Why we dont use MSE in logistic regression?

Why we dont use MSE in 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.

Why is MSE not good for classification?

There are two reasons why Mean Squared Error(MSE) is a bad choice for binary classification problems: If we use maximum likelihood estimation(MLE), assuming that the data is from a normal distribution(a wrong assumption, by the way), we get the MSE as a Cost function for optimizing our model.

What is MSE in logistic regression?

Mean Square Error (MSE) is the most commonly used regression loss function. MSE is the sum of squared distances between our target variable and predicted values. Below is a plot of an MSE function where the true target value is 100, and the predicted values range between -10,000 to 10,000.

Why can we directly use a cost function like least square error in logistic regression?

Cost Function Linear regression uses Least Squared Error as loss function that gives a convex graph and then we can complete the optimization by finding its vertex as global minimum. The loss function of logistic regression is doing this exactly which is called Logistic Loss . See as below.

What are the advantages of logistic regression?

Logistic regression is easier to implement, interpret, and very efficient to train. If the number of observations is lesser than the number of features, Logistic Regression should not be used, otherwise, it may lead to overfitting. It makes no assumptions about distributions of classes in feature space.

What is the difference between MSE and RMSE?

The MSE has the units squared of whatever is plotted on the vertical axis. The RMSE is directly interpretable in terms of measurement units, and so is a better measure of goodness of fit than a correlation coefficient. One can compare the RMSE to observed variation in measurements of a typical point.

Why cross-entropy loss is better than 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.

Can you use MSE for logistic regression?

One of the main reasons why MSE doesn’t work with logistic regression is when MSE loss function is plotted with respect to weights of the logistic regression model, the curve obtained is not a convex curve which makes it very difficult to find the global minimum.

Can you use MSE for classification?

Technically you can, but the MSE function is non-convex for binary classification. Thus, if a binary classification model is trained with MSE Cost function, it is not guaranteed to minimize the Cost function.

What are the disadvantages of logistic regression?

The major limitation of Logistic Regression is the assumption of linearity between the dependent variable and the independent variables. It not only provides a measure of how appropriate a predictor(coefficient size)is, but also its direction of association (positive or negative).

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 do we use Mle instead of logistic regression?

However there are number of reasons why MLE is a more attractive option. In addition to those in the comments, here are two more: Because the likelihood function of a logistic regression model is a member of the exponential family, we can use Fisher’s Scoring algorithm to efficiently solve for β.

How to calculate RMSE for a logistic regression?

To understand why ” [t]he response is either 0 or 1 [but] the predictions are probabilities between 0 – 1 “, you need to understand the type of model you are working with. Strip away the penalization methods and the cross validation, and you are running a basic logistic regression. The parameters are fit on the log odds / logistic scale.

Why not use the same cost function for logistic regression?

When watching the machine learning course on Coursera by Andrew Ng, in the logistic regression week, the cost function was a bit more complex than the one for linear regression, but definitely not that hard. But it got me thinking, why not use the same cost function for logistic regression?