Many first-time investors who want to buy property assume their price range is limited to the amount of cash they own. Obtaining a buy to let mortgage allows you to expand your portfolio faster than buying with cash and can give you a much higher return on your investment.
In this article, we will discuss just what mortgages are, the process of getting one and just how they can help you build your own property portfolio.
A mortgage is a loan you can borrow from various lenders, most notably a bank, that you put towards buying a property. Many people use this to buy properties for themselves to live in, but others utilise buy to let mortgages to buy properties in order to rent out.
Typically, the maximum amount you can borrow from a lender towards a BTL property is 75% of the purchase price. This is paid back by the buyer in instalments over the mortgage term, which can be anything from 10-30 years. The property you've bought can be sold before then- it just means you have to pay off the mortgage you obtained sooner rather than later.
What can I use a mortgage for?
Habitable – so there's a kitchen and bathroom, and somebody could live there in its present state.
Every lender will have their own criteria as to what they will and won't lend on. Some will only consider properties in certain areas for example, whereas others are more open minded. Most will pay attention though should your property meet the requirements above.
There are two main types of mortgages available on a Buy to Let property- interest only or repayment.
As the name suggests, interest only mortgages mean you only pay off interest on the money you've borrowed each month. You will owe the full amount by the end of the mortgage term.
Repayment mortgages require you to pay off a portion of the mortgage as well as interest every month. The idea is that by the end of the mortgage term you will own your property 100% after having fully paid off what you've borrowed.
We feel that interest only mortgages are more practical when purchasing a Buy to Let property. A repayment mortgage requires you to pay more off every month which can heavily impact your rental returns on your property to the point where it's hardly worth it. An interest only mortgage means you can pay off less- bear in mind also you are free to sell the property before the mortgage term expires on an interest only meaning you can pay it off easily (providing you at least get your money back at resell value).
What is required for a mortgage?
This type of borrower clearly has some degree of experience (without being over-extended), has a steady source of income elsewhere to service the debt, and has a track record of managing credit.
It's very possible for someone who doesn't meet one or more of these criteria to get a mortgage. It's just that the further you diverge from the "ideal customer", the more restricted your choice of lenders will be.
A mortgage broker is a great option as they inform you of all the available products out there and advise you on the best options to take. It's best to employ a professional in this field, particularly if you're a first-time buyer and slightly inexperienced.
If you're buying off plan property, you will get a Decision In Principle (DIP) once you and your broker are satisfied with the mortgage rates. This is confirmation that the lender will almost certainly lend to you once your property is closer to completion. This is offered early on as to definitively confirm you can actually get a mortgage- after all, the last thing you want is to get a few months away from completion only to find you can't get lending.
Your broker, on your behalf, will make a full mortgage application. Your broker will inform you of the information you need to provide should they come back requesting anything further. Your DIP will help you at this stage as it shows you're organised and creditworthy.
The next step is valuation. The lender will send a surveyor to judge the value of the property and the amount it expects to receive in rent every week/month. If you've bought in a good area with trusted developers who've done their research on all of this, then any potential problems are minimised, and you can breathe easy.
If the valuer is satisfied, all that's left now is to wait until completion for the mortgage funds to be sent to your solicitor and then subsequently to the vendor.
And that's the mortgage process from a layman's perspective. A mortgage broker is ideal for this process and they can explain the steps in more detail, but hopefully this gives you a summary of what to expect.
For more information on our latest investment opportunities, click on the Investments tab on our homepage. Alternatively, give us a call on 0208 445 6542 or email us at info@tarquinjones.com for more details.
Tarquin Jones is a dynamic and specialist property Investment company that focuses and delivers on property Investment solutions to our discerning clients throughout the world.


The Musculoskeletal Institute at UT Health Austin works to improve the overall health of every patient. Whether you are suffering from chronic joint pain or an injury, our doctor-led care teams work to find treatment goals to fit your lifestyle.
We understand that improving your quality of life is important to you, which is why our team will work with you to personalize your treatment plan. For some patients, your goal may be to set a personal record when you run your next marathon. For others, it may be to comfortably play with your grandkids at the park. Whatever your goals, we'll work with you to understand how we can best help you achieve them.
We've assembled a team of experts that includes orthopedic surgeons, physiatrists, physical therapists, chiropractors, nurse practitioners, dietitians, and social workers. This team enables us to provide the right care for the right patient at the right time. For some patients, nonsurgical interventions such as lifestyle modifications, physical therapy, medication and injections can help improve pain and function, while surgery may be the best course of action for others. Whatever your needs, our team is here to listen and work with you to develop a treatment plan that is right for you.
Improving your overall health and wellness can often get you closer to your goals and improve your pain and function. Customized exercise and nutrition plans are often a key component of our treatment plans. We also recognize the critically important role that mental health plays in your overall health, which is why we built a team that includes therapists who can work with you to develop a comprehensive approach to your health.
Based on the progression of your disease, medical intervention may be the best course of action. Our team will work with you to weigh your options and to help you understand the risks and benefits of interventions like medication or injections to help you manage and improve your pain and function.
Physical therapy is an important component of the orthopedic treatment process here at UT Health Austin. Physical therapy provides a variety of benefits throughout the recovery process from an injury or surgery including reduced pain, improved function, increased range of motion, proper alignment and more.
Sometimes surgery is the best option to help you get back to living your life the way you want to live it. Our team of nationally recognized surgeons work with you to understand the risks and benefits of surgery and to help prepare you for your procedure. Whether it's a revision joint replacement or a routine carpal tunnel release, our team will support you before, during, and after the surgery to help keep you on track toward achieving your goals.


Image Thief and Kitty Poisoner?
The Family Research Council pulled a prank on Max Blumenthal and The Huffington Post. Apparently, the latter had hotlinked an image from the FRC's website. So the FRC changed the image of some people to one that included text claiming that Max Blumenthal was an "Image Thief" and a "Kitty Poisoner." It also included an image of a dead cat. You can read the details and see the images here.
This is a pretty funny prank, though I worry about the intent. This was not innocent fun among friends. Instead, the FRC was taking on one of its biggest critic and this is likely only to add to the bad blood. After all, Blumenthal has previously exposed the problems with the FRC's leader, Tony Perkins, when it comes to issues of race. The FRC might be pulling pranks, but Blumenthal's piece on them is no laughing matter.
The FRC might be pulling pranks, but Blumenthal's piece on them is no laughing matter.
We agree completely. We tried to get Blumenthal to issue a correction after it was proven that he was misinformed about his facts (see here, for an example: http://www.frc.org/get.cfm?i=LH05F09) but he isn't much interested in being honest. Blumenthal wants to be the next Michael Moore.
True, it's not a prank between friends but we tried to keep it light-hearted. It's a silly thing to do but it's meant in a spirit of good-humor.
"(The FRC's "correction" contains no mention of Perkins' speech at a Council of Conservative Citizens fundraiser for some reason. And I was never contacted by Carter or anyone else to issue a correction of facts confirmed years prior by members of the Louisiana media. There simply was nothing to correct.)"
Thus, I am still quite troubled by Perkins when it comes to racial issues.
I checked out the correction you pointed out. However, I must say that it ignored the part of Blumenthal's article that I found most troubling—the speech by Tony Perkins at a meeting of the Council of Conservative Citizens.
While a state legislator in Louisiana, Perkins gave a speech at a luncheon for the CCC. At the time, he did not know the group was a neo-confederate racist organization. I don't find that surprising. The first I ever heard of the group was when I read about it in Max B.'s article. Had you ever heard of them before?
It would be rather odd for Perkins to speak in black churches on Sunday and to knowingly speak to a racist group in the same time period.
I would challenge anyone to present a single bit of evidence that Perkins is a racist. He's been a national figure for over a decade. Why hasn't any of the media ever picked up on his racial views if they are troubling? Why are the only stories that accuse him of being a racist written by Max B?
Joe: I had actually heard of the C of CC before Blumenthal's article, which is why I was so stunned by it. A few seconds on their website would have made it very clear that this group has serious problems. Why did he go speak to a group without knowing who they were?
What I think would really help in this case would be if Perkins had publicly apologized for this. Once he figured out who they were, he should have come out against their beliefs. And after Blumenthal's article he should have made that clear. He should set the record straight.


