# bias variance decomposition for classification problem

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.

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

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

• yes. I am currently reading this to decompose bias-variance for general loss function. www-bcf.usc.edu/~gareth/research/bv.pdf.. Also searching(both intuition and mathematically) why decreasing bias increases variance and vice versa! – IamTheRealFord Jun 25 '19 at 11:13

Bias and Variance in Classification problems