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Winners Announced For The BroadwayWorld 2021 St. Louis Awards
BILLY ELLIOT THE MUSICAL - COCA - Center of Creative Arts
by BWW Awards Jan. 14, 2022
Winners have been announced for the 2021 BroadwayWorld St. Louis Awards. The 2021 Regional Awards honor productions which had their first performance between October 1, 2020 through September 30, 2021.
Streaming productions were eligible this year in the categories designated as such. This year BroadwayWorld also enabled audiences to vote on which theatres they are most excited to return to, and which productions they are most excited to see.
The BroadwayWorld Regional Awards are the largest theatre audience awards, with over 100 cities worldwide participating.
Want to be the first to know about the 2022 BroadwayWorld Regional Awards? Sign up for our local newsletter here.
2021 BroadwayWorld St. Louis Award Winners
Best Choreography Of A Play Or Musical
Kim Klick - SHREK - Kirkwood Theatre Guild
Best Costume Design Of A Play Or Musical
Jenna Gove - LITTLE SHOP OF HORRORS - Ozark Actors Theatre
Blane Pressler - LITTLE SHOP OF HORRORS - Ozark Actors Theatre
Ron Himes - SWEAT - The Black Rep
Best Direction Of A Stream
Jacqueline Thompson and Gaby Rodriguez - SUFFER THE CHILDREN - COCA - Center of Creative Arts
Best Editing Of A Stream
Kyle Himsworth - I REMEMBER HARLEM - The Black Rep
Best Lighting Design Of A Play Or Musical
Kevin Shaw - LITTLE SHOP OF HORRORS - Ozark Actors Theatre
Best Performer In A Musical
Shaina Vencel - LITTLE SHOP OF HORRORSSS - Ozark Actors Theatre
Best Performer In A Play
Brian McKinley - SWEAT - The Black Rep
Best Performer In A Streaming Musical
Jesmelia - DO I MOVE YOU? - The Black Rep
Best Performer In A Streaming Play
Christina Yancy - HOME - The Black Rep
SWEAT - The Black Rep
Best Production Of The Year (In Person)
Best Scenic Design Of A Play Or Musical
Britton Lynn - LITTLE SHOP OF HORRORS - Ozark Actors Theatre
Best Sound Design Of A Play Or Musical
Michael Smedley - LITTLE SHOP OF HORRORS - Ozark Actors Theatre
Best Streaming Play
HOME - The Black Rep
Best Supporting Performer In A Musical
Chris Moore - SHREK - Kirkwood Theatre Guild
Best Supporting Performer In A Play
Kelly Howe - SWEAT - The Black Rep
Best Supporting Performer in A Streaming Musical
Christina Yancy - DO I MOVE YOU? - The Black Rep
Most Anticipated Upcoming Production Of A Musical
SINGIN' IN THE RAIN - Kirkwood Theatre Guild
Most Anticipated Upcoming Production Of A Play
THE MAN WHO CAME TO DINNER - Kirkwood Theatre Guild
Student Blog: Academic Integrity and its Benefits
Academic integrity may not seem like topic that is super important to read about, but is definitely ignored a lot more than it should be. Seeing how practicing integrity in a academic setting now can help you in the future with your job and in general.
The Repertory Theatre Of St. Louis Presents Dominique Morisseau's CONFEDERATES This February
The Repertory Theatre of St. Louis will present Confederates. From award-winning playwright and writer Dominique Morisseau, this production will unite and enlighten audiences.
Rock Band Kansas To Bring 50Th Anniversary Tour to The Fabulous Fox In July 2023
America's preeminent progressive rock band, KANSAS, will be touring 50 select North American cities to celebrate the band's 50th Anniversary that will include a stop in St. Louis at the Fabulous Fox Theatre on Saturday, July 29 at 7:30 p.m. The tour will showcase two hours of hits, fan favorites, and deep cuts rarely performed live.
Photos: First Look At BROADWAY BOUND At New Jewish Theatre
The New Jewish Theatre kicks off its 2023 season with the Neil Simon comedy Broadway Bound on January 19 – February 5. See photos from the production.
From This Author - BWW Awards
Winners Announced For The 2022 BroadwayWorld Rockland / Westchester Awards
The winners have been announced for the 2022 BroadwayWorld Rockland / Westchester Awards, honoring the best in regional productions, touring shows, and more which had their first performance between October 1, 2021 through September 30, 2022.
Winners Announced For The 2022 BroadwayWorld Washington, DC Awards
The winners have been announced for the 2022 BroadwayWorld Washington, DC Awards, honoring the best in regional productions, touring shows, and more which had their first performance between October 1, 2021 through September 30, 2022.
Winners Announced For The 2022 BroadwayWorld Rhode Island Awards
The winners have been announced for the 2022 BroadwayWorld Rhode Island Awards, honoring the best in regional productions, touring shows, and more which had their first performance between October 1, 2021 through September 30, 2022.
Winners Announced For The 2022 BroadwayWorld Palm Springs Awards
The winners have been announced for the 2022 BroadwayWorld Palm Springs Awards, honoring the best in regional productions, touring shows, and more which had their first performance between October 1, 2021 through September 30, 2022.
Winners Announced For The 2022 BroadwayWorld Oklahoma Awards
The winners have been announced for the 2022 BroadwayWorld Oklahoma Awards, honoring the best in regional productions, touring shows, and more which had their first performance between October 1, 2021 through September 30, 2022.
Review: LES MISERABLES at Fox Theatre, St. Louis
TO KILL A MOCKINGBIRD Comes to the Fabulous Fox Theatre Next Month
VIDEO: Watch Reneé Rapp Duet With Jennifer Hudson
Video: Stephanie J. Block, Derek Klena & More Get Ready to Bring SUNSET BOULEVARD to the Kennedy Center
SHOP WICKED
St. Louis SHOWS
Spells of the Sea
Grandel Theatre (2/05-3/05) PHOTOS VIDEOS CAST
Kirkwood High School (4/20-4/22)
Parkway West High School (2/24-2/25)
Capital City Productions (10/12-10/21)
Hillsboro High School (4/20-4/23)
Central High School (4/07-4/10)
Roald Dahl's Willy Wonka Kids
Southern Boone Middle School (8/29-8/29)
Disney's Winnie The Pooh Kids
10 West Lockwood Event Space (6/23-6/24)
Macklanburg Playhouse (3/17-3/24)
Gladstone Park And Recreation (8/11-8/13)
Wentzville South Middle School (8/03-8/03)
Concord Church (3/16-3/18)
How I Became a Pirate Younger@Part
Jabberwocky Studios (4/01-4/01)
A Funny Thing...forum
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Elf-the Musical
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Diablo Magazine November 2006 /
Many East Bay wine shops are also perfect places to swirl, sniff, and sip
Tim Patterson and Nancy G. Freeman
"In vino veritas," the old saying goes. In wine there is truth—and these days, residents of the East Bay don't need to drive to Napa or Sonoma to get the facts.
That's because tasting opportunities are popping up at wine shops all over. Tastings run the gamut from simple drop-in-and-taste sessions to structured classes, and wine is poured by knowledgeable employees, visiting winemakers, or distributors eager to try out new offerings on both the management and potential consumers.
These affairs aren't just for staunch oenophiles, either: While the scene on most weeknights and Saturdays tends to be comprised of a focused, thirtysomething-and-up crowd, Fridays often feature a younger, more relaxed group celebrating TGIF. At any rate, with the variety of programs available, there's something in the mix for everyone from nouveau wine hound to established connoisseur.
Prima Vini
Prima's guided tastings reflect the breadth and quality of the wines stocked by this premier wine shop. Importers, visiting winemakers, and a savvy staff take participants through thematic selections of six to eight wines, and the kitchen turns out scrumptious antipasti. The restaurant bar has 40 wines available by the glass at all times, including weekly flights. 1520 N. Main St., Walnut Creek, (925) 945-1800, www.primawine.com. "Open house" tastings Sat. 3–5 p.m. on a drop-in basis, $8–$15; guided tastings with visiting experts, various times, $20–$30 with antipasti.
Ristorante Amoroma
Free tastings from this restaurant and wine shop's extensive collection of Italian and California wines focus on specific regions and producers. The tastings always include four or more wines, and the shop is also a great source for gourmet products such as pasta, olive oil, and candy. 360 Park St., Moraga, (925) 377-7662. Tastings Thurs. 5:30–7:30 p.m., free.
Wine Thieves
The mission here is to make good wine available at great prices and to educate customers in "wine speak." In addition to Friday night tastings with distributors and winery representatives, bottles are open at the tiny bar all day every day. The staff is knowledgeable, the atmosphere is laid back, and the values are astonishing—more than half the selection is $10 or less per bottle. 3401 Mt. Diablo Blvd., Lafayette, (925) 299-9070; 5443 Clayton Rd., Clayton, (925) 672-4003, www.winethieves.com. Tastings in Lafayette on Fri. 5:30–7 p.m. Tastings in Clayton Fri. 6–8 p.m. and Sat. 1–5 p.m; both stores charge a $1 tasting fee.
Jackson's Wines & Spirits
Jackson's has been selling a worldly array of wines for nearly 40 years, making its Saturday tastings—a mixed selection of 10 to 15 wines—something of a Lamorinda institution. Tasting regulars range from collectors stocking their cellars to locals eschewing the drive to Wine Country. 3524 Mt. Diablo Blvd., Lafayette, (925) 284-4100. Tastings Sat. 1–4 p.m., about $20.
Winecentives
Structured, sit-down tastings here manage to be fun and serious at the same time, thanks to a good-natured, entertaining staff. Sessions focus on a broad range of international and domestic regions and varieties. Longtime attendees arrive with notebooks bulging with information acquired over the years. A four-class wine series is also available for $45 and up per class. 6040 Dougherty Rd., Dublin, (925) 829-3222, www.winecentives.com. Formal tastings Fri. 6:30 p.m., $10–$25.
Bella Vino
The dramatic black granite wine bar is the perfect setting for Bella Vino's selection of boutique Napa-focused Chardonnay and Cabernet, and selected imports. Evenings at the wine bar are largely social, although Thursdays feature wineries or distributors showing off their wares. 3450 Camino Tassajara Blvd., Danville, (925) 648-1300, www.bvino.com. Wine bar open Tues.–Wed. noon–7 p.m., Thurs.–Fri. noon–9 p.m., Sat. 11 a.m.–7 p.m., Sun. 11 a.m.–5 p.m.; Thurs. winemaker tastings, about $8–$15.
The Wine Steward
Like the shop itself, the Wine Steward's upstairs tasting bar offers one of the East Bay's broadest international selections of wines—but by the glass, taste, or flight. Prices range from $4 a glass to $20 for a six-wine flight. The Wine Steward features a sharp staff, mind-broadening themes, and plenty of gourmet edibles to take home with the bottles you discover. 641 Main St., Pleasanton, (925) 600-9463, www.thewinesteward.com. Wine bar open Thurs.–Fri. 5–8 p.m., Sat. 1–8:30 p.m.; $4–$20.
First Street Wine Co.
First Street's focus is on California, especially Napa and Sonoma, with an emphasis on high-end and hard-to-find bottles. Tastings (five wines, $5–$25) range from varietal themes to new arrivals. Friday and Saturday evenings can draw 30 to 60 of the curious and thirsty. 2211 First St., Livermore, (925) 294-5825, www.wineco.com. Focused tastings Fri. 6–9 p.m., wines open Sat. 11 a.m.–7 p.m., Sun. noon–5 p.m.; $5–$25.
Come to this restaurant and shop, located in the Epicurious Garden, for an intelligent selection of reds, whites, and dessert wines, either by the glass or from the spouts of a gleaming Enomatic dispenser. Purchase a "smart card," put it in the slot, and a perfectly measured ounce tumbles into your glass. The advantage here is that you get to do the mixing and matching; the disadvantage is that you're on your own. Full-service dining with a menu of California cuisine as well. 1513 Shattuck Ave., Berkeley, (510) 540-7800, www.epicuriousgarden.com. Wine-dispensing machines pour Mon.–Sat. 11:30 a.m.–10 p.m., Sun. 11:30 a.m.–9:30 p.m.; cost of tasting varies according to wine, ranging from $1.25–$17 for a one-ounce pour.
Solano Cellars/Vintage Berkeley
Solano Cellars and Vintage Berkeley have the same owners, but each shop has its own personality. Solano Cellars, which has been a local magnet for decades, today boasts a diverse wine selection, including small producers and some wines you've probably never heard of. Comestibles include small plates of cheese, Fatted Calf charcuterie, and salads. Vintage Berkeley, which is loacted around the corner from Taste, specializes in bottles $25 and under and offers tastes from a bottle or two every afternoon. Saturdays, you can taste several wines from individual wineries. 1580 Solano Ave., Albany, (510) 525-9463, www.solanocellars.com . 2113 Vine St., Berkeley, (510) 665-8600, www.vintageberkeley.com. Solano Cellars wine bar open Tues.–Sat. 4–9 p.m., Sun. noon–6 p.m.; prices for tasting are $14–$16 per flight and $5–$12 per glass. Vintage Berkeley tastings Mon.–Fri. 4–7 p.m., Sat. 2–4 p.m.; free.