text:
Guess Who Prime Minister Theresa May Intends to Appoint As Britain's Next Chancellor?
By Graham Vanbergen
True Publica 18 May 2017
Theme: Global Economy
In October 2011 The Telegraph reported that: Dr Liam Fox became the first Tory Cabinet minister in David Cameron's government to stand down, after more than a week of revelations about his relationship with his best man, Adam Werritty. The Defence Secretary announced that he was resigning after detailed disclosures showed Mr Werritty's activities were funded by companies and individuals that potentially stood to benefit from Government decisions.
In February 2016 the New Statesman headlined with: In a less shameless world, Liam Fox's career would have ended in 2011. They quite rightly pointed out that Fox should never hold a government job again, let alone a senior cabinet role. They also pointed out that Fox was branded a national security risk. And so did cabinet secretary Sir Gus O'Donnell –
"The disclosure outside the MoD of details about future visits overseas posed a degree of security risk."
Liam Fox (picture on the right), although marched out in disgrace, who should never, ever been allowed to walk the corridors of power again, was last year given the plumb role of Secretary of State for International Trade and also no less, President of the Board of Trade.
In July last year The Independent went with: Appointing Boris Johnson is bad, but letting the disgraced Liam Fox back into frontline politics is downright dishonourable
"Britain used to take international affairs and our relationship with other countries with the seriousness it deserved. But with just two strokes of her pen, new Prime Minister Theresa May has returned Britain to its newly found status as an international joke. When a US State Department spokesman was told about Boris Johnson becoming Foreign Secretary last night, he almost laughed, while German TV presenters didn't even hold back. A friend who was at the Foreign Office messaged me last night to say: "Boris fucking Johnson in Beirut dealing with Syria? I can't even deal with this lunacy."
The Independent then went on to say: "But if appointing Johnson is a joke, the PM's decision to put Liam Fox on front-line politics again is nothing short of dishonourable."
You know where this is going don't you?
Ex British ambassador Craig Murray has let the cat out of the bag.
"A week ago an old Whitehall colleague told me that Treasury mandarins expect to be briefing Liam Fox as the new Chancellor should the Tories be re-elected – and they were not much looking forward to the experience."
It is clear that the current Chancellor – Philip Hammond is for the chop. Vox Political said of Hammond
"Philip Hammond has threatened to launch a trade war against the European Union if he doesn't get what he wants out of Brexit –Ye Gods. And this idiot is the Chancellor of the Exchequer."
Theresa May seems to have a bit of thing – with idiots.
And of course we should not let it pass that Hammond's last budget wasn't exactly a success. The Times reported:
"Perhaps the last time a Conservative chancellor caused such immediate consternation among Tory MPs was in 1993, when Norman Lamont put VAT on energy bills."
That was being kind – Hammond was shredded in the days that followed, much to the embarrassment of the Tories.
Hammond, adding his (light) weight to the election started the week being ripped to shreds again, this time by John Humphreys on the Today programme and getting the cost of HS2 radically wrong. Of course the mainstream media would not shred a labour chancellor in waiting for making a similar cock-up now would they Diane?
Craig Murray makes the point that Theresa May was asked quite directly three times if Hammond would continue in his role as Chancellor, and she refused to back him -as did the Torygraph Telegraph newspaper and it's unambiguous headline "Theresa May refuses to say Philip Hammond will be Chancellor in June."
And let's not forget that Liam Fox's pal at the centre of the scandal that should have sent them both down a coal mine in deepest Yorkshire forever, opened a private health company when Fox was Health Secretary and a defence consultancy business when Fox was Minister of Defence. Lets also not forget that his best buddy illegally handed out business cards falsely describing him as one of Fox's official advisers when he wasn't (even security cleared) and was investigated by police for fraud.
At the same time, there was skullduggery going on by Fox and his best mate and tory party donors. The Guardian reported that:
"Pargav (a company that Werrity was a director of) which received £147,000 of funds from four high-profile Tory-donating businessmen and an international investigation company staffed by ex-MI6 employees, paid for Werritty to take a string of first-class flights to meet up with Fox at 18 exotic locations while the former cabinet minister was on government business. Fox also hosted Werritty at the Ministry of Defence's headquarters on Whitehall 22 times between the 2010 general election and his resignation."
Craig Murray also makes the point that:
"the prospect of Fox becoming Chancellor is truly alarming. The hard right links he forged through the now defunct Atlantic Bridge to the American Legislative Exchange Council and the Heritage Foundation give him direct access into the heart of the Trump administration, and align him with the nastiest millionaires and hedge fund managers, with the funders of climate change denial and with those who wish to abolish literally all workers' rights and consumer protections."
The fact that Liam Fox, disgraced through his crookedness has been allowed back into politics in the first place fully demonstrates the state of politics today. Politics is utterly shameless, disreputable and downright unprincipled. But employing this charlatan at the heart of government in the role of chancellor is not just contemptible it shows that Theresa May is creating a swamp, just like Donald Trump for the future we have coming at us with Brexit.
So how did this come about? Well, my suspicion is that Liam Fox went to put his hat in the ring when David Cameron decided it was a good and proper thing to to quit after leading the country into chaos after the Brexit result. This from GuidoFawkes June 29th last year-
"A source close to Liam Fox tells Guido he will announce his leadership bid tomorrow. This comes after speculation he was in talks with Theresa May, which is denied by both sides. Of course this could be some snakes and ladders in the hope of being offered a top Cabinet post."
They don't get much more toppy than Chancellor of the Exchequer do they?
The types of trade deals we can expect with American corporations and people like Fox at the helm will be positively dangerous for all of us. New Economics Foundation has reported various government leaks that conclude we are heading for trade deals that threaten endangered species, our environment, workers rights (what remains of them that is), food supplies, cosmetics, toys, happiness, life in general – the list is endless.
Let's hope Craig Murray is wrong. Personally, I would have thought that once the May coronation is done, not even she would have the audacity – but then again, she did employ a bumbling swivel-eyed idiot as Foreign Secretary, so who knows. You can imagine it though. Fox, although laying low for the duration of this election, will come bounding out the door on reshuffle day, pants on the outside, one arm pointed to the sky – announcing he is now in control of the nation's bank account as if he thoroughly deserved it because of his unswerving dedication and sense of duty to her majesty.
If Badman does coming flying out of No 10 in charge of the sixth largest economy in the world – it's confirmation that this lot will stop at nothing in pursuit of self aggrandisement irrespective of the consequences for the rest of us for generations to come. Neo-liberal capitalism will reach new highs, whilst exploitation of the poor, the environment and frankly anything else that could turn a profit will reach new lows. Hey-ho – I feel a bank holiday of civil unrest would be a nice day out in London. Oh – there's a new law against that – Humph!
The original source of this article is True Publica
Copyright © Graham Vanbergen, True Publica, 2017
Articles by: Graham Vanbergen

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Map kit does not show on the cell phone I am trying to implement the huawei map kit with quasar and cordova but I don't know why it doesn't work. I am following the documentation step by step, adding the methods and dependencies that are needed but still the map is not displayed. Annex my code
<template>

</template>

export default {
 methods: {
 async createMapView() {

  const mapInstance = await HMSMap.create("my-map-view", {
    zoomGesturesEnabled: true,
    zoomControlsEnabled: true,
    cameraPosition: {
      target: { lat: 39.707187, lng: 37.530353 },
      zoom: 7
    }
  });
}
},
mounted() {
document.addEventListener("deviceready", async () => {

  await HMSMap.init();

  this.createMapView();

});
}
};

if someone has a reference code it would be very helpful

A: Maybe div has no width and height properties. Try setting them in CSS:
css
#my-map-view {
  width: 200px;
height: 200px;
}

Otherwise logs or a minimal example that reproduces the issue is needed.

redpajama_set_name: RedPajamaStackExchange


text:
Il castello di Oranienstein è un palazzo degli Orange-Nassau che fu costruito a Diez, nella Renania-Palatinato, per Albertina Agnese di Nassau verso la fine del XVII secolo sulle rovine dell'abbazia di Dierstein.
.

Il castello di Oranienstein è uno dei quattro castelli in Germania che portano il nome della Casa d'Orange. Oltre all'Oranienstein, si tratta del Castello di Oranienburg nel Brandeburgo e del Palazzo di Oranienbaum nell'Anhalt. Furono costruite per quattro sorelle che erano originarie di questa casa. Il quarto, il Palazzo Oranienhof vicino a Bad Kreuznach, non esiste più.

Storia
Quando il castello di Oranienstein fu costruito, parti degli edifici del monastero romanico furono incorporate. Dal 1704 al 1709, il castello fu ricostruito per la prima volta sotto la nuora di Albertina, Enrichetta Amalia. I progetti per la trasformazione in palazzo barocco furono elaborati dall'architetto Daniel Marot, figlio del costruttore del complesso di Versailles. In sostanza, la struttura a cinque ali che esiste ancora oggi è stata creata in quel periodo. Le ricche decorazioni in stucco sono state realizzate dagli italiani Eugenio Castelli e Antonio Gentone, mentre i dipinti del soffitto sono stati a lungo ritenuti opera dell'olandese Jan van Dyk, ma in realtà sono stati creati da Carlo Lodovico Castelli, fratello del maestro stuccatore.

