Which is better log loss or mean squared error?

Which is better log loss or mean squared error?

In this blog post, we mainly compare “ log loss ” vs “mean squared error” for logistic regression and show that why log loss is recommended for the same based on empirical and mathematical analysis. Equations for both the loss functions are as follows:

Can a mean squared error function be negative?

A standard Mean Squared Error function cannot be negative. The lowest possible value is 0, when there is no output error from any example input. How can our cost function which is mean squared error have a value under 0? It cannot.

Which is the root mean squared error in regression?

Root Mean Squared Error (RMSE): The only issue with MSE is that the order of loss is more than that of the data. As my data is of order 1 and the loss function, MSE has an order of 2. So we cannot directly correlate data with the error. Hence, we take the root of the MSE — which is the Root Mean Squared Error:

What is the mean square error for point 3?

For point 3 the error is negative as predicted value is lower. Whereas for point 1, the error is positive and of almost the same magnitude. For point 2 it is 0. Adding all of these up would lead to a total error of 0! But the error is certainly much more than that.

Why is MSE not convex in logistic regression?

Hence if the loss function is not convex, it is not guaranteed that we will always reach the global minima, rather we might get stuck at local minima. Before diving deep into why MSE is not a convex function when used in logistic regression, first, we will see what are the conditions for a function to be convex.

Why is mean squared error ( MSE ) a convex function?

In the below image f (x) = MSE and ŷ is the predicted value obtained after applying sigmoid function. From the above equation, ŷ * (1 – ŷ) lies between [0, 1]. Hence we have to check that if H (ŷ) is positive for all values of “x” or not, to be a convex function. We know that y can take two values 0 or 1.

How to write error term for logistic regression?

The only thing one might be able to consider in terms of writing an error term would be to state: y i = g − 1 ( α + x i T β) + e i where E ( e i) = 0 and V a r ( e i) = σ 2 ( μ i). For example, for logistic regression, σ 2 ( μ i) = μ i ( 1 − μ i) = g − 1 ( α + x i T β) ( 1 − g − 1 ( α + x i T β)).