redpajama_set_name: RedPajamaCommonCrawl


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Washington-Lee High School Closed Due to Threat
ARLnow.com April 6, 2010 at 3:46pm
Update at 9:30 a.m. — The school and the aquatic center have reopened after getting the "all clear" from police.
An unspecified threat at Washington-Lee High School has prompted officials to cancel all after-school activities at the high school, including adult education classes. The W-L aquatic center has also been closed.
Administrators learned of the threat this afternoon, school officials said in an email. Police investigated and determined that there was no imminent danger to students and staff.
The building was closed at 3:00 p.m., immediately after classes ended. Police are now conducting a more thorough search of the building.
Arlington Public Schools will announce whether there will be any further cancellations early tomorrow morning. The W-L aquatics center will open at 6:30 a.m., at the earliest, the school system said.
police threat Washington-Liberty
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LOVE BEANIES BACK IN STOCK!!
Love Cycles knit beanies 100% AMERCAN MADE.
We only make 200 of these unique knit caps once a year. They are a very high quality, hand-made, heavy weight, 90% cotton, 10% poly. They are sure to keep your head warm at a solid 6 ounces.
They come in Black with white text and orange stripes.
These are handmade by Al and Brittany from the Blackboard cafe located in the heart of Los Angeles, real American made goods.
These beanies will ship December 9, just in time to arrive for Christmas! Every beanie comes with some free stickers.
Get one while you can. We are only making a small run for winter time.


Initially, I planned on focusing this post on my first boyfriend ever, a landscaper named Joey. Then it hit me that he wasn't my first love, after all. Long before Joey came along, I completely loved my first dog, Frosty, a precious white Samoyed puppy. As I pushed my brain's memory cells to the limit, I realized there was another love that came long fourteen years earlier than Frosty: my parents. True, every little girl loves her mommy and daddy, but my relationship with them eventually morphed into something more—an undying friendship. Sadly, they're gone now. I miss them both terribly, and always will.
Ironically, when I laid my mother to rest beside my father about two years ago, among those standing with me were my brother, Matt, and the only other men I've ever loved, all of them ex-boyfriends. Joey, who'd coincidentally become manager of the cemetery we were standing in; Brian, the cop; and Ned the Fed, whom I'm still close friends with. I know my mother was looking down on us, smiling, while my dad was no doubt rolling his eyes about all the exes I'd accumulated in my life. Oh, well. I loved you all.
Special thanks to Tee O'Fallon for sponsoring this giveaway.
Thanks for sharing... adding this to my want list!
How sweet that those exes are still in your life in a positive way!
I don't know what to say. My first thought was aww. But I want to hug you.


We're pleased to announce the releases of Storage Made Easy Azure Storage Drive and Storage Made Easy Azure Storage Explorer for Microsoft Azure Blob storage. Joining our family of standalone desktop apps, these new drive and explorer releases allow end users to interact with Azure object storage through familiar interfaces.
With high scalability and availability Azure object storage is increasingly a secure and cost-effective choice for hosting corporate documents and files. The challenge is that object storage can be difficult for end users to use particularly given that the object paradigm is different from what users are used to with traditional file and block storage.


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Is Pat Sajak Bald?
Shows For Kids
Pat Sajak - with his own hair. Courtesy CBS
by Carrie Grosvenor
Carrie Grosvenor is the author of "So You Want to Be on Wheel of Fortune." A freelance entertainment writer, Grosvenor has contributed to CNN, MSNBC, and the Game Show Network.
Question: Is Pat Sajak Bald?
On April 1st 2008, Wheel of Fortune host Pat Sajak closed the show with co-host Vanna White with an April Fool's Day prank -- he pulled his hair piece off to reveal a bald head. Is Sajak really bald?
The quick answer to this question is a resounding no. Loads of fans speculated that they could see "shaving bumps" on Sajak's head, or that there was no way the bald head was fake because they didn't see any lines or other tell-tale signs.
In reality, Sajak is not bald and that's his real hair that he's sporting on the show. The big April 1st reveal was just a joke, though rumors and speculation persist to this day. You can see the clip from the end of that show on YouTube.
Oddly enough, Sajak's hair has now earned the same kind of fan obsession as Alex Trebek's moustache.
What's a Game Show Host's Salary Worth?
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24 Hilarious Jokes About Golf: Did You Har-Har the One About ...
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In case you don't know, the 25th of January marks the birth of Robert Burns, Scotland's most famous national poet, writer of Auld Lang Syne (AKA the New Years song 😉 ) and pioneer of the Romantic movement.
The day is marked with a celebratory Burns Night supper of haggis, neeps and tatties, plus a wee dram of whisky.
To translate, that's Scotland's national dish (made of meat, oatmeal, onions, suet & spices encased in sheeps' stomach); turnips, potatoes and whisky, or Scotch, as it's known outside our borders.
Burns' ever appropriate poem 'Address to a Haggis' is recited to the haggis… after a bit of bag piping to mark its entrance, if you're really committed to it. Basically, it's the night Scots are Scottish to the nth degree.
Purists would argue that the whisky is non-negotiable — it's a Scottish holiday for a Scottish poet! — but, as it turns out, we're not purists.
Can there be a better night to drink gin that's been aged in whisky barrels? Scottish barrel aged gin should no doubt grace your table on Burns Night. Let's have some fun.
Featuring no less than Robert Burns' favourite tea, Lassie's Toast by Dunnet Bay Distillery couldn't be more fitting for Burns night.
Glasgow Distillery's entry in the barrel aged gin is a beautiful one. Matured in virgin oak wood casks, Makar Oak Aged Gin is gorgeously hued, complex and peppery. It even won the Scottish Gin Awards 2017 gold medal in aged gin.
Pickering's, makers of the much coveted Christmas baubles, carry a little fleet of barrel aged gins. The Pickering's Oak Aged Gin collection, which launched in 2016, boasts five differently aged bottles.
The gins have all been rested in casks from different Scottish whisky regions: the lowlands, islands, Speyside, Highlands and Islay.
The range come in handy half bottles so you can really experiment.
Light, luscious and creamy. Expect lemon and vanilla on the nose with "dried dates and fig" on the palate with a warm malted biscuit finish.
This gin has been aged in casks from island distilleries like Orkney, Skye, Mull, Arran and Jura.
Bold on the peat like it's whisky predecessor, the Island gin's saline notes float through beside dried fruits and citrus.
Amazingly, over half of Scotland's whisky distilleries lie in the northeast. Watch out anise on the nose plus oak, vanilla and rich fruitcake to taste.
Big on the juniper and woody, the Highland gin carries sweet dried fruit notes well balanced by wood.
Punchy and peaty as you'd expect with an Islay whisky, this barrel aged gin is for total smoke heads.


UKSaabs • View topic - back to black.
Post subject: back to black.
Having had a very good look around my new to me toy have found the black trim is faded and white.Looking for good tips to restore the black bits back to looking good, before i spend loads on commercial treatments.
Post subject: Re: back to black.
Hot air gun then coat with Gtechniq C4 and it will last for years.
Another vote for Autoglym Bumper and Trim Gel but again only lasts a few weeks.
I used a good product called Forever Black on very faded trim on my old Carisma. It worked really well and the trim was still black when I sold the car. It is quite pricy though and it is a permanent dye so you have to mask off paintwork or wipe off any overspill. I will be getting some for my c900 project when all the mechanicals are done.
Last edited by ame2 on Tue May 29, 2018 4:47 pm, edited 1 time in total.
And another vote for Autoglym Bumper and Trim Gel.
Boiled linseed oil is good but it stinks and takes time to dry. Also if you leave rags bundled up soaked in the stuff it can combust.
Is that the forever tyre gel?
Sorry, Raymond. I have only just seen your question. It's this product, though it was years ago so not from eBay.
It is a dye though so you do need to be careful.
I did my wife's CRV with boiled linseed oil at the weekend. I would expect it to last at least 6 months. I think anything which puts oil back into the plastic rather than just putting a shine on the surface works well. e.g. ground nut oil, peanut butter, linseed oil, gt85.
I believe the science behind the heatgun is that it brings the oils up to the surface of the plastic to much the same effect. That said I tried it on my wife's old S40 and it ruined a piece of trim. Volvo plastics from the early naughties were odd though, really hard and not much texture. The heat made the surface start to peel.
Cheers mate, I'll get some ordered.
I tried the linseed oil 3 months ago as my black plastic looked awful, and I had some linseed oil laying around. It looks like it could do with another application (not surprising that it needs a top up after 14 years). It was easy, no mess or effort.