Dopo che l'invasione repubblicana francese distrusse la Repubblica olandese nel 1795, Guglielmo V di Orange-Nassau, e la sua famiglia fuggirono dapprima in Inghilterra, prima di stabilirsi a Oranienstein per diversi anni. Qui Guglielmo e suo figlio Guglielmo Federico emisero le "Lettere di Oranienstein", riconoscendo la Repubblica Batava e rinunciando al loro stadtholderate e alle loro rivendicazioni territoriali nei Paesi Bassi in cambio di una compensazione finanziaria e territoriale altrove, concessa dal Primo Console Napoleone Bonaparte.

Dopo l'annessione del Ducato di Nassau da parte della Prussia nel 1866, il palazzo fu consegnato all'esercito prussiano l'anno successivo. Ancora oggi è occupato dalla Bundeswehr, insieme alle caserme adiacenti, ma ospita anche un museo.

Note

Altri progetti

Diez
Orange-Nassau
Architetture della Renania-Palatinato
Palazzi della Germania

redpajama_set_name: RedPajamaWikipedia


text:
C/C++ Compiler Package for R8C and M16C Families
This compiler package makes it possible to code, build and debug (software simulation) any application program for R8C and M16C families. It supports the integrated development environment "High-performance Embedded Workshop". When connecting the emulator (sold separately), you can debug and evaluate on your target system in the same environment "High-performance Embedded Workshop".
C/C++ Compiler Package for R8C and M16C Families 2011.04
Latest Ver.: V.6.00 Release 00
Released: 01 Apr. 2011
Details of upgrade (See Tool News)
This package includes the following three compilers.
C Compiler Package for R32C Series
C Compiler Package for M32C Series [M3T-NC308WA]
C/C++ Compiler Package for M16C Series and R8C Family [M3T-NC30WA]
Compiler (includes assembler, linker and utilities), simulator and the integrated development environment "High-performance Embedded Workshop" are included in each compiler package. Compiler is based on the ANSI standard. The powerful optimizations offer the ultimate in execution speed and code efficiency. Furthermore, the MISRA C Rule Checker (included), which helps you write high-quality C source code, is also available.
C/C++ Compiler Package for R8C and M16C Families 2011.04 (Upgrades for this package will be charged.)
Compiler for R32C Series C Compiler Package for R32C Series V.1.02 Release 01A (No changes have been made to V.1.02 Release 01.)
C compiler V.1.02.01
Simulator debugger V.1.01 Release 00
Integrated development environment "High-performance Embedded Workshop" V.4.07.01 (Note1)
Compiler for M32C Series C Compiler Package for M32C Series [M3T-NC308WA] V.5.42 Release 00A (No changes have been made to V.5.42 Release 00.)
Compiler for M16C Series and R8C Family C/C++ Compiler Package for M16C Series and R8C Family [M3T-NC30WA] V.6.00 Release 00 (Much-improved in functionality from the previous version)
Object format ELF (Included converter converts the objects and libraries written in the IEEE695 format into the ELF format)
Static analysis tool MISRA C Rule Checker SQMlint V.1.03 Release 00C (No changes have been made to V.1.03 Release 00B in functionality.)
The updata to the latest version is still available free.
[How to Upgrade to the Latest Version]
Upgrade to the C/C++ Compiler Package for M16C Series and R8C Family V.6.00 Release 00
Even if you have the previous version, you need to buy the following package. An upgrade service is NOT available.
Upgrade to the latest version of the C Compiler Package for R32C Series
You can use on-line upgrade service.
Upgrade to the latest version of the C Compiler Package for M32C Series
Upgrade to the latest version of the Simulator Debugger
You can use separate on-line upgrade service.
Upgrade to the latest version of the High-performance Embedded Workshop
R8C Family
R8C/10
R8C/1A
R8C/1B
R8C/2C
R8C/2D
R8C/2E
R8C/2F
R8C/2G
R8C/2H
R8C/2J
R8C/2K
R8C/2L
R8C/32A
R8C/32C
R8C/32D
R8C/32G, R8C/32H
R8C/32M
R8C/33T
R8C/34E, R8C/34F, R8C/34G, R8C/34H
R8C/34K
R8C/34P, R8C/34R
R8C/34U
R8C/34W, R8C/34X, R8C/34Y, R8C/34Z
R8C/36T-A
R8C/3GA
R8C/3GC
R8C/3GD
R8C/3GM
R8C/3JA
R8C/3JC
R8C/3JM
R8C/3JT
R8C/3MK
R8C/3MQ
R8C/3MU
R8C/3NT
R8C/L35A, R8C/L35B
R8C/L35C
R8C/L35M
R8C/L3AA, R8C/L3AB
R8C/L3AC
R8C/L3AM
R8C/LA3A
R8C/LAPS
R8C/M11A
R8C/M13B
M16C Family (R32C / M32C / M16C)
M16C/1N
M16C/24 (M30245)
M16C/30, M16C/30L
M16C/30P
M16C/5L, M16C/56
M16C/5LD, M16C/56D
M16C/5M, M16C/57
M16C/62A (incl. M16C/62T), M16C/62M
M16C/62N (incl. M3062GF8NFP/GP)
M16C/63
M16C/64A
M16C/64C
M16C/6B
M16C/6C
M16C/6H
M16C/6N4, M16C/6N5
M16C/6NK, M16C/6NL, M16C/6NM, M16C/6NN
M16C/6S
M16C/6S1
M16C/6V
M32C/8A
R32C/111
R32C/116, R32C/117, R32C/118
R32C/116A, R32C/117A, R32C/118A
R32C/120, R32C/121
R32C/151, R32C/152, R32C/153, R32C/156, R32C/157
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text:
Q: Bootstrap navbar - fixed on mobile on horizontal website I'm making a horizontal website. I've tried setting the top menu (navbar) to position:fixed or giving it the navbar-fixed-top class, experimenting with %, but on mobile (iPhone 5 at least) I end up with the navbar either taking the width of the entire page (so the menu button is on the very right and only visible when I scroll to the last page), either it's only visible on the first page and scrolls away when I scroll to the right.
Here's the simplified code:
HTML:

   here goes the typical Boostrap navbar construction

CSS:
 html {position: relative;}
 html, body {height: 100%}
 .big-wrap {position: absolute;width: 400%}
 section {float:left;width:25%;}

How can I make the navbar appear as full width and sticking in the same place when scrolling to other sections, both on desktop and mobile (on desktop it's ok for now)?


/ Best Taco in Destin FL / Taco Tuesday BLAZING-HOT COLLEGE HOOPS Action, NBA, NHL|Taco, Margarita, & Corona Specials!
Taco Tuesday BLAZING-HOT COLLEGE HOOPS Action, NBA, NHL|Taco, Margarita, & Corona Specials!
Put some fun in your day with TACO TUESDAY here at Landshark's Pizza highlighted by ROCK'N BINGO, NCAA Basketball, NHL, NBA & other sports action here at Landshark's, your sports fest Taco Tuesday headquarters with Taco & Drink specials!
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1. The largest bouquet is perfect for the bride and has 24 peachy Coral open roses with a white bow. These open roses have a gorgeous shape and peachy Coral color. The handle is wrapped with a white sheer organza ribbon and bow. The bouquet measures 8 inches across and 10 inches tall.
2-3. The two smaller bouquets have 12 Coral roses each and measure 6 inches across and 10 inches tall. Each bouquet has a white sheer organza bow attached with lovely trailing ribbons. This white ribbon coordinates perfectly with the larger bouquet. The bouquet stem handle is hand wrapped with green florist tape. These bouquets are perfect for bridesmaids or maid of honor.
4-5. This package includes 2 pin-on corsages. Each corsage has three gorgeous silk peach Coral garden roses accented with several green rose leaves and a lovely white bow. The corsages both come with a pearl head pin for attachment. Each corsage measures approximately 4 inches wide by 6 inches long.
6-9. This package includes 4 boutonnieres. Each boutonniere has a single peach Coral rose with two green rose leaves. The boutonnieres all come with a pearl head pin for attachment. Each boutonniere measures approximately 2 inches wide by 3 inches long.
10. 250 peach Coral rose petals are included in this wedding package and they make great table decorations, or aisle accents. Some brides choose to decorate their honeymoon suite with these romantic accents. A classic and elegant look.
Everything shown in this package coordinates exactly with the rest of TheBridesBouquet.com Peach Silk Rose Collection. Matching garland, cake flowers, kissing balls and ribbons are also available for purchase.


