Regularization in Machine Learning

Regularization is a collection of techniques that can be used to prevent over-fitting(It could be memorizes relations and structures that are noise and coincidence). Regularization adds information to a problem often in the form of penalty against complexity, and it can be defined in different types of learning model like linear regression,Logistics regression and support vector machine etc.

Let suppose our linear equation is: y=ax+b where a=coefficient, b=intercept term, x=explanatory variable, y=predicted value

There are two different types of loss function:-(1)L1 (2) L2

L1 loss function is also known as Least absolute deviations(LAD), least absolute error(LAE). It is basically minimizing the sum of absolute difference(S) between the target value(Yi) and estimated value(f(xi)).

L2 loss function is also known as least square error(LSE).It is basically minimizing sum of square of difference(S), target value(Yi) and estimated value(f(xi)).

The difference between L1 and L2 just than L2 is the sum of the square of weight while L1 is the sum of the weight.

L1 regularization on least squares:

This equation is use for LASSO(Least Absolute Shrinkage and Selection Operators) implementation

1. LASSO adds penalty equivalent to absolute value of the magnitude of coefficients

2. LASSO Minimization objective = LS Obj + α * (sum of absolute value of coefficients)

1.a=0: Same coefficients  2. a= ∞: All coefficients zero and 3. 0 < a < ∞: between 0 and that of simple linear regression

L2 regularization on least squares:

 

This equation is use for Ridge regression  implementation.

1.  It adds penalty equivalent to square of the magnitude of coefficients.

2.  Ridge minimization objective = LS Obj + a * (sum of square of coefficients)

1.  a=0 : The objective becomes same as simple linear regression

2. a = ∞:The coefficients will be zero. Why? Because of infinite weightage on square of coefficients

3. 0 < a < ∞=The coefficients will be somewhere between 0 and ones for simple linear regression

 

 

Difference between Ridge and LASSO

  • Ridge regression produces models in which most parameters are small but nonzero but LASSO produces sparse parameters that is  most of the coefficients will become zero, and the model will depend on a small subset of the features.
  • When explanatory variables are correlated, the LASSO will shrink the coefficients of one variable toward zero but Ridge regression will shrink them more uniformly.
  • There is another technique know as Elastic-net which combines both L1 and L2 regularization to balance the advantages and disadvantages of L1 and L2.
About Mitra N Mishra 35 Articles
Mitra N Mishra is working as a full-stack data scientist.

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  187. After I initially commented I appear to have clicked on the -Notify me when new comments are added- checkbox and from now on each time a comment is added I receive 4 emails with the exact same comment. Is there a way you can remove me from that service? Thanks!

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  212. Can I just say what a comfort to find someone who genuinely knows what they’re discussing on the net. You certainly know how to bring an issue to light and make it important. More people should read this and understand this side of the story. I was surprised that you’re not more popular given that you definitely possess the gift.

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  224. Having read this I thought it was very enlightening. I appreciate you finding the time and energy to put this informative article together. I once again find myself personally spending way too much time both reading and leaving comments. But so what, it was still worth it!

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  228. May I simply say what a comfort to discover someone that genuinely understands what they’re discussing online. You certainly realize how to bring an issue to light and make it important. A lot more people have to look at this and understand this side of your story. I was surprised that you are not more popular since you definitely possess the gift.

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  235. I need to to thank you for this wonderful read!! I definitely enjoyed every little bit of it. I have got you bookmarked to look at new things you post…

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  237. The next time I read a blog, I hope that it does not disappoint me just as much as this one. After all, I know it was my choice to read, but I really believed you would probably have something interesting to talk about. All I hear is a bunch of crying about something that you could possibly fix if you were not too busy seeking attention.

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  239. Oh my goodness! Awesome article dude! Thank you so much, However I am experiencing issues with your RSS. I don’t understand the reason why I am unable to join it. Is there anybody getting similar RSS issues? Anyone who knows the answer will you kindly respond? Thanks!!

  240. After I initially commented I appear to have clicked on the -Notify me when new comments are added- checkbox and now whenever a comment is added I receive 4 emails with the exact same comment. Perhaps there is a way you are able to remove me from that service? Many thanks!

  241. The next time I read a blog, Hopefully it won’t disappoint me as much as this particular one. I mean, Yes, it was my choice to read, however I genuinely believed you would have something interesting to say. All I hear is a bunch of complaining about something you can fix if you were not too busy looking for attention.

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  247. Good post. I learn something totally new and challenging on blogs I stumbleupon on a daily basis. It will always be interesting to read content from other authors and practice something from other websites.