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Home / Science / Sizzling September
Photo Credit: Marie McLane The South Pole Station in September 2013, when a bevy of new weather records was set for the month, including a new one-day record high and new average high for September.
Sizzling September
More weather records fall as South Pole emerges from long winter
Another month at the South Pole. Another month of record high temperatures at the bottom of the world.
The 2013 winter – the months of June, July and August – will already go down as the warmest such season at the South Pole since records began in 1957. That trend continued into September – now the warmest on record – with four new daily maximum record temperatures falling in the middle of the month.
"Saying that it has been a warm winter this year is a bit of an understatement at this point," said Phillip Marzette, senior meteorologist at the South Pole Station .
South Pole Winter Weather 2013
Hot streak: South Pole experiences record heat in August to end warmest winter ever
Hitting a new high: South Pole sets record maximum temperature in middle of winter
Wild swings: South Pole temperatures roll between extremes, set new records
Of course, warm is a relative term at the South Pole, where the average annual temperature is about minus 56.9F (minus 49.4C).
The average temperature of minus 60.2 degrees Fahrenheit (minus 51.2 degrees Celsius) broke the previous highest average temperature for the month of September of minus 62.7F (minus 52.6C) set in 2005. In addition, the average maximum temperature of minus 53.5F (minus 47.5C) broke the previous highest average maximum temperature of minus 55.3F (minus 48.5C), also set in 2005.
The four new daily records include:
Sept. 11: Minus 28.3F (minus 33.5C) broke the previous maximum temperature record of minus 30.5F (minus 34.7C) set in 2001.
The record high on Sept. 13 also ranks as the new maximum temperature for the month of September, which was previously set on Sept. 28-29, 1994, with a high of minus 20.7F (minus 29.3C).
Photo Credit: Marie McLane
Frost covers the ceremonial pole in September.
In August of this year, the record average temperature of minus 63.9 degrees Fahrenheit (minus 53.3 degrees Celsius) broke the previous record of minus 64.5F (53.6C) set in August 1996. The departure from normal was 11.6 degrees Fahrenheit (or 6.4 degrees Celsius). The record average max temperature of minus 56.2F (minus 49.0C) broke the previous record of minus 57.3F (minus 49.6C), also set in August 1996.
However, June 2013 really set the tempo for the winter, when the all-time maximum temperature record for the month of June was set not once but twice.
On June 2, the wintertime temperature hit minus 22.2F (minus 30.1C), shattering the previous record for that day of minus 35.7F (minus 37.6C) set in 1987. The new June record barely lasted two weeks. On June 19, the temperature climbed to minus 19.8F (minus 28.8C). The record-setting day was bookended by two single day maximum temperature records as well.
June 2013 was tied for the third warmest June since 1957, with an average of minus 62.9F (minus 52.7C), the warmest it has been for the month since 2007 (warmest June). That was 10.4 degrees Fahrenheit (5.8 degrees Celsius) above normal.
"The same pattern occurred in the middle of [September] like it has since June – a wave of moisture from the western seas that gave us clouds, winds and high temperatures for a couple of days," Marzette said. "It has been unusual given that normally there is one month that is warm throughout the year, but nothing like this where it has been this for three out of four months."


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Caribou Andorra
By Vish Khanna
Keen to challenge listeners with forays into eclectic noise and electronica, Dan Snaith stakes out new territory with the remarkable Andorra, a stirring pop masterpiece. Since 2005's The Milk of Human Kindness, Snaith completed a doctorate in mathematics and re-released albums done under his old moniker, Manitoba. All that concentration and reflection obviously triggered something significant for Caribou because his latest batch of songs sends him down an adventurous route. The most obvious distinction about Andorra is the focus on Snaith's voice. Content to let a beat or drone speak for him in the past, Snaith sings his heart out here and the ambient, airy quality of his processed voice is glorious. With all the emotion of Pet Sounds and fantastical anarchy of The Piper at the Gates of Dawn, Andorra's music is expansive and brash, with swirling melodies gliding over inventive percussion. For all its insistent stomping, "Melody Day" is a mature yet exuberant emotional release, while "After Hours" is a sweeping production art piece. Jeremy Greenspan of the Junior Boys collaborates on "She's the One" and the result is the most haunting of the unexpected love songs found here, including the fluttery "Desiree." Always innovative, Caribou does no wrong with the unexpectedly cohesive and romantic Andorra.
What's got you singing?
It's not so much about lyrical songwriting, where I'm chronicling things going on in my life, but I realised that I hadn't done much with song composition — chord changes, melodies and harmonies all hooking together — and I wanted to explore that arc of a song.
Was this a tricky record to make?
With each track, I was writing the music and fitting the production in with what suited the song. I really love that lush sound with a lot of instrumentation flying at you, which is what was popular with the Zombies or the Beach Boys. The production wasn't an afterthought but this time I let the music be led by the song itself, which is something totally different for me.
Did the math degree profoundly affect your music?
Nothing profound, no. When I was doing both, they were kind of good foils — one was different from the other and they each gave me a break. They're both playing around with abstract ideas and fitting things together in different combinations and experimenting with ideas and seeing what results you get. They're both like a mental challenge for me. (Merge)
More Caribou
Mar 16 @ 8:00PM - Caribou Hamilton @ The Studio
Mar 17 @ 7:00PM - Caribou Toronto @ Danforth Music Hall
Mar 22 @ 7:00PM - Caribou Ottawa @ Bronson Centre Theatre
Mar 23 @ 8:00PM - Caribou Montreal @ MTelus (formerly Metropolis)
Caribou Shares "Never Come Back"
Ahead of the release of his forthcoming record Suddenly, Caribou has shared a new single titled "Never Come Back." According to a press r...
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text:
Q: kustomize uses wrong api version When I kustomize the cockroachdb helm chart with kubectl kustomize, the wrong kubernetes api version is used for some ressources.
kustomization
piVersion: kustomize.config.k8s.io/v1beta1
kind: Kustomization
namespace: apps

generators:
  - cockroachdbChart.yaml

Helm Chart Inflator:
apiVersion: builtin
kind: HelmChartInflationGenerator
metadata:
  name: crdb
name: cockroachdb
repo: https://charts.cockroachdb.com/
version: 10.0.3
releaseName: crdb
namespace: apps
IncludeCRDs: true

When I now run kubectl kustomize --enable-helm in the directory with those files, some are rendered with the v1beta1 version, even if the kubernetes version only supports version v1:
» kubectl kustomize --enable-helm crdb-test | grep -A 5 -B 1 v1beta
---
apiVersion: batch/v1beta1
kind: CronJob
metadata:
  labels:
    app.kubernetes.io/instance: crdb
    app.kubernetes.io/managed-by: Helm
--
---
apiVersion: batch/v1beta1
kind: CronJob
metadata:
  labels:
    app.kubernetes.io/instance: crdb
    app.kubernetes.io/managed-by: Helm
--
---
apiVersion: policy/v1beta1
kind: PodDisruptionBudget
metadata:
  labels:
    app.kubernetes.io/instance: crdb
    app.kubernetes.io/managed-by: Helm

These are the kubectl and helm versions I have installed:
» kubectl version --short
Client Version: v1.24.3
Kustomize Version: v4.5.4
Server Version: v1.25.4
» helm version --short
v3.10.3+gd506314

Is this a kustomize error?
Can I set the api Version that kustomize uses in the kustomization file?

A: Kustomize doesn't know anything about what API versions are supported by your target environment, nor does it change the API versions in your source manifests.
If you're getting output with inappropriate API versions, the problem is not with Kustomize but with the source manifests.
We see the same behavior if we remove Kustomize from the equation:
$ helm template cockroachdb/cockroachdb | grep -B1 CronJob
apiVersion: batch/v1beta1
kind: CronJob
metadata:
--
apiVersion: batch/v1beta1
kind: CronJob
metadata:

The problem here is the logic in the Helm chart, which looks like this:
{{- if and .Values.tls.enabled (and .Values.tls.certs.selfSigner.enabled (not .Values.tls.certs.selfSigner.caProvided)) }}
  {{- if .Values.tls.certs.selfSigner.rotateCerts }}
    {{- if .Capabilities.APIVersions.Has "batch/v1/CronJob" }}
apiVersion: batch/v1
    {{- else }}
apiVersion: batch/v1beta1
    {{- end }}

That relies on the value of .Capabilities.APIVersions.Has "batch/v1/CronJob", which requires Helm to query the remote Kubernetes environment to check if the server supports that API version. That doesn't happen when using helm template (or Kustomize, which is really just wrapping helm template when exploding helm charts).
The correct fix would be for the CockroachDB folks to update the helm charts to introduce a variable that controls this logic explicitly.
You can patch this in your kustomization.yaml:
apiVersion: kustomize.config.k8s.io/v1beta1
kind: Kustomization

generators:
  - cockroachdbChart.yaml

patches:
  - target:
      kind: CronJob
    patch: |
      - op: replace
        path: /apiVersion
        value: batch/v1

Which results in:
$ kustomize build --enable-helm | grep -B1 CronJob
apiVersion: batch/v1
kind: CronJob
--
apiVersion: batch/v1
kind: CronJob

redpajama_set_name: RedPajamaStackExchange


(1) 46th Legislature - 1/10/1939, p. 2, listed in "Roll Call of Senators-Elect." Senate Journal.
48th Legislature, HCR 150. Relatives: Charles Metcalfe - father; Penrose Metcalfe - son. Resolutions - Memorial.
"Charles B. Metcalfe Services Set Here at 3:30 P.M. Today," 12/12/1941, p. 1, 20. San Angelo Standard Times.
"Penrose Metcalfe, Area Pioneer Dies," 3/7/1970, p. 1A, 2A. San Angelo Standard Times.
Memorial, May 1970, p. 389. Texas Bar Journal.


Mission Space. If you find yourself at Epcot, you'll have to check out Mission Space. Arguably the most thrilling ride you'll find in Epcot, Mission Space made waves when it first opened as an exhilarating space launch simulator. While much of the initial popularity has faded, Mission Space is still a favorite among teens on the hunt for something a little more exciting than Spaceship Earth. Steer clear if you suffer from claustrophobia - riders are loaded into pods attached to a centrifuge that spins to create some intense G-forces, and there isn't a lot of room to move around once you're strapped in.
The Twilight Zone: Tower of Terror. Located in Hollywood Studios, this thrilling ride takes guests on a chilling journey through the Hollywood Tower Hotel. Climb into the elevator when your time is up and enjoy the ride to the top - until you drop! The Tower of Terror sends guests on a freefall through the elevator shaft, launching them skyward before falling again. The drop sequence is randomized so the ride won't lose its thrill if your teens are clamoring to go on this one again.
Expedition Everest. Holding the title of Guinness World Records most expensive roller coaster in the world, you and your teens will be amazed by the level of detail and attention that went into creating Expedition Everest, and you'll have a blast riding it, too! This rollercoaster - the tallest in Disney World - will take you on a trip through the mountain, twisting and turning until you encounter the Yeti. At that point, the ride reverses, sending you on a thrilling journey backwards.
Rock 'n' Roller Coaster. Themed around the popular rock band Aerosmith, this rollercoaster sends you on a wild ride to some of the band's most-loved songs. While that might not be a big draw for your teens, it's actually one of the most heart-pounding rides in Orlando. It's the only upside-down roller coaster in Disney World, and it starts with a shock as riders are launched from a dead stop to nearly 60 mph, so it's the perfect choice if you (or your teen!) are looking for a thrill.
Avatar Flight of Passage. One of the newest rides to appear in Disney World, you can find Flight of Passage in Pandora at Animal Kingdom. Using much of the same technology that made Soarin' in Epcot so successful, Flight of Passage takes a more thrilling approach, incorporating stunning visuals and effects as riders are taken on a journey through the landscapes of Pandora.
The idea of getting the whole family, teens include, on board for the family's next Disney World vacation can be tough, but they may even be excited to go once they realize how much fun they can actually have while they're there. These rides are just a few of the great options teens can enjoy in the parks!


text:
\section{Introduction}

In supervised classification, a classifier is trained with labeled training data points, which are usually collected through human annotation.
While collecting labeled data points is the traditional way to apply supervised classification, \emph{pairwise comparison} is often more appealing for human decision making~\cite{furnkranz2010preference}, where annotators are requested to compare two instances and give relative relationships between them;
e.g., which instance has stronger stimulus, whether two instances belong to the same category, and so on.
This is partly because (1) decision makers tend to be subjective at directly choosing a single hypothesis\footnote{\cite{thurstone1927law} has studied a relationship between relative comparison and a single hypothesis on stimuli, which is known as the law of comparative judgement.},
and (2) decision makers are often biased about picking an opinion.\footnote{This bias is known as social desirability bias~\cite{fisher1993social}; questionees are unconsciously led to a socially desirable opinion when they are asked to reveal their opinions in a direct way. Such a tendency is observed especially in answering their sensitive matters such as criminal records.}
Thus, pairwise comparison has been exploited in a number of applications such as pairwise ranking~\cite{furnkranz2010preference,jamieson2011active}, Bayesian optimization~\cite{eric2008active}, derivative-free optimization~\cite{jamieson2012query}, and analytic hierarchical processes~\cite{saaty1990decision}.
\\
One of the methods that incorporate pairwise comparison into identification of latent categories of data is \emph{semi-supervised clustering}~\cite{basu2008constrained},
which utilizes pairwise supervision indicating whether two instances belong to the same cluster or not (known as must-link and cannot-link constraints), guiding clustering as decision makers desire.
Recently, \cite{bao2018classification} and \cite{shimada2019classification} gave an empirical risk minimization (ERM) formulation to train an inductive classifier from pairwise comparison,
which has successfully connected supervised learning and pairwise comparison and avoided dataset-dependent assumptions used in semi-supervised clustering.

