In machine learning, entropic loss is a specific kind of loss function. A loss function measures the error between the predicted results and the desired results. Entropic loss uses the logistic function to show the error (or "loss") between the true answer and the predicted answer.

A general loss function is defined here:

Lφ= ∫ (φ(z) - y)dz, where the bounds of the integral are φ-1(y) (on the bottom) and φ-1(yhat) (on the top). yhat is the estimated (predicted) result, and y is the desired result.

The entropic loss function is defined here:

Lφ= ∫ (1/(1 + exp(-z)) - y)dz

As you can see, the entropic loss is a specific instance of a loss function. All I've done is I've chosen my loss function φ(z) to be the logistic function.

The logistic function is a common choice because it is a convex function, and therefore has only one local minimum (therefore it is also the global minimum). When we try to minimize loss, we want only one minimum so that when we set the derivative to zero, we know we've found what we want.

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