text:
Q: Не подключается база данных H2 Не могу подключиться к базе данных H2. Использую IDEA, Maven. Выдает следующую ошибку
java.lang.ClassNotFoundException: org.h2.Driver
Вот код:
import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.SQLException;
public class Util {
private final static String DB_DRIVER = "org.h2.Driver";
private final static String DB_URL = "jdbc:h2:~/test";
private final static String DB_USERNAME ="sa";
private final static String DB_PASSWORD = "";

public Connection getConnection(){
    Connection connection = null;
    try {
        Class.forName(DB_DRIVER);
        connection = DriverManager.getConnection(DB_URL, DB_USERNAME, DB_PASSWORD);
        System.out.println("Connection OK");
    }catch(SQLException e){
        e.printStackTrace();
        System.out.println("Connection ERROR");
    }
    catch (ClassNotFoundException e){
        e.printStackTrace();
        System.out.println("Connection ERROR");
    }
    return connection;
}

public static void main(String[] args) {
    Util util = new Util();
    util.getConnection();
}

}
файл pop.xml
<?xml version="1.0" encoding="UTF-8"?>

http://maven.apache.org/xsd/maven-4.0.0.xsd">
    4.0.0
<groupId>com.jdbc.tutorial</groupId>
<artifactId>jdbc-tutorial</artifactId>
<version>1.0-SNAPSHOT</version>

<dependencies>
    <!-- https://mvnrepository.com/artifact/com.h2database/h2 -->
    <dependency>
        <groupId>com.h2database</groupId>
        <artifactId>h2</artifactId>
        <version>1.4.196</version>
        <scope>test</scope>
    </dependency>
</dependencies>

A: У вас scope вашего JDBC драйвера ограничен:

< scope >test< /scope >

Уберите эту строку из maven dependency и попробуйте снова


text:
Q: creating a different database for each collection in MongoDB 2.2 MongoDB 2.2 has a write lock per database as opposed to a global write lock on the server in previous versions. So would it be ok if i store each collection in a separate database to effectively have a write lock per collection.(This will make it look like MyISAM's table level locking). Is this approach faulty?

A: There's a key limitation to the locking and that is the local database. That database includes a the oplog collection which is used for replication.
If you're running in production, you should be running with Replica Sets. If you're running with Replica Sets, you need to be aware of the write lock effect on that database.
Breaking out your 10 collections into 10 DBs is useless if they all block waiting for the oplog.
Before taking a large step to re-write, please ensure that the oplog will not cause issues.
Also, be aware that MongoDB implements DB-level security. If you're using any security features, you are now creating more DBs to secure.

A: Yes that will work, 10gen actually offers this as an option in their talks on locking.
I probably isolate every collection, though. Most databases seem to have 2-5 high activity collections. For the sake of simplicity it's probably better to keep the low activity collections grouped in one DB and put high activity collections in their own databases.


text:
Karen Hesse
This summary of Out of the Dust includes a complete plot overview – spoilers included!
Thank you for upvoting Out of the Dust
Out of the Dust Summary
SuperSummary, a modern alternative to SparkNotes and CliffsNotes, offers high-quality study guides that feature detailed chapter summaries and analysis of major themes, characters, quotes, and essay topics. This one-page guide includes a plot summary and brief analysis of Out of the Dust by Karen Hesse.
Out of the Dust, by Karen Hesse, tells the story of surviving the Great Depression through first-person, free verse poems. A free verse poem is one that doesn't adhere to any specific rhyme scheme or meter. Meter, in poetry, describes both the number of syllables in a line and the pattern of stressed and unstressed syllables. Published in 1997, Out of the Dust is a work of historical fiction that takes place over the course of two years, from the winter of 1934 to the autumn of 1935, and is so titled because many families were forced to try to survive in what became known as the Dust Bowl. The Dust Bowl earned its name because a severe drought hit the farmlands of the middle of the United States just as the Depression took hold. The area was subject to huge dust storms, and families had difficulty raising crops.
The main character in Out of the Dust is a girl named Billie Jo. At the start of the story, she's only thirteen years old, and decides to leave the barren Dust Bowl, only to regret it. She realizes how important her family is, and how crucial their connection to their land is. The story takes place near Joyce City, Oklahoma, which is part of the state's panhandle. This area suffered the brunt of the dust storms, as well as tornadoes. Her father, a wheat farmer, holds onto faith that rains will come, but all that comes is more dust.
Billie Jo's struggles are many over the two years covered in the book. She anticipates the birth of her baby brother, but he dies before she can ever meet him. Her mother dies in her childbirth efforts as well. Both Billie Jo and her mother are burned in a fire. Billie Jo's decision to leave her family's land is spawned by these tragedies and by the realization that by staying, she is consigning herself to more horrors. People around her are dying, being mutilated, and going insane because they have no other options in the economic and environmental climate that is the Dust Bowl during the Depression.
When she leaves, Billie Jo rides a train as a hitchhiker. A homeless man tells her about his family and shows her a picture. She falls asleep and, when she wakes, discovers that he's stolen all of her biscuits. He has left the photograph of his family behind, and it makes her long to return to her father. Billie Jo does just that, and convinces him to see a doctor because the spots on his face remind her of those on her grandfather's—whose spots turned out to be skin cancer. Her father, meanwhile, has been living with a woman named Louise, whom Billie Jo likes. At the end of the story, her father is happy and married to Louise, and Billie Jo feels hopeful for the future.
The book presents many themes; among the most prominent is death. Not just death of people, though the novel features many human deaths, caused by everything from dust inhalation during storms to depression and starvation. Crops and animals die, too. Even more pervasive is the death of hope. So many families are forced to give up hope, even after clinging to it for so long. Physical and emotional pain are also carried throughout the book, and become even more poignant following the fire that injures both Billie Jo and her mother. Abandonment is another important theme in Out of the Dust. On the larger scale, families are forced to abandon their homes. On a more personal level, after the fire, Billie Jo gives up playing the piano, despite having been a virtuoso at the instrument.
The fire—which damages her hands to the point that she decides to abandon the piano—is a crucial turning point in Out of the Dust. This book is what's known as a bildungsroman, a coming-of-age story. When Billie Joe decides not to play any longer, she must mourn that loss. It is only through the healing of her hands that she is reborn; that transformation includes her growing up. She sheds the ideals and dreams of her childhood and sees the world through an adult's eyes.
Karen Hesse's awards for Out of the Dust include the Newbery Award and the Scott O'Dell Award. She has also received the International Reading Association Award, the National Jewish Book Award, the Phoenix Award, and the Christopher Award. Hesse studied poetry at Towson State College, which contributed to her choice of format for Out of the Dust. In 2002, she was a MacArthur Fellow. She has published a wide variety of works, from children's books to young adult novels. Among her most notable titles, in addition to Out of the Dust, are Letters from Rifka, Phoenix Rising, and Witness.


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For over 20 years, Palladian Design Group has been transforming their clients' desires into their dream homes. Throughout the country, our firm has created hundreds of unique residences that not only provide its owners with a wonderful place to call home, but an enduring investment that showcases the individuality of those that will live there for generations to come. Passion for all types of architectural styling and traditions, detailed interior spaces and a balanced flowing layout have created homes that are a testament to our firm's attention to every element needed for a home of unprecedented style and livability.
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text:
\section{Introduction}
A key research question in empirical science in the presence of high dimensional data is variable selection. Especially, if the number of variables is relatively high compared to the number of observations. In bio-statistics, this is a common setting, for example in gene sequencing \cite{johnstone_statistical_2009}. Two common variable selection strategies are the use of a lasso penalty \cite{tibshirani_regression_1996} or component-wise boosting \cite{breiman_arcing_1998} \cite{friedman_additive_2000}. Often the variables in the data can be clustered into groups. These could be pathways of genes or items of a construct in a questionnaire, used for example in the social sciences or psychology \cite{gogol_my_2014} \cite{agarwal_verifying_2011}. In these cases, it can be of interest to perform variable selection in a way that this group structure is accounted for. Through the group lasso penalty \cite{yuan_model_2006} \cite{meier_group_2008} and group-wise boosting this can be achieved. A solution where variable selection is based on groups, as well as variables, can be of interest if one wants to identify important groups as well as "important" variables within a group. This can be achieved by the sparse group lasso \cite{simon_sparse-group_2013}. However, to our knowledge, an in-depth analysis of such sparse group variable selection in the context of component-wise boosting has not been conducted. In this manuscript, we show the issues and potential biases as well as their correction occurring in the presence of variable selection between and within groups in the context of boosting. We provide an algorithm for sparse group boosting and discuss its advantages over alternative definitions. Differences and similarities between the sparse group lasso and the sparse group boosting are described with special attention to sparsity.  We apply the sparse group boosting to a gene-related dataset, as well as to an agricultural dataset, and compare its results to component-wise boosting and the sparse group lasso. The same comparison will be conducted with extensive simulations.

