of targets
Lead identification by stochastic and rational strategies
Lead validation and preclinical efficacy and toxicology testing, proof of concept
iCAIR partners
Navigation and Social Media
Fraunhofer Institute for Toxicology and Experimental Medicine
Institute for Glycomics of Griffith University (IfG)
Hannover Medical School
Helmholtz Centre for Infection Research (HZI)
Publishing Notes
Source: Fraunhofer-Gesellschaft
Fraunhofer-Gesellschaft - About iCAIR
Online in Internet; URL: https://www.icair.fraunhofer.de/en/about-icair.html


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100 People Are Killed by Mystery Disease in South Sudan: Who Taskforce Sent to Investigate
💭 በደቡብ ሱዳን መቶ/፻ ሰዎች በምስጢራዊ በሽታ ሞቱ፡ የዓለም ጤና ድርጅት ግብረ ኃይል ለምርመራ ተልኳል
The World Health Organisation (WHO) has begun investigating the deaths of almost 100 people in South Sudan. The deaths occurred in Fangak and Jonglei State in South Sudan.
The BBC noted that initial samples collected in the area returned negative for cholera, and spoke to the WHO's Sheila Baya who explained the ongoing concerns. She said so far there had been 89 deaths and an investigation was ongoing.
Baya told the BBC: "We decided to send a rapid response team to go and do risk assessment and an investigation.
"That is when they will be able to collect samples from the sick people but provisionally the figure that we got was that there were 89 deaths."
She also noted that it has become increasingly difficult to reach the Fangak area due to flooding that has made it inaccessible by land. She and her team subsequently waited for a helicopter.
The flooding in the area has been so severe it has caused over 200,000 people to flee their homes. Humanitarian agency Concern Worldwide has said it has been the worst flooding in almost 60 years.
Concern's County Director in South Sudan, Shumon Sengupta, explained the dire situation.
He said: "The magnitude of the flooding this year has been immense. Over 200,000 people, more than a quarter of the local population in Unity State have been forced to leave their homes as a result of rising floodwaters.
"There has not been flooding on this scale in the region since 1962, according to local records, and despite agencies like Concern Worldwide working tirelessly to respond to the escalating humanitarian crisis, (with financial assistance of donors such as BHA/USAID, ECHO, GAC, EFP and UNICEF) the needs far exceed the current scale of the humanitarian response, both within and outside the camps for internally displaced people.
"Families have been displaced and are sheltering on higher ground, in public buildings or with neighbours or family. Access to basic services including health and nutrition support has been disrupted as clinics have been damaged, submerged in floodwaters, or are inaccessible."
International charity Médecins Sans Frontières has also previously commented on how the flooding has put pressure on health facilities.
They said: "We are extremely concerned about malnutrition, with severe acute malnutrition levels two times the WHO threshold, and the number of children admitted to our hospital with severe malnutrition doubling since the start of the floods."
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Posted in Ethiopia, Health, News/ዜና, War & Crisis | Tagged: Aksum, Axum, በሽታ, ተላላፊ, ትግራይ, አክሱም, ኢትዮጵያ, ደቡብ ሱዳን, ጎርፍ, ጦርነት, Disease, Ethiopia, Flood, South Sudan, Tigray, War, WHO | Leave a Comment »
Ethiopia: The UN is Failing its Ethnic Tigrayan Peacekeeping Troops
There Has Been Little To No Action Taken To Address The Ethiopian Government's Ethnically-Based Expulsion And Arrest Of Tigrayan Peacekeepers.
When Tigrayan members of the Ethiopian National Defense Forces. ENDF were deployed to UN peacekeeping missions, they did so under the banner of "Together for Peace".
Respecting and honouring the brave few who put their own lives at risk in the service of their country and for the cause of world peace is a cherished norm. However, Tigrayan members of UN peacekeeping missions are getting the opposite treatment.
When the Ethiopian government launched an armed offensive against the Tigray region in November 2020, it withdrew troops from international peacekeeping missions to bolster its offensive. Citing fears over their loyalty to the federal government and ENDF, Tigrayan members of this contingent were also purged from their ranks without cause. Other Tigrayans were left with no choice but to seek asylum in order to escape abduction and internment.
Evidence of this purge was first attested to in a leaked video published by The Associated Press in which an Ethiopian military leader speaks of the need to 'clean out our insides' in a reference to the removal of Tigrayan service members.
Soon after, an article published in Foreign Policy on 23 November revealed an internal UN document that detailed concerns that these troops were likely to face torture or execution.