However, there is one important gap that has not been addressed in classification with pairwise supervision---real world data collection is bound to be noisy. Several previous works address noise in ordinary supervision with class-labeled data---\cite{natarajan2013learning,patrini2017making,jiang2017mentornet,han2018co}.
For pairwise supervision, there are two unique types of error.
The first error results from \emph{pairing corruption}: some pairs of instances are hard to identify whether they belong to the same category or not.
The second error is from \emph{labeling corruption}: labels of some instances are intrinsically ambiguous thus subsequent pairwise comparison is also affected.
Depending on these situations, we can consider two types of noise models in pairwise supervision.

In this paper, we investigate classification with noisy pairwise supervision, where noise is present in pairwise comparison and follows either pairing corruption or labeling corruption.
Our first strategy is inspired by previous work \cite{patrini2017making,natarajan2013learning} that uses standard class-labeled data with class-conditional noise to learn a classifier.
We introduce a corrected loss function, which induces an unbiased estimator of the classification risk in the presence of noise for pairwise data.
Subsequently, a classifier can be obtained through the minimization of the corrected loss.
The second strategy is based on  weighted empirical risk minimization, or  cost-sensitive classification \cite{elkan2001foundations,scott2012calibrated}.
This is motivated from the insight that the Bayes classifier of the classification risk under the noise-free distribution corresponds to that of the weighted risk under the noisy distribution.

To the best of our knowledge, this is the first work to investigate learning from noisy pairwise data and the following are our main contributions :

\begin{itemize}
\item Definition of realistic noise models for the S-D learning problem.
\item Providing two algorithms based on loss correction and weighted classification that can effectively learn from noisy S-D training data (under either noise model) and still give good performance (standard binary classification accuracy) on clean test data.
\item Proving that the Bayes classifier for noise-free and symmetric-noise S-D learning is identical to the Bayes classifier for standard binary classification.
\item We analyze the generalization bounds of our algorithms and provide two new generalization bounds for clean S-D learning \cite{shimada2019classification}
\item Performing experiments on various datasets to show that the proposed algorithms work well in practice.
\end{itemize}

\iffalse
\section{Related Work}
This paper studies learning from one kind of alternative, weaker supervision under label noise. Thus, we briefly survey some related work in \textit{weak supervision} and in \textit{learning from noisy labels}.

With the increasing application of machine learning in real-world scenarios, practitioners are stumbling when a vast number of traditional class labelings are hard to obtain. To address this learning from Similar-Unlabeled data~\cite{bao2018classification}, learning from Similar, dissimilar and Unlabeled data~\cite{shimada2019classification}, learning from positive unlabeled data \cite{elkan2008learning,du2015convex}, learning from complementary labels~\cite{ishida2017learning}, learning from positive-confidence labeled data~\cite{ishida2018binary}, learning from only sets of unlabeled data~\cite{lu2018minimal}, are some of the works that propose algorithms to learn from alternative, weaker forms of supervision. As mentioned before, certain semi-supervised clustering methods are related to learning from Similar-Dissimilar data pairs but these are unsupervised or semi-supervised methods while in this paper we design algorithms under the umbrella of supervised learning (similar to \shortcite{bao2018classification} and \shortcite{shimada2019classification})---so the two are different fundamentally and the advantage of the supervised learning approaches is formulating the ERM which can give generalization guarantees which are not straightforward for clustering based methods.
These are the broad three lines of work for these semi-supervised clustering methods : (1)~must-link, cannot-link constraints~\cite{basu2008constrained}, (2)~clustering performed with metric learned from semi-supervised metric learning~\cite{davis2007information,niu2014information}, and (3)~matrix completion to predict the missing links~\cite{yi2013semi,chiang2014prediction}.

The other major issue in large-scale data collection is that of noisy annotation. Learning from noise corrupted training data has been widely explored from a theoretical as well as an empirical standpoint and these methods can be categorized into three broad categories : (1)~Train only on selected ``clean'' samples~\cite{jiang2017mentornet,han2018co} (2)~Explicit~\cite{belkin2006manifold} and implicit~\cite{tarvainen2017mean} regularization techniques and (3)~Noise rate estimation---some works follow a two step approach~\cite{natarajan2013learning,patrini2017making}--- by first estimating the noise rates and then using them to develop unbiased estimators of the loss or reducing risk minimization under noisy labels to weighted ordinary risk minimization--- while others follow an end-to-end strategy~\cite{sukhbaatar2014training,goldberger2016training}. The noise rate estimation methods are superior to the other two because it does not suffer from any biases while the first two categories suffer from selection bias and regularization bias respectively. Further, the two step approach of \shortcite{natarajan2013learning} and it's multiclass extension~\cite{patrini2017making} is theoretically very well founded and gives a good understanding of why their proposed methods are able to learn from noisy datasets. However, all these methods can only deal with the ordinary classification scenario with class labels for each datapoint as supervision.  To the best of our knowledge, we are the first to extend this line of work to learning from noisy S-D data.

\fi

\section{Problem Setup}
Let $\mathcal{X}$ denote the instance space, $\mathcal{Y}$ the label space and $\mathcal{Z}$ the
the underlying distribution over $(\mathcal{X},\mathcal{Y})$. $\mathcal{Z}$ is the distribution with respect to which we want to perform well---the test data is drawn from this distribution and the performance metric is classification accuracy : $\sum_{(x,y)\in test_data}\mathbbm{1}[y_{predicted} \neq y]$, where $\mathbbm{1}[\cdot]$ denotes the indicator function. However, we assume that due to the domain constraints we are unable to procure direct class-labeled data from $\mathcal{Z}$ and only have access to pairwise supervision---whether a pair of instances $(X,X')$ is from the same class ($Y=Y'$) or from different classes ($Y \neq Y'$). There is a latent variable $Q$ dictating whether the sample is drawn from similar data ($Q=1$) or it is drawn from dissimilar data ($Q=-1$). Let $\mathcal{Z}_Q$ denote the distribution over $(\mathcal{X},Q)$. Further let $\pi=P(Y=+1)$ denote the class prior and $P_+(X)=P(X|Y=+1)$ and $P_-(X)=P(X|Y=-1)$. Now we present the two noise models that reflect what we may expect in real-world data.

\begin{figure}
    \centering
    \includegraphics[width=\linewidth]{Untitled_drawing.png}
    \caption{The two noise models}
    \label{fig:my_label}
\end{figure}

\subsection{Noise Model 1 : Pairing Corruption}
This model is motivated by the following scenario--- imagine non-perfect crowd-workers who are given a pool of instances $X_i$ and annotate pairs $(X_i,X_j)$ as $Q=1$, if they believe $Y_i=Y_j$ and $Q=-1$ otherwise. Since they are non-perfect, they make mistakes in this process and sometimes assigns $Q=-1$ when it should have been $Q=1$ and vice versa. Thus, in this model two samples $(X,Y)$ and $(X',Y')$ are drawn from the underlying distribution $\mathcal{Z}$ and if $Y=Y'$, this pair of sample is classified as Similar ($Q=1$) with probability $1-\rho_S$ and if $Y \neq Y'$ this pair is classified as Dissimilar ($Q=-1$) with probability $1-\rho_D$. In other words, the noise rate for similar (S) and dissimilar (D) data are $\rho_S$ and $\rho_D$ respectively. Thus, under this noise model, each of the S and D samples are drawn from mixtures of the true S and D distributions :  $P(Q=1|Y=Y')=1-\rho_S$ and $P(Q=-1|Y \neq Y')=1-\rho_D$. This noise model is instance-independent but label-dependent (different noise rates for $Q=1$ and $Q=-1$).

\subsection{Noise Model 2: Labeling Corruption}
Consider that we are dealing with a privacy sensitive domain and responders do not want their individual labels sent to the learning module---further, some of them lie about their labels so the labels are noisy. A moderator converts the point-wise data $(X,Y)$ to pairwise data $(X,X',Q= \pm 1)$, to preserve privacy. Mathematically, we first generate two samples $(X,Y)$ and $(X',Y')$ from the underlying distribution $D$ and then the label is flipped with probability $\rho_y$ (this is class conditioned : if a sample originally has label $+1$ it is flipped to label $-1$ with probability $\rho_{+}$ and respectively, $\rho_{-}$ for the other case). $P(\tilde{Y}=+1|Y=-1)=\rho_{-}$ and $P(\tilde{Y}=-1|Y=+1)=\rho_{+}$ Then in the next step the similar or dissimilar labels are assigned (there is assumed to be no noise in this step since the moderator is an expert). Thus, $P(Q=1|\tilde{Y}=\tilde{Y'})=1$ and $P(Q=-1|\tilde{Y} \neq \tilde{Y'})=1$.

If there were no noise corruption, the S data would comprise of two positive instances or two negative instances and the $D$ data would comprise of one positive instance and one negative instance. Accordingly, in the noise-free pairwise data scenario the densities ($P_S(x,x')$,$P_D(x,x')$) of the S and D data are respectively :
\begin{equation} \label{eq1}
\begin{split}
P_S(x,x') & = \frac{\pi^2 P_+(x)P_+(x')+(1-\pi)^2P_-(x)P_-(x')}{\pi^2+(1-\pi)^2},
\\
P_D(x,x') & = \frac{\pi (1-\pi) P_+(x)P_-(x')+\pi(1-\pi)P_-(x)P_+(x')}{2\pi(1-\pi)}.
\end{split}
\end{equation}
Further, one can marginalize out $x'$ and get the densities in terms of a single $x$ being drawn from either $S$ or $D$. This view is important for our analysis and has been previously used in \cite{bao2018classification}. The implication is that we can now treat the S-D data as point-wise data from the Similar (S) and Dissimilar (D) classes.
\begin{equation} \label{eq2}
\begin{split}
P_S(x) & = \frac{\pi^2 P_+(x)+(1-\pi)^2P_-(x)}{\pi^2+(1-\pi)^2},
\\
P_D(x) & = \frac{ P_+(x)+P_-(x)}{2}.
\end{split}
\end{equation}
The above expressions are derived in \cite{bao2018classification} under the noise-free assumption. Here we present the expression for the densities ($\tilde{P}_S(x)$---similar expressions can be obtained for $\tilde{P}_D(x)$)  under each of the noise models presented above. For the pairing corruption model we get :
\begin{equation} \label{eq2}
\tilde{P}_S(x) = (1-\rho_S)P_S(x) + \rho_DP_D(x) ,
\end{equation}
and for the labeling corruption model we get, $\tilde{P}_S(x)$
\begin{equation} \label{eq2}
\begin{split}
& = \frac{(\pi(1-\rho_{+})P_+(x)+(1-\pi)\rho_{-}P_-(x)) \Tilde{\pi}}{\Tilde{\pi}^2+(1-\Tilde{\pi})^2},
\\
& +\frac{((1-\pi)(1-\rho_{-})P_-(x)+\pi\rho_{+}P_+(x))(1-\Tilde{\pi})} {\Tilde{\pi}^2+(1-\Tilde{\pi})^2},
\\
& \text{where} \quad \Tilde{\pi}=(\pi(1-\rho_{+})+(1-\pi)\rho_{-}).
\end{split}
\end{equation}