\section{The sparse group Lasso}
Let's consider a linear regression framework with outcome $y \in \mathbb{R}^n$ design matrix $X$ including $n$ variables, $p$ variables divided into $G$ groups, in a possibly high dimensional setting or even $p>n$. Then the sparse group lasso can fit a model, that not only performs variable selection on a variable basis but also on a group basis \cite{simon_sparse-group_2013}.
The sparse group lasso achieves this by combining the group lasso penalty \cite{yuan_model_2006} $ \sum_{g=1}^G \sqrt{p_g}$
and the lasso penalty $\norm{\beta}_1$ \cite{tibshirani_regression_1996} with a mixing parameter $\alpha \in [0,1]$
\begin{equation}\label{sgl_loss}
    \text{min}_{\beta} \frac{1}{2n} \norm{y- \sum_{g=1}^G X^{(g)}\beta^{(g)}}_2^2 + (1-\alpha)\lambda \sum_{g=1}^G \sqrt{p_g} \norm{ \beta^{(g)}}_2 + \alpha \lambda \norm{\beta}_1.
\end{equation}
There are two tuning parameters $\alpha$ and $\lambda >= 0$. $\alpha$ decide on how much we want to penalize the individual variables (increase $\alpha$) versus how much we want to penalize groups (decrease $\alpha$). $\alpha = 1$ yields the lasso fit and $\alpha = 0$ yields the group-lasso fit. As in \cite{simon_sparse-group_2013} we differentiate between the two types of sparsity: "within-group sparsity" refers to the number of nonzero coefficients within each nonzero group, and "group-wise sparsity" refers to the number of groups with at least one nonzero coefficient.
Depending on $\alpha$ both types of sparsity can be balanced. This gives the statistician the flexibility to include secondary knowledge regarding the two types of sparsity. If $\alpha$ is not known before, it has to be estimated, for example by using cross-validation on a two-dimensional grid including parameters for $\lambda$ and $\alpha$. This has the downside, that two hyper-parameters have to be tuned \\
The sparse group lasso can also be extended to more general loss functions by replacing the least squared loss with other loss functions. This way also generalized leaner models can be fitted by using the log likelihood $\mathcal{L}(\beta)$, with group-wise and within-group sparsity
\begin{equation}
    \text{min}_{\beta} \mathcal{L}(\beta) + (1-\alpha)\lambda \sum_{g=1}^G \sqrt{p_g} \norm{ \beta^{(g)}}_2 + \alpha \lambda \norm{\beta}_1.
\end{equation}

\section{Model-based Boosting}

Another way of fitting sparse regression models is through the method of boosting. The fitting strategy is to consecutively improve a given model by adding a base-learner to it. This base-learner is usually a regression model, that only considers a subset of the variables at each step.  \\
\textit{General functional gradient descent Algorithm} \cite{buhlmann_boosting_2007}
\begin{enumerate}
\item Define base-learners of the structure $g: \mathbb{R}^n \to \mathbb{R}$
\item Initialize $\widehat{f}^{(0)} \equiv 0$ and $m=0$, or
\begin{equation*}
l \equiv \text{argmin}_{c} \quad \frac{1}{n} \sum_{i=1}^n l(y_i,c)
\end{equation*}
\item Set $m = m+1$ and compute the negative gradient $-\frac{\partial}{\partial f} l(Y,f)$ and evaluate it at $\widehat{f}^{(m-1)}$. Doing this yields the pseudo-residuals $U_1,...,U_n$ with
\begin{equation*}
U_i^{(m)} = -\frac{\partial}{\partial f} l(y_i,f)|_{f = \widehat{f}^{(m-1)}},
\end{equation*}
for all $i = 1,..., n$.
\item Fit the base-learner with $g$ with the response $(U_1^{(m)},...,U_n^{(m)})$ to the data. This yields $\widehat{g}^{(m-1)}$, which as an approximation of the negative gradient.
\item Update
\begin{equation*}
\widehat{f}^{(m)} = \widehat{f}^{(m-1)} + \eta \cdot \widehat{g}^{(m-1)}.
\end{equation*}
here $\eta$ can be seen as learning rate with $\eta \in ]0,1[$.
\item Do step 3,4 and 5 until $m=M$.
\end{enumerate}

Through early-stopping, or setting $M$ relatively smaller compared to the number of variables in the dataset, and considering the learning rate $\nu$ a sparse overall model can be fitted. For a given learning rate, a base-learner that considers viewer variables compared to one that considers more variables in each step tends to be relatively sparser.
\section{Unbiased variable selection respecting groups}\label{sectionunbiasedvar}
For model-based boosting the goal is unbiased variable selection, meaning that no base-learner is favored over another in the selection process. This is achieved by Ridge penalization in the way, that all base-learners have the same degree of freedom. But in the presence of groups, we do not want unbiased variable selection based on the individual variables but based on the group. We propose an adjustment to regularize base-learners, such that all groups have the same chance of being selected, regardless of their group size and type of base-learner.
The update step in some boosting iteration is given by

\begin{equation}
    \argmin_{f(\cdot)} \sum_{i=1}^n l(u_i, f(x_i^{(g)}) + \lambda \int (f''(x^{(g)}))^2 \,dx,
\end{equation}
for some loss function $l$, gradients (pseudo-residuals) $(u_i)_{i \leq n}$ from the previous step and group $g \in \{1,...,G\}$ from $G$ groups. Here, the penalty term on the right hand side corresponds to a P-Spline and in the case of a linear base-learner $\lambda^g \norm{f(x^g))}_2^2$ is applied.
Usually $\lambda$ is set in the way, that the degrees of freedom $ \text{df}(\lambda)$ are set to the same for all base-learners. A common choice is $ \text{df}(\lambda) = 1$. We relax this assumption and set $\lambda$, such that the following two conditions hold:
\begin{align}
    \sum_{g=1}^G \sum_{k=0}^{p_g}  \text{df}(\lambda_k^{(g)}) = \gamma_1, \\
    \forall g \leq G: \sum_{k=0}^{p_g} \text{df}(\lambda_k^g) = \gamma_2,
\end{align}
for some constants $\gamma \in \mathbb{R^+}$. Here, $p_g$ is the number of base-learners in group $g$ $p$ is the total number of variables and $\lambda^{(g)}_j$ is the ridge regularization parameter of the $j$-th base-learner in the group $g$. The first condition makes sure, that the degree of freedom of each base-learner is smaller than one. The second condition makes sure that the sum of the degrees of freedom within each group is the same. It can easily be seen that both conditions are met by setting
\begin{equation}
     \text{df}(\lambda^g) = \frac{1}{p_g G}.
\end{equation}

The following statements will give some justification for this adjustment.

\begin{lemma}[] \label{theo:df}
Let $X^{(1)}$ and $X^{(2)}$ be the design matrices of the two ridge penalized group base-learners $x^{(1)}$ and $x^{(2)}$ of group sizes $g_1$ and $g_2$, $\lambda_1$ and $\lambda_2$ be the corresponding ridge penalties and $S^{(1)} = X^{(1)}[(X^{(1)})^T X^{(1)}+ \lambda_1 K^{(1)}]^{-1} (X^{(1)})^T$.
Let $u \in \mathbb{R}^n$ be the negative gradient vector derived from the first boosting step with i.i.d. normally distributed response variable $y \in \mathbb{R}^n$ with variance $\sigma^2$ being independent of $x_1$ and $x_2$. $\widehat{\beta_1}$ and $\widehat{\beta_2}$ are the unpenalized effect estimates derived from least squares base-learners.
Define the residual sums of squares as $\Delta = (u-X^{(1)} \widehat{\beta}_1)^{T}(u-X{(1)} \widehat{\beta}_1)-(u-X{(2)} \widehat{\beta}_2)^{T}(u-X{(2)} \widehat{\beta}_2)$. Then
\begin{equation*}
    \mathbb{E}[\Delta] = 0 \Leftrightarrow \mathrm{tr}(2S^{(1)}-(S^{(1)})^TS^{(1)}) = \mathrm{tr}(2S^{(2)}-(S^{(2)})^TS^{(2)})
\end{equation*}
\end{lemma}
As concluded  in \cite{hofner_framework_2011}
the degrees of freedom should be defined as $\text{df} =\text{tr}(2S-S^TS)$ and set equal for two competing base-learners to avoid selection bias. \\
The previous Lemma gives a condition for unbiased variable selection on a base-learner selection. However, if we want the variable selection to be unbiased on a group level, another condition is more useful. The following Theorem shows that setting the degrees of freedom equal across all base-learners in the presence of individual and group base-learners introduces bias on a group level.
\begin{theorem}
Consider the same setting as in Lemma \ref{theo:df} and further assume that the response variable u is standardized meaning $\sigma^2 = 1$ and $\mu = 0$.
Assume that each of the $p_g$ variables in base-learner $x^{(g)}$ has their own base-learner $x^{(g)}_j$ for $j \in \{1,...,p_g \}$ and $g \in \{1,2\}$. Set all the degrees of freedom of all base-learners to one.\\
Then the residual sum of squares of the individual base-learners $x^{(g)}_j$ is Chi squared distributed $\chi^2_{n-1}$ with $n-1$ degrees of freedom. Moreover, the selection probability of each base-learner is 0.5 and the selection probability of a base-larner belonging to group one over group two $\pi(1;2)$ is
\begin{equation*}
\pi(1;2) := P \Big{[} \min_{j \in \{1,...,p_1 \}}{\mathrm{RSS(x^{(1)}_j)}} \leq \min_{j \in \{1,...,p_2 \}}{\mathrm{RSS(x^{(2)}_j)}} \Big{  ]} = \frac{p_1}{p_1+p_2}.
\end{equation*}
This means, that the selection probability of one group over the other is zero if and only if their group sizes are equal.
\end{theorem}
A proof can be found in the Supplement.
\begin{theorem}
Consider the same setting as in Lemma \ref{theo:df}. Assume that there are $G$ groups of base-learners with and each group contains $p_g$ base-learners. Then
\begin{align*}
    \mathbb{E}[\tilde{\Delta}] = 0 \Leftrightarrow &\sum_{j \in \{1,...,p_1\}}
    \mathrm{tr}(2S_j^{(1)}-(S_j^{(1)})^TS_j^{(1)}) \\
    = &\sum_{k \in \{1,...,p_2\}} \mathrm{tr}(2S_k^{(2)}-(S_k^{(2)})^TS_k^{(2)}).
\end{align*}
with
\begin{equation*}
    \tilde{\Delta} =  \sum_{j \in \{1,...,p_1\}}  \mathrm{RSS}(x^{(1)}_j)- \sum_{k \in \{1,...,p_2\}} \mathrm{RSS}(x^{(2)}_k)
\end{equation*}