The UN's fears were confirmed after it was revealed that military tribunals are being held to sentence Tigrayan security officers to death. The Ethiopian government is seemingly using the judicial system to make a show of passing judgment on defendants who were in fact criminalised by virtue of ethnic profiling alone. The risk to the lives of these service members, including those who served under the auspices of the UN peacekeeping missions, is real.
In such a context, where identity is being used as evidence of guilt, Tigrayans require protection and open legal proceedings that are monitored and corroborated by independent organisations. The international community's inaction and silence regarding the horrible reality of these Tigrayans have allowed the Ethiopian government to prolong their suffering.
This same government expelled seven UN officials who were operating in Ethiopia, accusing them of 'meddling', and arbitrarily arrested 16 local UN staff members.
The UN Secretary-General stated that "Ethiopia has no legal right to expel" the UN officials. However, the institution has not taken any steps to protect its representatives, who are crucial to address the enormous humanitarian needs in northern Ethiopia.
The UN entrusts peacekeepers to uphold its broader mission of maintaining peace and security around the world, and, in return, these servicemen and women bravely put their lives on the line for this noble cause. Accordingly, the UN has a contractual and moral obligation to protect these brave men and women. However, when it comes to Tigrayan peacekeepers, the UN and the rest of the international community have turned a blind eye.
The UN's unwillingness to address the imminent threat faced by Tigrayans who served in peacekeeping missions – and lack of persistence in demanding protection for humanitarian workers and respect for international humanitarian law – is emboldening Ethiopia's violations.
To the honourable men and women inside of the UN peacekeeping apparatus, as well as those in donor and member countries, I ask: If you are unable to protect the bravest who have worn the uniform to promote world peace, then how can you ever realise the dream of standing "Together for Peace"?
While silence or disengagement is to be expected at a certain level from diplomatic actors and entities, given their prerogative to not fuel further division in a space as polarized as Ethiopia's, the case of Tigrayan peacekeepers exceeds the demands of neutrality and political sensitivity.
Their silence is even more worrying as the decision of the Ethiopian government has created a security vacuum in those areas where they were deployed, such as Darfur and Abyei in Sudan and Somalia, undermining the peacekeeping efforts. These actions also overstretched the capacity of UN peacekeeping troops that are present in these areas, leaving vulnerable communities at risk of immediate violence.
Moreover, since most peacekeeping troops operate under UN contracts, their treatment is a direct violation of the UN's policy and commitment to world peace. The UN's inaction may cause other countries to lose trust in future missions, given that there is no guarantee for the safety of their soldiers. Any atrocity committed against Tigrayan peacekeeping troops due to an internal political conflict is, by extension, an attack against peacekeepers around the world.
How the UN handles the case of Tigrayan peacekeepers in Ethiopia – many of whom have been incommunicado for over a year – will be a testament to how much the intergovernmental organisation values those it entrusts to uphold its mission.
Ethiopian Peacekeepers Who Brought Peace to South Sudan Attacked by The Nobel Peace Laureate PM
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Posted in Ethiopia, News/ዜና, War & Crisis | Tagged: Abiy Ahmed, ማዕቀብ, ረሃብ, ስምምነት, ሽብር, ትግራይ, አብይ አህመድ, አክሱም ጽዮን, ኤርትራ, ዘር ማጥፋት, የምግብ እርዳታ, የተኩስ አቁም, የአውሮፓ ህብረት, የጦር ወንጀል, ጀነሳይድ, ጆሴፕ ቦሬል, ግድያ, ጠላት, ጥላቻ, ጦርነት, ጭፍጨፋ, ፀረ-ተዋሕዶ, ፀረ-ኢትዮጵያ ሤራ, Borrell, Cease-fire, Eritrea, EU, Famine, Genocide, Humanitarian Aid, Massacre, Monastery, Peace Keepers, Sanction, Tigray, War Crimes | Leave a Comment »
Failure on Ethiopia Sanctions 'My Biggest Frustration' This Year, Says EU's Top Diplomat
💭 My Note: In other words, Mr. Borrell is telling us: "As long as war criminals Abiy Ahmed Ali, Isaias Afewerki, the Oromo & Amhara special forces continue blocking Tigrayans (potential migrants to Europe heading for EU) from crossing the Ethio-Sudanese border in whatever possible form: By rounding them up, mutilating & dismembering — at the border within Africa – and throwing their dead bodies to the Tekeze river across the border, EU won't issue sanctions against Abiy Ahmed, Isaias Afewerki and their partners in crime. The are doing a good job in preventing undesired ancient Christian Ethiopian migrants (We saw that when the UN The US and EU all blocked ancient Christians of Syria. Read this: No Christians Allowed: Muslim UN Officials Block Syrian Christian Refugees from Getting Help.
