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.

  • $\begingroup$ I don't fully understand the question, what are you looking for exactly? $\endgroup$
    – Djib2011
    Jun 19, 2019 at 13:32
  • $\begingroup$ 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.? $\endgroup$ Jun 21, 2019 at 8:51
  • $\begingroup$ WHAT classification? Logit? $\endgroup$
    – Peter
    Jun 21, 2019 at 20:01
  • $\begingroup$ If you are looking for the concept, see datascience.stackexchange.com/questions/53758/… and deeplearningbook. $\endgroup$ Jun 25, 2019 at 6:43
  • 1
    $\begingroup$ ya already gone through that. But how will it work for classification problem.? (we dont have mse there know) $\endgroup$ Jun 25, 2019 at 7:17

1 Answer 1


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.


Additional link

  • $\begingroup$ This answer addresses the mathematically imprecise "bias-variance tradeoff", but not the mathematically precise "bias-variance decomposition" (which is well-known for MSE but not, to my knowledge, for other losses including common classification ones). $\endgroup$
    – Ben Reiniger
    Sep 12, 2022 at 1:31

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