\begin{figure*}[!h]
    \centering
\begin{subfigure}{0.18\textwidth}
  \includegraphics[width=\linewidth]{synth_train.png}
  \caption{Underlying P-N distribution $D$}
  \label{fig:1}
\end{subfigure}\hfil
\begin{subfigure}{0.18\textwidth}
  \includegraphics[width=\linewidth]{synth1.png}
  \caption{Test Set of $3000$ points}
  \label{fig:2}
\end{subfigure}\hfil
\begin{subfigure}{0.18\textwidth}
  \includegraphics[width=\linewidth]{synth2.png}
  \caption{S and D points ($20,000$) }
  \label{fig:3}
\end{subfigure}
\begin{subfigure}{0.18\textwidth}
  \includegraphics[width=\linewidth]{synth3.png}
  \caption{Weighted Classification: $99.8\%$ accuracy}
  \label{fig:2}
\end{subfigure}\hfil
\begin{subfigure}{0.18\textwidth}
  \includegraphics[width=\linewidth]{synth4.png}
  \caption{Loss Correction: $99.8\%$ accuracy}
  \label{fig:3}
\end{subfigure}
\medskip
\begin{subfigure}{0.15\textwidth}
  \includegraphics[width=\linewidth]{synth_04_noisy_sd.png}
  \caption{noisy S-D data (Pairing Noise)}
  \label{fig:4}
\end{subfigure}\hfil
\begin{subfigure}{0.15\textwidth}
  \includegraphics[width=\linewidth]{synth_noisy4_sd_weighted.png}
  \caption{Weighted Classification: $99.73\%$ accuracy}
  \label{fig:5}
\end{subfigure}\hfil
\begin{subfigure}{0.15\textwidth}
  \includegraphics[width=\linewidth]{synth_noisy4_losscorr.png}
  \caption{Loss Correction: $99.73\%$ accuracy}
  \label{fig:6}
\end{subfigure}\hfil
\begin{subfigure}{0.15\textwidth}
  \includegraphics[width=\linewidth]{noisyn_pn_04.png}
  \caption{noisy S-D data (Labeling Noise)}
  \label{fig:5}
\end{subfigure}\hfil
\begin{subfigure}{0.15\textwidth}
  \includegraphics[width=\linewidth]{noisyn_pn_04_weight.png}
  \caption{Weighted Classification: $99.67\%$ accuracy}
  \label{fig:6}
\end{subfigure}\hfil
\begin{subfigure}{0.15\textwidth}
  \includegraphics[width=\linewidth]{noisy_pn_04_loss_corr.png}
  \caption{Loss Correction: $99.67\%$ accuracy}
  \label{fig:4}
\end{subfigure}

\caption{In this figure, we depict the underlying distribution with $\pi=0.2$ and the corresponding S and D data. The top row shows the test data accuracy of our proposed algorithms trained on the clean S-D training data. The bottom row shows the test data accuracy for the same test data but now training is done on noisy S-D data for each noise model with a high degree of noise (noise parameter set at $0.4$). We see that the proposed approaches perform well even under severe noise corruption.}
\label{fig:images}
\end{figure*}

\begin{table*}[t]
\centering
\caption{\textsc{Pairing Noise} : The best P-N column denotes the test accuracy after training on the standard class-labeled train dataset provided. $\protect d,\pi,N$ denote the feature dimension, class prior and the size of the entire class-labeled data respectively. clean S-D denotes test accuracy after training on clean S-D data generated from the train dataset. T-Loss indicates the test accuracy after training on S-D data with the loss correction approach (by the matrix $\protect T$) and SD-Loss denotes the non-corrected variant of \protect \cite{shimada2019classification}. Similarly, weighted and unweighted denotes the test accuracy after training on S-D data using weighted ERM and normal ERM respectively---note, they are identical for symmetric noise. KM denotes the KMeans baseline and KM-COP is the KMeans with constraints. Accuracies within $\protect 1\%$ of the best in each row are bolded. }\smallskip

\begin{tabular}{l|l|l|l|l|l|l|l|l|l}
\makecell{Dataset \\ $(d,\pi)$ \\ $N$} &
best P-N &
clean S-D &
\makecell{Noise Rates \\ $(\rho_S,\rho_D)$} &
T-Loss &
SD-Loss &
Weighted &
Unweighted &
KM &
KM-COP  \\
\hline
\makecell{\textsc{diabetes} \\ (8,0.35)\\ 768 } &
\makecell{77} &
\makecell{77} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{\textbf{76.57} \\ 74.95 \\ \textbf{75.52}} &
\makecell{75 \\ 75.52 \\ 73.95} &
\makecell{74.95 \\ \textbf{77.61} \\ 74.48} &
\makecell{74.95 \\ 76.04 \\ 74.48} &
\makecell{65.63}   &
\makecell{64.58 \\ 65.10 \\ 64.06} \\
\hline
\makecell{\textsc{adult} \\ (106,0.24)\\ 48842 } &
\makecell{83.09} &
\makecell{83.03} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{\textbf{82.49} \\ 77.8 \\ \textbf{81.42}} &
\makecell{\textbf{82.22} \\ 76.26 \\ 80.26} &
\makecell{\textbf{82.35} \\ \textbf{82.41} \\ \textbf{81.10}} &
\makecell{\textbf{82.35} \\ 75.92 \\ \textbf{81.10}} &
\makecell{71.25}   &
\makecell{71.25 \\ 71.25 \\ 53.14} \\

\hline
\makecell{\textsc{cancer} \\ (30,0.37) \\569 } &
\makecell{97.2} &
\makecell{97.2} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{\textbf{97.18} \\ \textbf{97.18} \\ \textbf{97.18}} &
\makecell{\textbf{96.47} \\ \textbf{97.18} \\ 95.07} &
\makecell{95.78 \\ 95.78 \\ 95.78} &
\makecell{95.78 \\ 95.78 \\ 95.78} &
\makecell{88.7}  &
\makecell{92.95 \\ 91.54 \\ 92.25} \\

\hline

\iffalse

\makecell{\textsc{ionosphere} \\ (34,0.64)} &
\makecell{90.91} &
\makecell{90.91} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{90.9 \\ 86.36 \\ 88.63} &
\makecell{85.22 \\ 86.36 \\ 84.09} &
\makecell{89.77 \\ 89.82 \\ 86.36} &
\makecell{89.77 \\ 85.24 \\ 86.36} &
\makecell{70.45}   &
\makecell{71.59 \\ 71.59 \\ 71.59} \\

\hline
\makecell{\textsc{spambase} \\ (57,0.39)} &
\makecell{91.83} &
\makecell{89.74} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{87.56 \\ 83.74 \\ 85.304} &
\makecell{83.22 \\ 84.15 \\ 75.65} &
\makecell{82.78 \\ 86.78 \\ 78.44} &
\makecell{82.78 \\ 85.56 \\ 78.44} &
\makecell{78.08}   &
\makecell{78.61 \\ 77.83 \\ 77.73} \\
\hline

\makecell{\textsc{magic} \\ (10,0.65)} &
\makecell{84.12} &
\makecell{83.40} &
\makecell{$(0.2,0.2)$ \\ $(0.2,0.1)$ \\ $(0.3,0.3)$ } &
\makecell{80.06 \\ 73.27 \\ 79.39} &
\makecell{81.13 \\ 73.61 \\ 78.42} &
\makecell{82.21 \\ 81.67 \\ 79.50} &
\makecell{82.21 \\ 79.70 \\ 79.50} &
\makecell{59.09}  &
\makecell{63.22 \\ 68.03 \\ 59.67} \\
\hline

\fi
\end{tabular}
\label{table1}
\end{table*}

\begin{table*}
\centering
\caption{\textsc{Labeling Noise}: The setup is same as Table \ref{table1} but now we use the labeling corruption noise model to generate the noisy S-D data.}

\begin{tabular}{l|l|l|l|l|l|l|l|l|l}
\makecell{Dataset \\ $(d,\pi)$\\ $N$ } &
best P-N  &
clean S-D &
\makecell{Noise Rates \\ $(\rho_+,\rho_-)$} &
T-Loss &
SD-Loss &
Weighted &
Unweighted &
KM &
KM-COP  \\
\hline

\iffalse

\makecell{\textsc{diabetes} \\ (8,0.35) } &
\makecell{77} &
\makecell{77} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{69.79 \\ 71.89 \\ 65.11} &
\makecell{65.10 \\ 72.91 \\ 65.11} &
\makecell{71.88 \\ 73.96 \\ 64.59} &
\makecell{71.88 \\ 73.43 \\ 64.59} &
\makecell{65.63}  &
\makecell{65.10 \\ 64.58 \\ 64.58} \\

\hline
\makecell{\textsc{adult} \\ (106,0.24) } &
\makecell{83.09} &
\makecell{83.03} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{80.4 \\ 82.06 \\ 76.10} &
\makecell{79.05 \\ 81.9 \\ 75.2} &
\makecell{79.5 \\ 82.5 \\ 73.8} &
\makecell{79.5 \\ 81.8 \\ 73.8} &
\makecell{71.25}   &
\makecell{53.14 \\ 53.14 \\ 53.06} \\
\hline
\makecell{\textsc{cancer} \\ (30,0.37) } &
\makecell{97.2} &
\makecell{97.2} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{96.48 \\ 97.88 \\ 95.07} &
\makecell{95.77 \\ 90.14 \\ 93.66} &
\makecell{92.95 \\ 97.18 \\ 92.95} &
\makecell{92.95 \\ 92.95 \\ 92.95} &
\makecell{88.7}  &
\makecell{90.85 \\ 90.14 \\ 90.85} \\

\fi

\makecell{\textsc{ionosphere} \\ (34,0.64)\\351} &
\makecell{90.91} &
\makecell{90.91} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{\textbf{88.67} \\ 85.24 \\ 87.5} &
\makecell{85.23 \\ 80.68 \\ 80.7} &
\makecell{86.4 \\ \textbf{90.91} \\ \textbf{88.64}} &
\makecell{86.4 \\ 85.23 \\ \textbf{88.64}} &
\makecell{70.45}  &
\makecell{71.59 \\ 71.59 \\ 71.59} \\

\hline
\makecell{\textsc{spambase} \\ (57,0.39)\\4601} &
\makecell{91.83} &
\makecell{89.74} &
\makecell{$(0.2,0.2)$ \\ $(0.1,0.2)$ \\ $(0.3,0.3)$ } &
\makecell{\textbf{87.56} \\ 83.74 \\ \textbf{85.304}} &
\makecell{83.22 \\ 84.15 \\ 75.65} &
\makecell{82.78 \\ \textbf{86.78} \\ 78.44} &
\makecell{82.78 \\ 85.56 \\ 78.44} &
\makecell{78.08} &
\makecell{78.96 \\ 79.13 \\78.61} \\
\hline