\end{theorem}
This follows by using the same derivation as is Lemma \ref{theo:df} and using the linearity of the expectation. \\
We conclude, that just by adjusting the degrees of freedom, we can perform variable selection, such that all groups are treated equally leading to desirable between-group sparsity, and that all variables within a group have equal selection chance, leading to within-group sparsity. The only drawback is, that we are not able to weight how much we want to enforce within-group sparsity vs. between-group sparsity. But this has also the advantage, that no prior guessing or cross-validation to estimate this factor is needed.

\section{Sparse group boosting}
As proposed by \cite{hofner_gamboostlss_2014}, one can define one base-learner as group of variables, as well as an individual variable. Using a similar idea as in the sparse group lasso, we define sparse group boosting. We do this again by modifying the degrees of freedom. Each variable will get its own base-learner, that we will refer to as individual base-learner, and each group will be one base-learner, containing all variables of the group. For the degrees of freedom of an individual base-learner
$x_j^{(g)} \in \mathbb{R}^{n \times 1}$  we will use
\begin{equation}
     \text{df}({\lambda}^{(g)}_{j}) = \frac{1}{p_g G}\cdot \alpha,
\end{equation}
and for the variables in the group base-learner we will use
\begin{equation}
     \text{df}(\Tilde{\lambda}^{(g)}_{g_j}) = \frac{1}{p_g G}\cdot (1-\alpha).
\end{equation}

$\alpha \in [0,1]$ is the mixing parameter. Note that the group-size correction from the previous section is also used. Alternatively, also $\text{df}({\lambda}^{(g)}_{j}) =\alpha$ and $\text{df}(\Tilde{\lambda}^{(g)}_{g_j}) = (1-\alpha)$ if additional group regularization is not desired. Since $ \text{df}(\lambda) = 0$ means $\lambda \to \infty$, $\alpha = 1$ yields group boosting, and $\alpha = 0$ yields the component-wise boosting.
\begin{lemma}\label{theo:trace_present}
Let $S = X(X^TX+\lambda K)^{-1}X^T$ be the ridge hat matrix with symmetric penalty matrix $K$ of a desgin matrix $X$ of rank $p$. Let $X^TX = R^TR$ be the Cholesky decomposition of the design matrix with rank $p$ in some boosting iteration. Then, the degrees of freedom $\mathrm{tr}(2S-S^TS)$ are equal to
\begin{equation*}
\mathbb{E}[\mathrm{RSS}(x)] = \mathrm{tr}(2S-(S)^TS)) = 2 \sum_{j=1}^p \frac{1}{1+\lambda d_j}- \sum_{j=1}^p \frac{1}{(1+\lambda d_j)^2},
\end{equation*}
where $d_j$ are the singular values of $R^{-T}KR^{-1}$.
\end{lemma}
This result can be found in \cite{hofner_framework_2011} and a derivation can be found in Appendix B1.1 in \cite{ruppert_semiparametric_2003}.

\begin{corollary}\label{theo:lambda}
The ridge regularization parameter $\lambda \in \mathbb{R}^{+}$ in a sparse group boosting iteration for an individual base-learner is given by
\begin{align*}
\lambda &= \frac{\sqrt{1-\mathrm{df}(\lambda)}+1-\mathrm{df}(\lambda)}{d \cdot \mathrm{df}(\lambda)} \\
&=\frac{\sqrt{1-\frac{1}{p_g G}\cdot \alpha}+1-\frac{1}{p_g G}\cdot \alpha}{d \cdot \frac{1}{p_g G}\cdot \alpha}
\end{align*}
\end{corollary}
This follows directly form Lemma \ref{theo:trace_present} and solving for $\lambda$.
From Lemma \ref{theo:lambda} we see that the penalty $\lambda$ is not linearly weighted by $\alpha$. However, increasing $\alpha$ does lead to decreasing the penalty term in a continuous way and vice versa. We also don't get the nice result for using $\alpha \in \{0,1\}$, because then always one penalty would be infinite. However, we can let $\alpha$ converge to either one or zero and get the group boosting or regular boosting \ref{sectionunbiasedvar}. \\
One may ask the question, why the degrees of freedom are used and not the penalty parameter itself, which could be defined this way in a boosting step
\begin{align*}
   a_{g} = \mathcal{L}(\beta^{(g)}) + (1-\alpha)\lambda \sqrt{p_g}\norm{\beta^{(g)}}_2 \\
   b^{(g)}_{j} =  \mathcal{L}(\beta^{(g)}_j) + \alpha \lambda \norm{\beta^{(g)}_j}_2 \\
\end{align*}
The main reason is, that using the degrees of freedom has the advantage, that a variety of base-learners e.g. P-Splines and linear effects can be used simultaneously without introducing bias. Also, with the statements in the fourth section we can avoid bias on a group level through the degrees of freedom.
\section{Extensions}
The algorithm can easily be extended to exponential families as well as general loss functions. Also, nonlinear base-learners, like p-splines can be used, adding additional flexibility. There are still open questions regarding the implementation of sparse group regularization for Splines. The degrees of freedom of a Spline in boosting can't be lower than the dimension of the null space. So, one has to be careful in defining the model formula to ensure that the lowest number of degrees of freedom is higher than the null space. Another option would be to include another mixing parameter for a zero-centered nonlinear effect. In the presence of zero centering the degrees of freedom can be set arbitrarily small and the above definition of the sparse group boosting can be applied. However, then there would be twice the number of covariates in the design matrix and one has to think about the ratio of regularizing the linear and nonlinear base-learner. A common choice would be to assign each base-learner half the degrees of freedom compared to not using nonlinear base-learners. An extension to generalized additive models for location scale and shape (gamlss) \cite{stasinopoulos_generalized_2008} and their boosting variant (gamboostLSS) \cite{hofner_gamboostlss_2014} is also possible. This would allow the data analyst to also apply sparse group penalization to the linear predictor for other moments of the conditional distribution of the outcome given covariates. We believe that (group) - sparsity is especially important for higher-order moments due to the overall model complexity and the number of variables to be interpreted.

