Why mean square error is not used as a cost function for logistic regression?

Mean Squared Error, commonly used for linear regression models, isn’t convex for logistic regression. This is because the logistic function isn’t always convex. The logarithm of the likelihood function is however always convex.

Can we use MSE for multi class classification?

Here we have shown that MSE is not a good choice for binary classification problems. But the same can be extended for multi-class classification problems given that target values are one-hot encoded.

Can you use RMSE for classification?

A small RMSE means good prediction and large means bad model. In classification, you have (finite and countable) class labels, which do not correspond to numbers. Therefore you can not use RMSE because it is difficult to find difference between, say, label ‘a’ and ‘b’.

Why use cross entropy instead of MSE?

First, Cross-entropy (or softmax loss, but cross-entropy works better) is a better measure than MSE for classification, because the decision boundary in a classification task is large (in comparison with regression). For regression problems, you would almost always use the MSE.

Is mean squared error a convex function?

Answer in short: MSE is convex on its input and parameters by itself. But on an arbitrary neural network it is not always convex due to the presence of non-linearities in the form of activation functions.

Why is MSE used?

MSE is used to check how close estimates or forecasts are to actual values. Lower the MSE, the closer is forecast to actual. This is used as a model evaluation measure for regression models and the lower value indicates a better fit.

When would you use the categorical cross-entropy loss and the mean squared error?

Cross-entropy loss, or log loss, measure the performance of a classification model whose output is a probability value between 0 and 1. It is preferred for classification, while mean squared error (MSE) is one of the best choices for regression. This comes directly from the statement of your problems itself.