Mr. Borrell said it clearly, albeit concerning Belarus and Ukraine: "We cut the flowing of migrants to Europe…for me this is a source of satisfaction"
May be now The EU is giving money to the dictators of Ethiopia and Eritrea as a reward, instead of sanctioning them?!
After all, EU countries have awarded and honored to those evil monsters with the Nobel Peace Prize in 2019, and just two months ago, one of the enablers of the #TigrayGenocide, Daniel Bekele with the German Africa Prize. Just unbelievably cruel – the world upside down, isn't it?!
💭 EU top diplomat Josep Borrell criticised EU member states on Monday (13 December) for failing to agree on sanctions against those suspected of war crimes in Ethiopia's civil war, expressing frustration over Europe's failure to give an effective policy response to "large scale human rights violations" there.
The EU's response to the civil war in Ethiopia was "one of my biggest frustrations" of the year, said Borrell, the EU's foreign affairs high representative. He said the EU had not been able to stop "mass rapes using sexual violence as a war aim, killings and concentration camps based on ethnic belonging," pointing to the lack of unanimity among EU governments.
It is understood that Germany is one of the leading countries reluctant to impose sanctions, though Borrell told reporters that "many countries felt that it (sanctions) wasn't an adequate solution."
While the Biden administration in the United States has imposed sanctions under its human rights Magnitsky Act, the EU has not followed suit beyond freezing $107 million in budget support to Ethiopia.
Last month, EU officials told EURACTIV that sanctions were being discussed within the context of the bloc's Human Rights Sanctions regime, but little progress has been made.
EU prepared to issue sanctions over Tigray war, officials confirm
The European Union is prepared to issue sanctions against those responsible for the war and humanitarian crisis in Ethiopia's Tigray province, EU officials confirmed to EURACTIV on Thursday (5 November).
In the meantime, the EU has continued to supply humanitarian aid, despite continued difficulties in aid reaching those in need. Aid experts in Ethiopia say that only around 10% of aid reaches those who need it most.
Borrell acknowledged that while sanctions would not have halted the conflict, they "would have, in my view, influenced the behaviour of the actors."
Alongside multiple reports of human rights abuses by both sides in the conflict, the fighting has had devastating humanitarian consequences. According to the UN's World Food Programme, more than 400,000 people are estimated to be living in famine conditions in Tigray. Around 9.4 million people in Ethiopia are now in dire need of food aid, it said.
The war has derailed the economic and political reform agenda, which had earned wide international praise to Ethiopia's Prime Minister Abiy Ahmed.
The civil war started last November when federal forces entered the country's northern province after rebels from the Tigrayan People's Liberation Front launched an attack on a government military base.
The Abiy government subsequently cracked down mercilessly on the insurgents and ignored all demands by the international community for a ceasefire and peace settlement with the TPLF. Instead, Abiy has stated that nothing short of total military victory will be sufficient.
African Union mediator Olesegun Obasanjo and Kenyan President Uhuru Kenyatta have been leading regional efforts to broker peace.
Earlier this week, local media reported that TPLF forces had retaken the historic town of Lalibela, in the neighbouring Amhara province, though government forces are also reported to have recaptured towns in Tigray in recent weeks.
Slovenia, in its capacity as head of the EU's Council presidency, on Monday requested a special session of the UN Human Rights Council on the situation in Ethiopia.
More than 50 countries supported the call, Slovenia's Permanent Mission to the UN Office in Geneva announced.
The United Nations Human Rights Council will hold a special session on Friday on the "grave" situation in Ethiopia at the request of the EU, according to a UN statement issued on Monday.
The Ethiopian government has reacted furiously to the calling of the special session, and described it as an "unjust and counterproductive attempt by some to exert political pressure".
The UN Council had ignored calls to investigate human rights violations and atrocities by the TPLF in Amhara and Afar province, said Ethiopia's foreign ministry.
Posted in Ethiopia, News/ዜና, War & Crisis | Tagged: Abiy Ahmed, ማዕቀብ, ረሃብ, ስምምነት, ሽብር, ትግራይ, አብይ አህመድ, አክሱም ጽዮን, ኤርትራ, ዘር ማጥፋት, የምግብ እርዳታ, የተኩስ አቁም, የአውሮፓ ህብረት, የጦር ወንጀል, ጀነሳይድ, ጆሴፕ ቦሬል, ግድያ, ጠላት, ጥላቻ, ጦርነት, ጭፍጨፋ, ፀረ-ተዋሕዶ, ፀረ-ኢትዮጵያ ሤራ, Borrell, Cease-fire, Eritrea, EU, Famine, Genocide, Humanitarian Aid, Massacre, Monastery, Tigray, War Crimes | Leave a Comment »