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Types of Learning: Output Space, Labels, Protocol, and Input Space | NTU Hsuan-Tien Lin Machine Learning Foundations Lecture 3

This lecture takes the learning flow diagram from Lecture 1 and swaps one part at a time along four directions: the output space Y (binary classification, multiclass classification, regression, structured learning), the labels yₙ (supervised, unsupervised, semi-supervised, reinforcement learning), the way data reaches the algorithm (batch, online, active), and the input space X (concrete, raw, abstract features). Each direction has one core option, and together they mark the home ground for the rest of Foundations: batch, supervised binary classification and regression on concrete features.

Nonlinear Transformation: The Price of Curved Boundaries | NTU Hsuan-Tien Lin Machine Learning Foundations Lecture 12

When no straight line separates the data, you do not need to redesign the algorithm: use a feature transform Φ to turn x into z, run a linear model in Z-space as usual, and the line in Z-space is a quadratic or higher-order curve in X-space. The Q-th order polynomial transform raises the dimension to d̃ = C(Q+d, d) − 1, and computation, storage, and the VC dimension (at most d̃+1) all grow with it, so the lecture concludes that you should try the linear model first and move to higher orders only when it is not enough.

Trading Expressiveness for Stability with Features and Regularization | CMU 07-280 Lecture 10

Lecture 10 uses φ(x) to let linear models express nonlinear functions, then controls the resulting overfitting with train/validation/test separation, L1/L2 regularization, and model selection.