\makecell{\textsc{magic} \\ (10,0.65)\\19020} &
\makecell{84.12} &
\makecell{83.40} &
\makecell{$(0.2,0.2)$ \\ $(0.2,0.1)$ \\ $(0.3,0.3)$ } &
\makecell{80.06 \\ 73.27 \\ \textbf{79.39}} &
\makecell{81.13 \\ 73.61 \\ 78.42} &
\makecell{\textbf{82.21} \\ \textbf{81.67} \\ \textbf{79.50}} &
\makecell{\textbf{82.21} \\ 79.70 \\ \textbf{79.50}} &
\makecell{59.09} &
\makecell{63.28 \\ 66.03 \\ 62.34} \\
\hline
\end{tabular}

\label{table2}
\end{table*}

\section{Loss Correction Approach}
In this section, we present the first of our two proposed algorithms for learning from noisy pairwise data. In this method, we use the parameter values of the noise model to obtain an unbiased estimate of the loss function. In other words, we cast the loss of learning from noisy S-D data in terms of learning from standard class-labeled data and thus, we can do loss correction. In deriving the following expressions, we methodically account for all the different ways we can derive an S (or D instance) under each noise model (Figure \ref{fig:my_label}).
For the pairing noise model we obtain :
\begin{equation}
\label{pos1}
\begin{split}
P(Q=1|X) & = P(Y=1|X)[(1-\rho_S)\pi+\rho_D(1-\pi)] \\
    & +P(Y=-1|X)[\rho_D \pi+(1-\rho_S)(1-\pi)].
\end{split}
\end{equation}
On the other hand, for the labeling corruption noise model we obtain $ $:
\begin{equation}
\label{pos2}
\begin{split}
 P(Q=1|X) & =  P(Y=1|X)  [(1-\rho_+)\Tilde{\pi} + \rho_-(1-\Tilde{\pi})] \\
    & + P(Y=-1|X)[\rho_-\Tilde{\pi}+(1-\rho_+)(1-\Tilde{\pi})].
\end{split}
\end{equation}
We obtain similar equations for $P(Q=-1|X)$ under each noise model. It is noteworthy that the structure of the posterior probabilities is remarkably similar between the two noise models once we introduce the modified prior $\tilde{\pi}$, defined in \eqref{eq2}. In other words, the labeling noise model can be interpreted as first corrupting the ordinary class-labeled P (Positive)-N (Negative) data to get a noisy P-N data with the modified class prior and then mimicking the pairing noise model with noise rate $\rho_+,\rho_-$. Once we have expressed the posterior probabilities of the noisy S-D data in terms of the original class posteriors, we can adopt the technique of backward correction \cite{patrini2017making} to construct the corrected losses ---
Assume there exists coefficients $\alpha_1,\alpha_2,\beta_1,\beta_2$ such that $P(Q=1|x)= \alpha_1 P(y=1|x) + \alpha_2 P(y=-1|x)$ and   $P(Q=-1|x)= \beta_1 P(y=1|x) + \beta_2 P(y=-1|x)$, we can construct a new loss function such that the minimizer of the expected risk with this new loss function over the noisy S-D data is the same as the minimizer of the expected risk with the original loss function over $\mathcal{Z}$ (the test distribution). Let $l(t,y)$ be a loss function estimating $t$ by $y$ and let $\tilde{l} (t, Q)$ be the corresponding back-ward corrected loss function estimating $t$ by $Q$. Then we have $l(t,y)=T \tilde{l}(t,Q)$  where
$T=
\begin{bmatrix}
\alpha_1 & \alpha_2 \\
\beta_1 & \beta_2
\end{bmatrix}
$
and therefore, $\tilde{l}(t,Q)=T^{-1}l(t,y)$. We can use the modified loss to train our classifier $f \in F$(model class) on the noisy S-D data directly by ERM. Next, we state the generalization bounds for this approach. Here are some important notations:
\begin{itemize}

    \item
    $\hat{R}_{\tilde{l}}(f)=\frac{1}{n}\sum_{i=1}^n \tilde{l}(f(X_i),Q_i)$,
    \item
    $ \hat{f} = \mathrm{argmin}_{f \in F} \hat{R}_{\tilde{l}}(f)$,
    \item
    $R_{\tilde{l},\mathcal{Z}_Q}(f)=E_{(X,Q) \sim \mathcal{Z}_Q}[\tilde{l}(f(X),Q)]$,
    \item
    $R_{l,\mathcal{Z}}(f)=E_{(X,Y) \sim \mathcal{Z}}[l(f(X),Y)]$.
\end{itemize}

Because $\tilde{l}$ is corrected appropriately, the empirical estimate of the risk converges to $R_{l,\mathcal{Z}}(f)$---by performing ERM on the noisy S-D data, the empirical risk converges to the true risk on the standard P-N data drawn from the underlying distribution $\mathcal{Z}$. Let $L_Q$ denote the Lipschitz constant of the loss $\tilde{l}$, $\mathcal{R}(F,N)$ denote the Rademacher complexity of the function class $F$ for $n$ noisy S-D instances.
\\
\textbf{Lemma 1} : With probability at least $1-\delta$,
\begin{equation}
    \max_{f \in F} |\hat{R}_{\tilde{l}}(f)-R_{\tilde{l},\mathcal{Z}_Q}(f)| \leq 2L_Q \mathcal{R}(F,n)+ \sqrt{\frac{\log(1/\delta)}{2n}}.
\end{equation}
\\
\textbf{Theorem 1} : With probability at least $1-\delta$,
\begin{equation}
R_{l,\mathcal{Z}}(\hat{f}) \leq \min_{f \in F} R_{l,\mathcal{Z}}(f)+4L_Q \mathcal{R}(F,n)+2\sqrt{\frac{\log(1/\delta)}{2n}}.
\end{equation}

 \textbf{Special Case of Clean S-D Learning} : When there is no noise $\rho_S$ = $\rho_D$ = $0$ or $\rho_+$ = $\rho_-$ = $0$, for both the noise models,
\begin{equation}
\begin{split}
T =
\begin{bmatrix}
\pi & 1-\pi \\
1-\pi & \pi
\end{bmatrix} &
\implies T^{-1} =
\begin{bmatrix}
\frac{\pi}{(2\pi-1)} & \frac{-(1-\pi)}{(2\pi-1)} \\
\frac{-(1-\pi)}{(2\pi-1)} & \frac{\pi}{(2\pi-1)}
\end{bmatrix}
\end{split}
.
\end{equation}
We see this matches the loss function derived for clean S-D learning in \cite{shimada2019classification} (on setting $X'$ as $X$ and replacing $\pi_S E_{X_S}[1] = \pi_D E_{X_D}[1] = \frac{1}{n}$) :
\begin{equation}
\begin{split}
&\hat{R}_{\tilde{l}}(f) =\frac{1}{n} \sum_{i=1}^n [\mathcal{L}(f(X_i),Q_i)], \\
   \mathrm{where \quad} &\mathcal{L}(z,t)=\frac{\pi}{2\pi-1}l(z,t)-\frac{1-\pi}{2\pi-1}l(z,-t).
\end{split}
\end{equation}
Our analysis through the lens of loss correction helps provide the generalization bound for clean S-D learning as a special case of noisy S-D learning.
The Lipschitz constant for the corrected loss in the clean S-D case is $L_Q = \frac{L}{|2\pi-1|}$, where $L$ is the Lipschitz constant for $l$. The generalization bound for noise-free S-D learning is : With probability at least $1-\delta$,
\begin{equation}
R_{l,\mathcal{Z}}(\hat{f}) \leq \min_{f \in F} R_{l,\mathcal{Z}}(f)+\frac{4L}{|2\pi-1|} \mathcal{R}(F,n)+2\sqrt{\frac{\log(1/\delta)}{2n}}.
\end{equation}
\\
\textbf{Optimization} : While we have a generalization guarantee, efficient optimization is a concern especially because the corrected loss $\tilde{l}(\cdot,\cdot)$ may not be convex. We present a condition which will guarantee the corrected loss to be convex.
\\
\textbf{Theorem 2} : If $l(t,y)$ is convex and twice differentiable almost everywhere in $t$ (for each $y$) and also satisfies :
\begin{itemize}
    \item
$\forall t \in Q, \quad l''(t,y)=l''(t,-y)$,
\item
$\mathrm{sign}(\alpha_1-\beta_1)=\mathrm{sign}(\beta_2-\alpha_2)$, where $\alpha_1,\alpha_2,\beta_1,\beta_2$ are elements of $T$.
\end{itemize}
then $\tilde{l}(t,y)$ is convex in $t$.
The first condition is satisfied by several common losses such as squared loss ($l(y,t)=(1-ty)^2$) and logistic loss ($l(t,y)=\log(1+\exp(-ty))$).
The second condition depends on the noise rates and the prior. We can simplify this for each noise model to :
\begin{equation}
\begin{split}
\frac{1-2\rho_S}{1-2\rho_D} & \in \left[\frac{1-\pi}{\pi}, \frac{\pi}{1-\pi}\right] \mathrm{\quad or  \quad} \left[\frac{\pi}{1-\pi}, \frac{1-\pi}{\pi}\right],
\\
    \frac{1-2\rho_+}{1-2\rho_-} & \in \left[\frac{1-\Tilde{\pi}}{\Tilde{\pi}}, \frac{\Tilde{\pi}}{1-\Tilde{\pi}}\right] \mathrm{\quad or  \quad} \left[\frac{\Tilde{\pi}}{1-\Tilde{\pi}},\frac{1-\Tilde{\pi}}{\Tilde{\pi}}\right].
    \end{split}
\end{equation}
where either the first bound or the second bound applies depending on whether the class prior is greater or less than $0.5$ respectively. For all cases of noise-free or symmetric-noise S-D learning, any noise rates will satisfy this condition and thus, we can always perform efficient optimization.

\begin{figure*}
    \centering
\begin{subfigure}{0.23\textwidth}
  \includegraphics[width=\linewidth]{ban1.png}

  \label{fig:1}
\end{subfigure}\hfil
\begin{subfigure}{0.23\textwidth}
  \includegraphics[width=\linewidth]{ban2.png}

  \label{fig:2}
\end{subfigure}\hfil
\begin{subfigure}{0.23\textwidth}
  \includegraphics[width=\linewidth]{ban3.png}

  \label{fig:3}
\end{subfigure}
\begin{subfigure}{0.23\textwidth}
  \includegraphics[width=\linewidth]{ban4.png}

  \label{fig:2}
\end{subfigure}\hfil

\caption{The first two images depict the gradual decrease in classification accuracy of the learned classifier (from either algorithm) on the test dataset as the noise rate in the noisy S-D training data increases, for each noise model. The last two images depict the gradual increase in classification accuracy of the learned classifier (from the weighted classification method) on the test dataset as the number of noisy S-D training samples increases, for different noise rates in each noise model. The accuracy achieved from training on clean P-N training data provided by the banana dataset is $90.8\%$ }
\label{fig:imagesb}
\end{figure*}