\section{Empirical Data}
The analysis was performed with  R Studio  \cite{rstudio_team_rstudio_2020}. For visualizations tha R package ggplot was used \cite{wickham_ggplot2_2016}.
All computations were conducted on a 3600 MHz Windows machine.
\subsection{Gene Data}
As the first application, we used the breast cancer
data of \cite{ma_two-gene_2004}. We used a modified version of the code of \cite{simon_sparse-group_2013}, which also analyzed the data. The data preparation was left unchanged, including the mean imputation, as was the grouping by the GSEA C1 dataset \cite{subramanian_gene_2005}. We changed the inclusion criteria for missing values. We changed the requirement of having at least 50 percent of the values for each variable to 70 percent because we wanted to also fit nonlinear effects. This leaves us with the same final design matrix consisting of 3302 genes in 267 pathways. We also used an equal training test split of the 60 observations. However, we did slightly adjust the model evaluation. Instead of using one random split into training and one test data, we used a 10-time repeated training and test splitting, to create more reproducible evaluation metrics. For the evaluation, we used the "Area under the curve" (auc) \cite{robin_proc_2011} compared to the classification accuracy to somewhat balance the weight of the true positive and the true negative rate. Stratified sampling was not used because of the small sample size. \\
For each of the 10 folds, a paths 100 sub-models were fitted. The sgl model was fit for a path of 100 $\lambda$-values, as in the original analysis. The sparse group boosting was fit for a path of 100 boosting iterations with a learning rate of 1, as well as the model-based boosting model. We would like to address the issue, that sgl faced random execution errors and sgb faced deep recursion problems due to the length of the R formulas required for the model fitting. We set $\alpha = 0.05$ for the sgl and sgb model. For each $\lambda$-value we averaged the auc across all 10 folds and plotted it in Figure \ref{figure:auc_curve_gene}. \\
We can see that the curve of the sgb model is almost always higher than the curve of the mb model. Comparing the sgb curve with the sgl curve is not as comparable to comparing the two boosting models, since there is no one-to-one translation of boosting iterations to $\lambda$- parameters. However, there are some similarities between the regularization paths of boosting and the lasso \cite{zhao_boosted_2004} and an argument can be made, that this similarity also transfers to the group derivatives of mb and the lasso. In any case, we see that sgb peeks slightly higher than sgl. Referring to table \ref{table:auc_curve_gene}, we can see that the best sgb model at least outperforms the best sgl model in 7, and 9 times the mb model out of the 10 folds. Averaging each best model of the 100 fitted sub-models of each fold across all 10 folds sgb arrives at an auc of 0.70, sgl at 0.68 and mb at 0.63. \\
This confirms the findings of \cite{simon_sparse-group_2013}, that the group information improves the predictiveness of variable selection. Moreover, by using the sparse group boosting we can even slightly improve the auc.

\begin{figure}[!ht]
        \centering
        \includegraphics[scale=0.55]{Tables/gene_auc_curve.png}
        \caption{Genom data AUC paths averaged across 10 repeated resamples}\label{figure:auc_curve_gene}
\end{figure}

\begin{table}[ht!]
  \begin{center}
 \begin{tabular}{l|l|l|l|l|l|l|l|l|l}%
     fold &  mean mb &  mean sgb & mean sgl & sd mb & sd sgb & sd sgl & best mb & best sgb & best sgl
    \csvreader[head to column names]{Tables/gene_summary.csv}{}
    {\\\hline\csvcolii&\csvcoliii&\csvcoliv&\csvcolv&\csvcolvi&\csvcolvii&\csvcolviii&\csvcolix&\csvcolx&\csvcolxi}
\end{tabular}
\end{center}
\caption{Mean (mean), standard deviation (sd) and best (best) of all 100 models fitted for each model type (sgb, mb and sgl)}\label{table:auc_curve_gene}
\end{table}

\FloatBarrier

\subsection{Agricultural data}
Biomedical data are prominent examples of where sparse-group selection can be used. To show the variety of possible applications we analyze an agricultural dataset. Climate change impacts on the agricultural sector are well documented.  The type and level of impacts are crop and region-specific. Not surprisingly, exposure to climate change makes many orchard farming communities in Chile and Tunisia vulnerable to climate change impacts. There are many susceptibility-related factors that may affect farm vulnerability to climatic impacts. A number of adaptation resources (measures/tools) are available to directly reduce the impact on farm operations or to reduce the number or sensitivity of susceptibility-related factors. The final objective is increased resilience of the farming communities. \\
The dataset contains 24 outcome variables of interest that measure climate change vulnerability. The independent variables can be grouped into 7 groups depending on the construct the variable belongs to. Two group examples are social variables as well as the past adaptive measures.
801 farmers have been included in the study.

We use $\alpha \in (0,0.1,0.5,0.95,1)$ as mixing parameter for sgl and sgb. In addition, a mb model was fit. For each outcome variable we, randomly split 70 percent of the data into the training data and 30 percent into test data. We used this percentage since, for the training data we used a 10-fold cross-validation to estimate the optimal stopping parameter for the boosting models and the optimal $\lambda$ value for the sgl models. We used 100 $\lambda$ values and 10000 boosting iterations with a learning rate $\nu = 0.2$. The remaining test data was used for the model evaluation. As in the previous section we used the auc as evaluation criterion, since all outcome variables are binary.

Referring to figure \ref{figure:vul} and table \ref{table:auc_vul} it becomes apparent, that overall the models performed similarly regarding predictability. Overall the higher auc values were achieved for lower $\alpha$ values and sgb very marginally outperformed sgl for equal $\alpha$ values. The worst auc value of 0.677 was attained by model-based boosting compared to the highest of 0.692 attained by sgb with the alpha values of $0, 0.1$ and $0.5$. Regarding computation time, for this specific dataset sgb was faster than sgl as \ref{figure:vul} (c) suggests. It is important to note that the number of groups is relatively small compared to the number of observations. There were also substantial differences regarding the overall sparsity. In Figure \ref{figure:vul} (b) it becomes apparent, that for higher $\alpha$ values, generally the overall sparsity increases for both sgl and sgb. Also relatively lower $\alpha$ values the sparsity of the sgl is higher compared to sgb and for relatively higher $\alpha$ values the opposite is true. In figure \ref{fig:esparsity} we repeated the same setting with an equally spaced grid of 50 $\alpha$ values between zero and one and averaged the overall sparsity across the 25 variables. There seems to be a linear dependency between $\alpha$ and the sparsity for the sgl, and a sigmoid-like relationship for the sgb. From Lemma \ref{theo:df} we saw that the expectation of the residuals sum of squares (RSS) in $\mathcal{L}^2$-boosting is a linear function of the degrees of freedom, which is a linear function of $\alpha$ in the sgb. Using a normal approximation of the RSS one can see that the difference in RSS of an individual variable vs. a group-based variable follows also approximately a normal distribution. Then the selection probability of an individual variable vs. a group base-learner in one boosting iteration is the cumulative distribution function (cfd) of a normal distribution with expectation $2\alpha-1$ and some standard deviation also depending on $\alpha$ equated at zero. The selection of a new individual base-learner decreases the sparsity of the overall model by $\frac{1}{p}$ and the selection of a new group base-learner by $\frac{p_g}{p}$. This way we can see the sparsity after $m$ boosting steps can be seen as some generalized Bernoulli process, where the trials are not independent. For a big number of groups $G$ relative to the boosting steps $m$ we can then formulate this very rough approximation for the expected sparsity $s(\alpha)$ as depicted in Figure \ref{fig:esparsity}  $s(\alpha)  \approx F_{2\alpha-1, \sigma(\alpha)}(0) \cdot \frac{1}{p}+ \sum_{g=1}^G (1-F_{2\alpha-1, \sigma(\alpha)}(0)) \cdot \frac{p_g}{p} $ is the expected sparsity depending on $\alpha$. This cdf shaped relationship between alpha and the sparsity seems to also translate to logistic regression and the use of cross-validation for early stopping as Figure \ref{fig:esparsity} suggests.

\begin{figure}[!ht]%
    \subfloat[\centering AUC]{{\includegraphics[scale=0.38]{Tables/auc_vulnerability.png} }\label{figure:auc_vul}}%
    \qquad
    \subfloat[\centering Sparsity]{{\includegraphics[scale=0.38]{Tables/sparsity_vulnerability.png} }}\\
    \subfloat[\centering Computation time]{{\includegraphics[scale=0.38]{Tables/time_vulnerability.png} }}%
    \caption{Comparison of 5 alpha values for various outcome variables in the dataset}%
    \label{figure:vul
\end{figure}

\begin{figure}[!ht]
        \centering
        \includegraphics[scale=0.55]{Tables/Esparsity_curve_vulnerability.png}
        \caption{Sparsity curve depending on $\alpha$ averaged across various outcomes in the dataset}\label{fig:esparsity}
\end{figure}

\begin{table}[ht!]
  \catcode`"=9
  \begin{center}
 \begin{tabular}{l|l|l|l|l|l|l|l|c}%
     alpha &   model &  auc mean & sparsity mean & time mean & auc sd & sparsity sd & time sd
    \csvreader[head to column names]{Tables/metric_vulnerability.csv}{}
    {\\\hline\csvcolii&\csvcoliii&\csvcoliv&\csvcolv&\csvcolvi&\csvcolvii&\csvcolviii&\csvcolix}
\end{tabular}
\end{center}
\caption{Evaluation metrics for various outcome in the dataset}\label{table:auc_vul}
\end{table}

