In this video we discuss why the mean squared error (MSE) loss is not used for classification problems. We take a look at three important aspects: (1) the MSE assumes a gaussian prior, (2) the MSE applied on classification problems results in a non-convex function and (3) the MSE doesn’t penalise well enough the errors in classification compared to the binary cross entropy loss function.

*References*
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Gaussian distribution explained: https://youtu.be/UVvuwv-ne1I
Binary cross entropy prior for Bernoulli distribution: https://towardsdatascience.com/where-did-the-binary-cross-entropy-loss-function-come-from-ac3de349a715
Demonstration that the binary cross entropy loss for classification is convex: https://towardsdatascience.com/why-not-mse-as-a-loss-function-for-logistic-regression-589816b5e03c

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Bias variance Trade-off: https://youtu.be/5mbX6ITznHk
Neural networks on tabular data: https://youtu.be/e62CBva4TYc
Why we divide by N-1 in the sample variance: https://youtu.be/E3_408q1mjo

*Contents*
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00:00 – Intro – MSE for classification
01:12 – Reason 1 – MSE assumes a gaussian prior
04:15 – Reason 2 – MSE non-convexity
08:03 – Reason 3 – MSE weak penalisation
08:42 – Outro

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