Is loss function of logistic regression convex?
Now we mathematically show that the MSE loss function for logistic regression is non-convex. For simplicity, let’s assume we have one feature “x” and “binary labels” for a given dataset.
Is loss function always convex?
Fortunately, hinge loss, logistic loss and square loss are all convex functions. Convexity ensures global minimum and it’s computationally appleaing.
Why mean square error is not used in 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.
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.
Is the log loss function convex for logistic regression?
We will mathematically show that log loss function is convex for logistic regression. Theta: co-efficient of independent variable “x”. As seen in the final expression (double derivative of log loss function) the squared terms are always ≥0 and also, in general, we know the range of e^x is (0, infinity).
Which is a better loss function MSE or log-loss?
Equations for both the loss functions are as follows: Let’s say we have a dataset with 2 classes (n = 2) and the labels are represented as “0” and “1”. Now we compute the loss value when there is a complete mismatch between predicted values and actual labels and get to see how log-loss is better than MSE.
When to use loss function in linear regression?
Decision boundary can be described as: Predict 1, if θᵀx ≥ 0 → h (x) ≥ 0.5; Predict 0, if θᵀx < 0 → h (x) < 0.5. 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. However, it’s not an option for logistic regression anymore.