1. Score → probability → decision
Manipulate a logistic model’s bias and weight. See how the same linear score creates a probability curve, how weight magnitude controls confidence, and how the 0.5 decision boundary stays linear.
Open activity2. Train logistic regression by hand
Step through gradient descent on a 2-D classification problem. Watch cross-entropy, the decision boundary, and individual point losses change together.
Open activity3. Generative vs. discriminative
Fit Gaussian Naïve Bayes and logistic regression to the same samples. Vary sample size and violate the generative assumptions to see why the two methods can win in different regimes.
Open activity4. Geometry of a linear discriminant
Rotate the weight vector, move the bias, and move a point. See the boundary stay perpendicular to w and verify the signed distance y(x)/||w||.
Open activity5. Fisher projection explorer
Rotate a projection axis and observe projected class distributions. Compare mean separation alone with Fisher’s ratio of between-class to within-class spread.
Open activity6. Multiclass linear discriminants
Three linear score functions partition the plane. Move the query point and edit class biases to see argmax decisions, pairwise boundaries, and convex decision regions.
Open activity7. Perceptron: learn from mistakes
Step one example at a time. Every mistake visibly changes w and b. Switch among easy, small-margin, noisy, and XOR data to see when convergence should or should not happen.
Open activity8. Feature lifting solves what a line cannot
Use XOR and rings. Add nonlinear features such as x₁x₂ or x₁²+x₂² and watch a problem become linearly separable in the transformed feature space.
Open activity