\FloatBarrier

\section{Simulated data}
In this section, we will compare the sparse group lasso and sparse group boosting. Therefore, we consider various mixing parameters $\alpha$ of 0,0.1, 0.5, 0.95 and 1 for both the sparse group lasso and sparse group boosting. This way the lasso and group lasso are covered. For the sparse group boosting we use the group penalization described in Section \ref{sectionunbiasedvar} for every base-learner, also for the non-group base-learners. Therefore, also solely component-wise model-based boosting (mb) was considered. \\
The covariate matrix X was simulated with different numbers of covariates, observations, correlation structures and groups. The response, y was set to
\begin{equation*}
    \sum_{g=1}^G X^{(g)} \beta^{(g)} + \sigma \epsilon.
\end{equation*}
Here, $\epsilon \sim \mathcal{N}(0, I)$. The signal-to-noise ratio was set to 2 through the value of $\sigma$. For the covariance structure of X we used a block correlation matrix to vary the within-group correlation as well as the between-group correlation. Always two groups contained effects and the number of groups $G$ was set to either 2 or 5, except in one scenario, where all groups and all variables have an effect. This leads to a changing between-group sparsity depending on the number of groups. We set $\beta^{(g)} = (1,1,0,... ,0)$.  The number of variables per group was set to two times the number of groups, which leads to a changing within-group sparsity depending on the number of groups.
\\
All models were tuned using a 10 fold cross-validation on training data and then evaluated with new simulated test data of the same structure. The tuned hyper-parameters were the number of iterations for all boosting models and the value of $\lambda$ or the sparse group lasso models. \\
As the main evaluation criterion we used the mean squared error (MSE), defined as
\begin{equation*}
    \text{MSE} = \frac{1}{n} \sum_{i=1}^n \big{(}(y_i-f(X_{i\cdot})\big{)}^2,
\end{equation*}
where $X_{i \cdot}$ is the $i$-th row of the design matrix. We also computed the proportion of correctly identified effects \begin{equation*}
    \frac{\mathds{1} \sum_{j=1}^p[\widehat{\beta_j} =  \beta_j ]}{p}
\end{equation*}

With the code, the evaluation metrics for all 18 scenarios can be viewed. \\
We would like to highlight a view metrics and results. First of all, we would like to note, that in all cases where generative groups were present, there was at least one $\alpha$, such that the MSE of the sparse group boosting was lower than the one of the standard boosting model.
Referring to Figure \ref{figure:5groups2effects_nocor}, Tables \ref{table:n50_2effects_nocor}, \ref{table:n250_5groups_nocor} and \ref{table:no_effects}, the MSE of the lasso and of boosting were very comparable, which is in line with \cite{hepp_approaches_2016}. In contrast to this, there are differences between the sgl and sgb. In the case of five groups and two groups with effect, those differences are in favor of the sgb. However, when all variables have an effect, the reverse is true. \\
We would like to note, that when many variables have an effect, it can easily happen, that the boosting algorithm gets "stopped out", meaning that the optimal stopping iteration is beyond the value set as maximum. Sgb does not perform well in this scenario, because the variables in bigger groups get regularized more than the variables in smaller groups. If now all variables have an effect, this leads to an inefficient attribution of shrinkage, and therefore to a longer convergence time. If the group structure is informative the converse is true. \\
Apart from the predictability also the proportion of correctly identified parameters is very important.
Regarding this property, the boosting models seem to outperform the lasso penalty-based models. The difference can be clearly seen in Table \ref{table:no_effects} and Figure \ref{figure:5groups2effects_nocor}, where no variable had any effect. In the applications, we already saw differences in the overall sparsity. There is a tendency for the sgb models to be sparser than their sgl counterparts. In this scenario, this tendency translates also in lower MSE. \\
Regarding the computation time, there is a clear trend of group boosting being faster than the sparse group boosting and regular boosting, which is also slightly faster than sgb. This was to be expected, since overall in each boosting iteration more base-learners are being fitted in the sgb than the group boosting and regular boosting. Comparing the computation time sgl and sgb, the picture is not so clear. In the agricultural data, sgb was much faster than sgl and in the simulated data mostly the converse is true. We believe this has something with the number of observations (n) and the number of covariates (p) in the design matrix. The bigger the number of observations and the smaller the number of covariates, the faster sgb is compared to sgl. But this general tendency is also dependent on the implementation and may change in the future. There are efforts to improve both the computation time of sgl \cite{ida_fast_2019} \cite{zhang_efficient_2020} and boosting \cite{staerk_randomized_2021}

\begin{figure}[!ht]%
    \subfloat[\centering n: 50, 5 groups, first 2 groups contain effect, uncorrelated predictors]{{\includegraphics[scale=0.38]{Tables/boxplot.50.png} }}%
    \qquad
    \subfloat[\centering n: 50, 5 groups, no effects, uncorrelated predictors]{{\includegraphics[scale=0.38]{Tables/boxplot.sparse.png} }}\\
    \subfloat[\centering n: 250, 5 groups, first 2 groups contain effect, uncorrelated predictors]{{\includegraphics[scale=0.38]{Tables/boxplot.250.png} }}%
    \caption{Simulation results}%
    \label{figure:5groups2effects_nocor
\end{figure}

\FloatBarrier

\begin{table}[ht!]
\catcode`"=9
  \begin{center}
\begin{tabular}{l|l|l|l|l|l|l|l}%
     alpha & model  & mse mean & mse sd & prop mean & prop sd & time mean & time sd
    \csvreader[head to column names]{Tables/table.5.2.50.small.csv}{}
    {\\ \hline \csvcoli & \csvcolii &\csvcolv & \csvcolvi &  \csvcoliii &\csvcoliv& \csvcolvii & \csvcolviii}
\end{tabular}
\end{center}
\caption{Simulation results: n: 50, 5 groups, first 2 groups contain effect, uncorrelated predictors (prop is the proportion of correct identification of the presence of effects)}\label{table:n50_2effects_nocor}
\end{table}

\begin{table}[ht!]
\catcode`"=9
  \begin{center}
\begin{tabular}{l|l|l|l|l|l|l|l}%
       alpha & model  & mse mean & mse sd & prop mean & prop sd & time mean & time sd
    \csvreader[head to column names]{Tables/table.5.2.250.big.csv}{}
    {\\ \hline \csvcoli & \csvcolii &\csvcolv & \csvcolvi &  \csvcoliii &\csvcoliv& \csvcolvii & \csvcolviii}
\end{tabular}
\end{center}
\caption{Simulation results: n: 250, 5 groups, first 2 groups contain effect, uncorrelated predictors (prop is the proportion of correct identification of the presence of effects)}\label{table:n250_5groups_nocor}
\end{table}

\begin{table}[ht!]
\catcode`"=9
  \begin{center}
\begin{tabular}{l|l|l|l|l|l|l|l}%
       alpha & model  & mse mean & mse sd & prop mean & prop sd & time mean & time sd
    \csvreader[head to column names]{Tables/table.all.csv}{}
    {\\ \hline \csvcoli & \csvcolii &\csvcolv & \csvcolvi &  \csvcoliii &\csvcoliv& \csvcolvii & \csvcolviii}
\end{tabular}
\end{center}
\caption{Simulation results: n: 250, 5 groups, uncorrelated predictors, all variables have an effect (prop is the proportion of correct identification of the presence of effects)}
\end{table}

\begin{table}[ht!]
\catcode`"=9
  \begin{center}
\begin{tabular}{l|l|l|l|l|l|l|l}%
      alpha & model  & mse mean & mse sd & prop mean & prop sd & time mean & time sd
    \csvreader[head to column names]{Tables/table.none.csv}{}
    {\\ \hline \csvcoli & \csvcolii &\csvcolv & \csvcolvi &  \csvcoliii &\csvcoliv& \csvcolvii & \csvcolviii}
\end{tabular}
\end{center}
\caption{Simulation results: n: 50, 5 groups, no effects, uncorrelated predictors (prop is the proportion of correct identification of the presence of effects)}\label{table:no_effects}
\end{table}

\FloatBarrier

\printbibliography

redpajama_set_name: RedPajamaArXiv


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text:
Printed from https://ideas.repec.org/p/ewp/wpaper/329web.html
Generalized rationing problems and solutions
Pere Timoner Lledó
(Universitat de Barcelona)
Josep Maria Izquierdo Aznar
An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims on some amount of a scarce resource, but also by some exogenous ex-ante conditions (initial stock of resource or net worth of agents, for instance), different from claims. Within this framework, we define a generalization of the constrained equal awards rule. We provide two different characterizations of this generalized rule. Finally, we use the corresponding dual properties to characterize a generalization of the constrained equal losses rule
Pere Timoner Lledó & Josep Maria Izquierdo Aznar, 2015. "Generalized rationing problems and solutions," UB Economics Working Papers 2015/329, Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics.
Handle: RePEc:ewp:wpaper:329web
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Rationing; Equal awards rule; Equal losses rule; Ex-ante conditions; Claims problema.;
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
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