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Logistic Regression Cost Function
For labeled training examples, the logistic regression cost is the average binary cross-entropy loss: Thus, aggregates the losses across the training set and is nonnegative. With , this cost is convex in the parameters and .
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A machine learning model is trained for a binary classification task where the goal is to predict a label
y(either 0 or 1). The model's prediction,ŷ, is a probability between 0 and 1. The performance on a single example is measured using the loss function:L(ŷ, y) = -(y*log(ŷ) + (1 - y)*log(1 - ŷ)).Consider two scenarios for an example where the true label
yis 1:- Scenario A: The model predicts
ŷ = 0.9. - Scenario B: The model predicts
ŷ = 0.1.
Which scenario results in a hig
- Scenario A: The model predicts
When training a logistic regression model for binary classification, the standard approach is to use the logarithmic loss function:
L(ŷ, y) = -(y*log(ŷ) + (1 - y)*log(1 - ŷ)). An alternative could be the squared error loss:L(ŷ, y) = (ŷ - y)². What is the primary reason the logarithmic loss is preferred for this task?Calculating Loss for a Single Prediction
Logistic Regression Gradient Descent Derivation
Logistic regression loss function vs. cost function
Logistic Regression Cost Function