\section{Weighted Classification Approach}
Now we develop our second algorithm for dealing with noisy S and D data. One key issue that we investigate here is how the Bayes classifier learned from noisy S-D data relates to the traditional Bayes classifier. \\
\textbf{Lemma 2} : Denoting $P(Q=1|x) = \eta_Q(x)$ and $P(Y=1|x)= \eta(x)$, the Bayes classifier under the noisy S-D distribution denoted by $\Tilde{f}^* = \mathrm{argmin}_{f \in F} E_{(X,Q) \sim \mathcal{Z}_Q}[{1}_{\lbrace \mathrm{sign}(f(X))\neq Q \rbrace }]$ is given by
\begin{equation}
\label{fin}
\tilde{f}^*(x)=\mathrm{sign}\left(\eta_Q(x)-\frac{1}{2}\right)=\mathrm{sign}\left(\eta(x)-T\right)
\end{equation}
For the pairwise corruption case,
$$
T= \frac{\frac{1}{2}-[(1-\rho_S)(1-\pi)+\rho_D\pi]}{(1-\rho_S-\rho_D)(2\pi-1)}.
$$
For the label corruption case, threshold $T$ is :
$$
\frac{\frac{1}{2}-\pi(\rho_{+}+\rho_{-}-\rho_{+}\rho_{-})-(1-\pi)(\rho_{+}^2+(1-\rho_{-})^2)}{(1-\rho_{+}-\rho_{-})[\pi(1-2\rho_{+})-(1-\pi)(1-2\rho_{-})]}.
$$
These expressions can be derived by using \eqref{pos1} and \eqref{pos2} in \eqref{fin}.
They give us an important insight---the Bayes classifier for the noisy S-D learning uses a different threshold from $\frac{1}{2}$ while the traditional Bayes classifier has $\eta(x)$ thresholded at $\frac{1}{2}$. Towards designing an algorithm we note that we can also obtain this Bayes classifier by minimizing the weighted 0-1 risk. Let
$$
U_\alpha(t,y)=(1-\alpha)1_{\lbrace y=1 \rbrace }1_{\lbrace t \leq 0 \rbrace}+\alpha1_{\lbrace y=-1 \rbrace}1_{\lbrace t > 0 \rbrace}.
$$
The following lemma from \cite{scott2012calibrated} is crucial in connecting the Bayes classifier threshold with the weight in weighted 0-1 classification.
\\
\textbf{Lemma 3} : Denote the $U_\alpha$ risk under distribution $\mathcal{Z}$ as
$$
R_{\alpha,D}(f)=E_{(x,y) \sim \mathcal{Z}}[U_\alpha(f(x),y)].
$$
Then $f^*_\alpha(x)=\mathrm{sign}(\eta(x)-\alpha)$ minimizes $R_{\alpha,\mathcal{Z}}(f)$.\\

We now show that there exists a choice of weight $\alpha$ such that the weighted risk under the noisy S-D distribution is linearly related to the ordinary risk under distribution $\mathcal{Z}$. \\

\textbf{Theorem 3} : There exist constants $\alpha$ and $A$ and a function $B(X)$ (that only depends on $X$ but not on $f$) such that
$$
R_{\alpha,\mathcal{Z}_Q}(f)=A R_{\mathcal{Z}}(f)+E_X[B(X)].
$$
For the pairing corruption case:
\begin{equation}
\begin{split}
    \alpha & =\frac{1-\rho_S+\rho_D}{2},
    \\
    A & =\frac{1-\rho_S-\rho_D}{2}(2\pi-1).
    \end{split}
\end{equation}

For the label corruption case :
\begin{equation}
\begin{split}
    \alpha & =\pi(1-\rho_{+}+\rho_{+}^2-\rho_{+}\rho_{-})
-\frac{1}{2}(1-\rho_{+}-\rho_{-}) \\
    & +(1-\pi)(1-\rho_{-}+\rho_{-}^2-\rho_{+}\rho_{-}),
    \\
    A & =\frac{(1-\rho_{+}-\rho_{-})}{2}[\pi(1-2\rho_{+})-(1-\pi)(1-2\rho_{-})].
    \end{split}
\end{equation}
\textbf{Remark 1}: The $\alpha$-weighted Bayes optimal classifier under the noisy S-D distribution coincides with the Bayes classifier of the 0-1 loss under the clean ordinary distribution.
\\
\textbf{Generalization Bound} : For the ease of optimization, we will use a surrogate loss instead of 0-1 to do weighted ERM. Any surrogate loss can be used as long as it can be decomposed as $l(t,Q)=1_{\lbrace Q=1 \rbrace}l_1(t)+1_{\lbrace Q=-1 \rbrace}l_{-1}(t)$. The square, hinge, logistic and most common losses can be expressed in this form.
Let $\hat{f}_\alpha$ denote the minimizer of the empirical risk using the weighted surrogate loss.
\begin{equation}
    \hat{f}_\alpha = \mathrm{argmin}_{f \in F} \frac{1}{n} \sum_{i=1}^n l_\alpha(f(x),Q).
\end{equation}
\textbf{Theorem}: If $l_\alpha$ is an $\alpha$-weighted margin loss of the form : $l_\alpha(t,Q)=(1-\alpha)1_{\lbrace Q=-1 \rbrace}l(t)+\alpha1_{\lbrace Q=1 \rbrace}l(-t)$ and $l$ is classification calibrated and $L$-Lipschitz, then for the above choices of $\alpha$ and $A$, there exists a non-decreasing function $\xi_{l_{\alpha}}$ with $\xi_{l_{\alpha}}(0)=0$ such that the following bound holds with probability at least $1-\delta$:
\begin{equation}
\begin{split}
R_{\mathcal{Z}}(\hat{f}_{\alpha}) -R^* \leq
A^{-1} \xi_{l_{\alpha}}\bigg(\min_{f \in F} R_{\alpha,\mathcal{Z}_Q}(f)-
\\
\min_{f} R_{\alpha,\mathcal{Z}_Q}(f)+4L \mathcal{R}(F,n)+2\sqrt{\frac{\log(1/\delta)}{2n}} )\bigg).
\end{split}
\end{equation}
where $R^*$ denotes the the corresponding Bayes risk under $\mathcal{Z}$.\\
\textbf{Remark 2}: For a fixed Lipschitz constant $L$, as $A$ decreases we get a weaker generalization bound. For the pairing noise model, its easy to see that as noise rates increase, $A$ decreases but the relationship is more complicated for the labeling noise model. When the noise is symmetric ($\rho_+=\rho_-=\rho$), $A=\frac{(1-2\rho)^2(2\pi-1)}{2}$. In this case, again we observe as $\rho$ increases, $A$ decreases and we get a weaker bound.
\\
\textbf{Remark 3}: When $\rho_S=\rho_D$ or $\rho_+=\rho_-$, we see that the optimal Bayes classifier for the (noisy) S-D learning problem is the same as the Bayes classifier for the standard class-labeled binary classification task under distribution $\mathcal{Z}$. \\
\iffalse
 Under both noise models we observe that $A = \frac{2\pi-1}{2}$ when there is no noise and accordingly we establish a generalization bound for S-D learning in the noise free case as :
\begin{equation}
\begin{split}
R_D(\hat{f}_{0.5}) -R^* \leq
\frac{2}{2\pi-1}\xi_{l_{0.5}}(\min_{f \in F} R_{0.5,\mathcal{Z}_Q}(f)-
\\
\min_{f} R_{0.5,\mathcal{Z}_Q}(f)+4L \mathcal{R}(F,n)+2\sqrt{\frac{\log(1/\delta)}{2n}}).
\end{split}
\end{equation}
\fi
\section{Estimation of Prior and Noise Parameters}
We briefly discuss the parameters we need to know or estimate to apply each method for each noise model.\\
\textbf{Loss Correction approach}: The noise rate parameters can be tuned by cross-validation on the noisy S-D data.
We also need to estimate the class prior to construct the loss correction matrix $T$, under both noise models. The class prior can be estimated as follows :
\begin{itemize}
    \item For the pairing corruption noise model : \\
$\frac{n_S}{n_D}=\frac{(1-\rho_S)(\pi^2+(1-\pi)^2)+2\rho_D\pi(1-\pi)}{\rho_S(\pi^2+(1-\pi)^2)+2(1-\rho_D)\pi(1-\pi)}$

\item For the labeling corruption noise model : \\
$\frac{n_S}{n_D}=\frac{(1-\rho_+)(\pi\Tilde{\pi}+(1-\pi)(1-\Tilde{\pi}))+\rho_-(\pi(1-\Tilde{\pi})+\Tilde{\pi}(1-\pi))}{\rho_+(\pi\Tilde{\pi}+(1-\pi)(1-\Tilde{\pi}))+(1-\rho_-)(\pi(1-\Tilde{\pi})+\Tilde{\pi}(1-\pi))}$
\end{itemize}
From each of the above equations we can solve for the class prior $\pi$. The above equations can be derived from \eqref{pos1} and \eqref{pos2} by marginalizing out $X$ and using $\frac{n_S}{n_D}=\frac{P(Q=1)}{P(Q=-1)}$.

 \textbf{Method of Weighted Classification}: The class prior only appears in the weight $\alpha$ in the labeling corruption model. In the pairing corruption model, knowledge of the class prior is not needed to calculate $\alpha$. However, since we just have one parameter $\alpha$ for the optimization problem, in practice we obtain $\alpha$ directly by cross-validation under both noise models.

\section{Experiments}
We empirically verify that the proposed algorithms is able to learn a classifier for the underlying distribution $\mathcal{Z}$ from only noisy similar and dissimilar training data.
All experiments are repeated $3$ times on random train-test splits of $75$:$25$ and the average accuracies are shown.
We conduct experiments on two noise models independently.
In the learning phase, the noise parameters and the weight $\alpha$ is tuned by cross-validation.
Evaluation is done on the clean class-labeled test dataset using standard classification accuracy as evaluation metric which is averaged over the test datasets to reduce variance across the corruption in the training data.
We use a multi-layer perceptron (MLP) with two hidden layers of $100$ neurons, ReLU activation and a single logistic sigmoid output, as our model architecture for all our experiments except the synthetic generated data, where we use a logistic linear model. We use the squared loss throughout : $l(t,y)=(t-y)^2$ and use Stochastic Gradient Descent (SGD) with a learning rate of $0.001$ and momentum of $0.9$.

\subsection{Synthetic Data}

We generate a two-dimensional dataset of points sampled from a normal distribution $N((2,2), \mathcal{I}_2)$ as one class and  $N((-2,-2), \mathcal{I}_2)$ as the other.
Here $\mathcal{I}_2$ denotes the two-dimensional identity matrix indicating that they are isotropic.
Note that the dataset generated in this manner may be non-separable.
In Figure~\ref{fig:images}, we show the data distribution, the test data, the noisy S-D data and the performance of the classifier learned from the noisy S-D data on the test data.

We use a non-separable benchmark ``banana'' dataset which has two-dimensional attributes and two classes. We perform two kinds of experiments. In the first experiment, for a given noise model, for different settings of symmetric noise parameters ($\rho_S=\rho_D$ and $\rho_+=\rho_-$) we plot the variation of clean test accuracy with the number of noisy S-D pairs ($n$) sampled for training.
For this experiment setting, we show the results for the weighted classification algorithm in Figure \ref{fig:imagesb}.
Since the Bayes classifier under the symmetric noise is identical to that of noise-free case under both the noise models,
we see that the accuracy improves as we get a better approximation of the Bayes classifier as we have more and more S-D data-points in training.
Note that the number of original training points in the dataset is fixed---what changes is only the number of S-D points we sample from them.
In the second experiment, for each noise model, for a fixed $n$ we show the gradual degradation of performance of the proposed algorithms (loss correction approach as well as the weighted classification approach) with increasing symmetric noise rates.
These experiments confirm that higher noise hurts classification accuracy and having more pairwise samples help it.

