Logistic regression loss function vs. cost function
For logistic regression, the loss function measures the error for one training example. The cost function aggregates these losses across all training examples, typically by taking their average: .
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Logistic Regression Cost Function
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
True or False: The cost function for logistic regression trained with m≥1 examples is always greater than or equal to zero.
Logistic regression loss function vs. cost function