Multinomial Logistic Regression › Visualizing Multinomial Logistic Regression

Michael BrenndoerferJune 15, 20254 min read
Machine Learning from ScratchAll chapters
Part 4 of 9Regression Models
Chapter 38Multinomial Logistic Regression › Visualizing Multinomial Logistic Regression
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Let's create visualizations to understand how multinomial logistic regression works with different numbers of categories and how the decision boundaries are formed.

Out[4]:
Visualization
Decision boundary plot showing regions for different classes in multinomial logistic regression.
Decision boundaries in multinomial logistic regression showing how the model partitions the feature space into regions corresponding to each class. Each colored region represents where the model predicts that class with highest probability.
Out[5]:
Visualization
Contour plot showing probability surfaces for different classes in multinomial logistic regression.
Class probability surfaces demonstrating how multinomial logistic regression assigns probabilities to each class across the feature space. The overlapping contours show how probabilities transition smoothly between classes, with all probabilities summing to one at every point.
Out[6]:
Visualization
S-shaped curves showing class probabilities vs predictor variable.
Class probabilities as a function of a single predictor variable. The probabilities sum to one by construction.
Linear plots showing log-odds relationships for different classes.
Log-odds relationships showing the linear dependence on predictor variables. The log-odds of each class relative to the reference class (Class 2) are linear functions of the predictor, which is the basic assumption of multinomial logistic regression.