\subsection{Real World datasets}
We further conduct experiments on several benchmark datasets from the UCI classification tasks.\footnote{Available at \url{https://archive.ics.uci.edu/ml/datasets.php}.}
All tasks are binary classification tasks of varying dimensions, class priors, and sample sizes.
We compare the performance of our proposed approaches against two kinds of baselines.

 Supervised Baseline : the noise-free versions of the proposed approaches are used, i.e, for loss correction approach we assume clean S-D classification risk formulation~\cite{shimada2019classification} and for weighted classification approach we assume clean S-D case and threshold at $\frac{1}{2}$. This baseline is simple but since there are no existing supervised algorithms that can handle S-D data except \cite{shimada2019classification} and \cite{bao2018classification}, and none for the noisy S-D supervision case, that is the only baseline to compare against that makes use of the whole data and supervision provided.

 Unsupervised Baseline :  We also compare against unsupervised clustering and semi-supervised clustering based methods. For unsupervised clustering, we ignore all pairwise information and apply KMeans~\cite{macqueen1967some} with, number of clusters as $2$, directly on the noisy S-D datapoints and use the obtained clusters to classify the test data. We further use constrained KMeans clustering~\cite{wagstaff2001constrained}, where we treat the S-D pairs as constraints to supervise the clustering of the S-D data pooled together. These two baselines are shown in Tables~\ref{table1} and~\ref{table2}.

\iffalse
We also tried ITML as a baseline, where the S-D pairs are used to regularize the covariance matrix (prior matrix is set as identity and slack parameter $\gamma=1$). The metric learned from ITML is used for KMeans clustering on the test data instead of standard Euclidean distance. However, the results were not significantly different from constrained KMeans and due to lack of space, they are ommited.\\
\fi

 From Tables~\ref{table1} and~\ref{table2}, we observe that for both noise models and for every noise rate, our proposed approaches outperform the baselines. Further, we see that the clean S-D performances match the best P-N performance which empirically verifies the optimal classifiers for learning from noise-free standard P-N and pairwise S-D data coincide .

\section{Conclusion and Future Work}
In this paper we investigated a novel setting---learning from noisy pairwise labels under two different noise models. We showed the connections of this problems to standard class-labeled binary classification, proposed two algorithms and analyzed their generalization bounds. We empirically showed that they outperform supervised and unsupervised baselines. For future work, it is worthwhile to investigate more complicated noise models such as instance-dependent noise~\cite{menon2016learning} in this setting.

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redpajama_set_name: RedPajamaArXiv


Based in a largely rural section of Rockingham County, Eden has nine facilities in the vicinity of the city that provides individuals a collection of care options of which to choose from. Moving around Eden isn't too difficult for anyone who has the ability to move easily and walk without pain. If needed, there are a number of nursing homes and hospitals in the surrounding areas around Eden.
It is also possible to find care facilities that are there to meet health needs. These amenities can be simple things like offering vegetarian meals, letting pet visits, as well as activities within common areas.
While not necessary, when contacting the facilities in these lists it can be helpful to have relevant medical history including any insurance, doctor, and contacts for any questions the facility coordinator might have. This can aid in outlining any special care the individual might need.
Compiling recent surveys the estimated cost for residential care facilities in and around the city can be around $3,200 to $3,800 every month. Neighboring Reidsville averages about $4,600 for long-term care facilities, which costs more than Eden. Residents that can't afford the cost of care may possibly be eligible for financial aid through local and/or federal governments. To get a better idea of averages, look through the cost table below for comparisons to nearby cities.
Arbor Ridge at Eden operates as an independent living facility that provides a number of services and benefits. This facility has devotional services for its residents and has nutritionist approved meals that are served to be sure your loved one gets the nutrition they require. See all Arbor Ridge at Eden reviews.
With eighty-two units, Brookdale Eden operates as an assisted living facility that offers its residents a number of amenities. This facility also offers nutritionist approved meals that are arranged several times a day. See all Brookdale Eden reviews.


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By Jayson MacLean Published on May 1, 2017 Last Updated on May 1, 2017 Filed under: Environment
There are just 500 North Atlantic right whales left, experts say
One of the rarest creatures on Earth has only 500 members of its species left.
The North Atlantic right whale has been hunted to near extinction by humans over the centuries, and now, after a brief window where the population seemed to be on a slow but steady increase, the lack of new births is a troubling sign.
So-called by whalers along the New England coast because they were the "right" whale to kill for oil and baleen, the North Atlantic right whale population has such low numbers that even losing a few every year (fishing net entanglements and ship strikes are two human-caused factors) makes a significant impact.
"The whole story on right whales is very simple arithmetic: How many die and how many are born?" says Charles "Stormy" Mayo, director of right whale ecology at the federally funded Center for Coastal Studies in Provincetown, Massachusetts, to the Associated Press. "The birth rate this year is extraordinarily low. We've only seen four whales born in the North Atlantic. And the mortality rate is up."
The right whale first received protection from commercial hunting in 1935 with the Convention for the Regulation of Whaling, yet since neither the Soviet Union nor Japan were signatories, hunting persisted and its population kept declining. By 1997, there were only an estimated 295 animals left.
Mayo says that although recent efforts to reduce shipping speeds along certain routes in the Atlantic seem to have reduced the number of serious collisions, net entanglements remain a major issue for the right whale. "Eighty percent of the population bears entanglement scars. As we speak, somewhere offshore there's a whale that's dragging gear," says Mayo. "There's some evidence that female right whales, if they've been entangled, are weakened and have a diminished capacity to reproduce. That may help explain the low calving rate."
Every winter, the right whales travel to the warmer waters off the coasts of Georgia and Florida where they give birth. This past winter marked a 17-year low with only three newborn whales spotted. Below-average birth numbers have been observed for the past five years, a noticeable trend, says Clay George, wildlife biologist for the Georgia Department of Natural Resources. "The preliminary data are starting to show the population may be flat or declining," George said. "But considering how the population turned around in the 2000s, I think it's too early to be too doom-and-gloom about it."
Last month, the US government put out new rules for seafood imports which require that suppliers provide proof that their catches were harvested in a way that minimizes harm to marine mammals like whales. For Canadian fisheries, the rules could mean changes to fishing seasons, fishing grounds or investment in different equipment.
For the right whale, the south coasts of Nova Scotia and New Brunswick are part of its summertime habitat, meaning that commercial fishing in those area may be affected by the new US regulations. One recommendation has been to close two fishing grounds to keep fishing gear out of the right whales' path, one around Grand Manan in the Bay of Fundy and the other at Roseway Basin in southwestern Nova Scotia.
"It's these two areas where we are making our recommendations that seem to be the easiest place to achieve significant conservation benefits with little cost to fishermen," says Sean Brillant, a conservation biologist with the Canadian Wildlife Federation in Halifax and co-author of the recommendations, to CBC News
About The Author / Jayson MacLean
Jayson is a writer, researcher and educator with a PhD in political philosophy from the University of Ottawa. His interests range from bioethics and innovations in the health sciences to governance, social justice and the history of ideas.


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Biobest opens bumblebee factory in China
Good news for Chinese vegetable and fruit growers. Soon, they will be able to buy bumblebees for crop pollination from a local production plant. The bumblebees will be produced in Biobest's brand new production facility in Shouguang, in the Shandong province. China is the world's number one tomato producer, with the largest crop area grown under protection. The use of bumblebees in tomato and other crops is very well established in many countries around the globe. Chinese growers however, have only limited access to bumblebees which are all imported from abroad. The import of bumblebees into China is subject to a lot of administrative formalities including quarantine.
Chinese horticulture has a strong need for pollinators. But just like in other parts of the world, natural pollinators have becoming scarce, partly due to the fact that many Chinese growers still rely heavily on the use of chemical pesticides.
In order to provide optimal service to Chinese growers, Biobest has built a brand new production facility for bumblebees on the site of its Shouguang subsidiary. The initiative to start a bumblebee production line in China originated in October 2011 in the framework of a Belgian economic mission to the People's Republic of China, led by Belgium's current King Philip.
"Starting up production in China was not an easy job" Says Kris Fivez, area manager at Biobest. "But finally, all obstacles have been removed. The new production line in Shouguang guarantees that we can deliver a product in line with our international quality standards and with China's strict quarantine requirements. The Chinese grower can count on us for healthy bees that will do a great pollination job."
Biobest is dedicating a lot of attention to the last steps in the start-up of its Chinese bumblebee activities. Kris Fivez, area manager at Biobest: "Our experts in production, but also in sales and technical support are frequently travelling to China to ensure a successful start. We invest a lot also in training our future local employees. The potential of the Chinese market is very large. Just like in other markets, we are convinced that the introduction of bumblebees will contribute significantly to a more selective use of chemical products.
Biobest, headquartered in Westerlo (Belgium), is active worldwide in pollination and biological control. The company was founded in 1987 and has multiple production sites across the globe including in Morocco, Turkey, Argentina, Mexico, Canada and the USA.
For more information, contact kris.fivez@biobest.be.


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JioFiber receives competition from AirtelXStream, ACT, and Tata Sky Broadband in March as the largest ISP index on Netflix in March.
Apr 19, 2021 Megan Nunez
JioFiber stands up to the competition in terms of broadband speed. While JioFiber continues to lead the speed according to the Netflix ISP Index in March 2021, other Internet Service Providers (ISPs) have been added such as AirtelXStream, ACT and Tata Sky Broadband, which also have an average speed of 3.6 Mbps .. JioFIber was at the top of the list. Netflix is a six-month internet service provider and launched a new offering that provides an additional 15 days and 30 days of validity for two-year and one-year broadband plans.
According to the streaming giant, Netflix's ISP Speed Index is a measure of the prime-time Netflix performance of some Internet Service Providers (ISPs) around the world. Netflix also notes that the ISP's speed rating is not a measure of the overall performance of any other service or data that can be transferred over the ISP's network.
Last year, Jio launched fiber optic broadband from 399 rupees after the work-from-home culture became the norm for people across the country. Other ISPs followed suit. AirtelXStream started offering unlimited internet access and also introduced broadband plans from Rs 399. Excitel also offered plans for 399 rupees with a one-year subscription.
Coming back to the Netflix ISP index, JioFiber, Airtel, ACT, Tata Sky Broadband 7 Star Digital, Alliance Broadband, Excitel Broadband, GTPL, Hathway, SPECTRA, Syscon Infoway and YOU Broadband came in second at 3.2Mbps.
One Broadband NXTDIGITAL, a 3Mbps broadband service, ranked third on the Netflix ISP Index, followed by state-owned telecom company Bharat Sanchar Nigam Limited (BSNL), D-Vois and Tikona at 2.8Mbps. MTNL. It was at the bottom of the ISP indicator at 2.4 Mbps.
See also Kate Garraway appeals to GMB viewers to adhere to covid guidelines to save Christmas
In the Medium-Sized Countries Index, India ranked second in the list with a rate of 3.2 Mbit / s, after Argentina, Austria, Bolivia, Brazil, Chile, France, Greece, Italy, Paraguay, Poland, Taiwan, Trinidad and Tobago and Uruguay. .
The following countries are ranked first with an average speed of 3.4 Mbps: Australia, Belgium, Canada, Denmark, Finland, Germany, Hong Kong, Hungary, Iceland, Ireland, Israel, Luxembourg, Malaysia, Netherlands, New Zealand, Norway, Panama, Portugal , Romania, Singapore, South Korea, Spain, Sweden, Switzerland, Thailand, UK, the United States.
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