  248. I must thank you for the efforts you’ve put in writing this blog. I am hoping to see the same high-grade content from you later on as well. In truth, your creative writing abilities has encouraged me to get my very own website now 😉

  249. Nice post. I learn something new and challenging on websites I stumbleupon everyday. It’s always interesting to read articles from other authors and practice a little something from other websites.

  250. This is a really good tip especially to those fresh to the blogosphere. Short but very accurate information… Many thanks for sharing this one. A must read article!

  251. Having read this I believed it was very enlightening. I appreciate you taking the time and energy to put this informative article together. I once again find myself spending a lot of time both reading and posting comments. But so what, it was still worth it!

  252. Hi, I do believe this is an excellent website. I stumbledupon it 😉 I may return yet again since I saved as a favorite it. Money and freedom is the greatest way to change, may you be rich and continue to guide other people.

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  271. After I initially left a comment I appear to have clicked on the -Notify me when new comments are added- checkbox and now each time a comment is added I recieve 4 emails with the exact same comment. Is there a means you are able to remove me from that service? Appreciate it!

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  273. May I simply just say what a relief to find someone who really understands what they are talking about online. You definitely realize how to bring an issue to light and make it important. More and more people really need to look at this and understand this side of your story. I was surprised you aren’t more popular because you certainly possess the gift.

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  276. When I initially left a comment I appear to have clicked on the -Notify me when new comments are added- checkbox and now whenever a comment is added I receive four emails with the exact same comment. Perhaps there is a means you are able to remove me from that service? Appreciate it!

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  337. May I simply just say what a relief to uncover a person that truly understands what they’re talking about online. You certainly realize how to bring an issue to light and make it important. More and more people should look at this and understand this side of your story. I was surprised that you’re not more popular given that you surely have the gift.

  338. An outstanding share! I’ve just forwarded this onto a friend who has been conducting a little research on this. And he actually ordered me dinner simply because I discovered it for him… lol. So let me reword this…. Thank YOU for the meal!! But yeah, thanx for spending time to talk about this topic here on your blog.

  339. An intriguing discussion is worth comment. I do think that you should write more on this subject matter, it may not be a taboo matter but usually people do not discuss these issues. To the next! Best wishes!!

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  344. Having read this I believed it was very enlightening. I appreciate you taking the time and effort to put this information together. I once again find myself spending a lot of time both reading and commenting. But so what, it was still worthwhile!

  345. Can I simply say what a relief to discover a person that actually understands what they’re discussing on the web. You definitely understand how to bring a problem to light and make it important. More and more people really need to look at this and understand this side of the story. I was surprised that you’re not more popular since you definitely have the gift.

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  360. Your style is so unique in comparison to other people I have read stuff from. Thanks for posting when you’ve got the opportunity, Guess I’ll just book mark this web site.

  361. I would like to thank you for the efforts you have put in penning this blog. I’m hoping to view the same high-grade content from you in the future as well. In fact, your creative writing abilities has inspired me to get my very own website now 😉

  362. Hi, I do believe this is a great site. I stumbledupon it 😉 I’m going to come back yet again since i have bookmarked it. Money and freedom is the best way to change, may you be rich and continue to help others.

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  374. Oh my goodness! Impressive article dude! Thank you so much, However I am encountering issues with your RSS. I don’t understand the reason why I can’t join it. Is there anybody else getting identical RSS problems? Anybody who knows the solution can you kindly respond? Thanx!!

  375. I really love your site.. Great colors & theme. Did you develop this web site yourself? Please reply back as I’m attempting to create my very own website and would like to know where you got this from or exactly what the theme is called. Thanks!

  376. Aw, this was an incredibly nice post. Taking the time and actual effort to make a really good article… but what can I say… I hesitate a lot and don’t manage to get nearly anything done.

  377. Hi there, I believe your site could be having web browser compatibility issues. When I look at your web site in Safari, it looks fine however, when opening in Internet Explorer, it’s got some overlapping issues. I simply wanted to give you a quick heads up! Apart from that, excellent site!

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  379. I seriously love your website.. Excellent colors & theme. Did you build this amazing site yourself? Please reply back as I’m looking to create my own personal site and want to find out where you got this from or just what the theme is named. Thank you!

  380. I’m amazed, I must say. Seldom do I come across a blog that’s equally educative and engaging, and without a doubt, you have hit the nail on the head. The issue is something not enough folks are speaking intelligently about. I’m very happy that I found this in my hunt for something relating to this.