bias variance decomposition for classification problem

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It is given that:

MSE = bias$^2$ + variance

I can see the mathematical relationship between MSE, bias, and variance. However, how do we understand the mathematical intuition of bias and variance for classification problems (we can't have MSE for classification tasks)?

I would like some help with the intuition and in understanding the mathematical basis for bias and variance for classification problems.

Any formula or derivation would be helpful.

IamTheRealFord

Posted 2019-06-19T12:59:00.703

Reputation: 81

I don't fully understand the question, what are you looking for exactly? – Djib2011 – 2019-06-19T13:32:08.263

oops sorry. Updated in the question itself. What to know mathematical intuition of bias variance for classification problem. Fore regression it has relation with MSE but classification how to relate them.? – IamTheRealFord – 2019-06-21T08:51:44.597

WHAT classification? Logit? – Peter – 2019-06-21T20:01:06.417

If you are looking for the concept, see https://datascience.stackexchange.com/questions/53758/math-behind-mse-bias2-variance and deeplearningbook.

– Fatemeh Asgarinejad – 2019-06-25T06:43:41.333

1ya already gone through that. But how will it work for classification problem.? (we dont have mse there know) – IamTheRealFord – 2019-06-25T07:17:25.747

I don't see why this was closed; the question seems pretty clear to me (after the June 25 edit anyway). MSE has a well-known bias-variance decomposition, so what about other (especially classification) losses? This doesn't depend on the specific model used. For a starting point, see https://stats.stackexchange.com/questions/393942/bias-variance-decomposition-for-non-squared-loss , but I haven't found a satisfactory answer for, e.g., log-loss.

– Ben Reiniger – 2019-06-29T13:57:32.623

yes i am puzzled why my question is put on hold :( – IamTheRealFord – 2019-06-30T14:17:49.600

Answers

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My opinion is that the bias variance trade off is rooted in the Uncertainty principle. It behaves absolutely the same.

Eugen

Posted 2019-06-19T12:59:00.703

Reputation: 445

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yes. I am currently reading this to decompose bias-variance for general loss function. http://www-bcf.usc.edu/~gareth/research/bv.pdf.. Also searching(both intuition and mathematically) why decreasing bias increases variance and vice versa!

– IamTheRealFord – 2019-06-25T11:13:54.000

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Bias and Variance in Classification problems

Check this link about Support Vector Machine.

You will directly understand bias and variance in classification. Basically, if your data is linearly separable you do not have a problem.

But imagine that your data is pseudo/semi linearly separable, however, few points land on the other side of their group.

Now imagine having a model that separates the data linearly, vs a model that will oscillate through the data so much to be able to classify correctly every point.

biasvariance

Additional link

ombk

Posted 2019-06-19T12:59:00.703

Reputation: 101