Basic Concepts - DDA3020H Honors Machine Learning

Two Basic Paradigms¶

Paradigm	Data	Goal	Typical Tasks
Supervised Learning	Input–label pairs $\{(x_i, y_i)\}_{i=1}^n$	Learn a mapping $x \mapsto y$	Classification, Regression
Unsupervised Learning	Unlabeled feature vectors $\{x_i\}_{i=1}^n$	Discover underlying structure	Clustering, Dimensionality Reduction

Concept	Definition
Target function $t : \mathcal{X} \to \mathcal{Y}$	The unknown ground-truth mapping that generates the data: $y_i = t(x_i) + \text{noise}$ . We only observe finite data, not this function.
Hypothesis $h$	A candidate function used to approximate $t$ . Example: $h(x) = \theta_1 x_1 + \theta_2 x_2 = \boldsymbol{\theta}^\top x$ .
Hypothesis space $\mathcal{H}$	The set of all allowable hypotheses. Example: $\mathcal{H} = \{h_{\mathbf{w}}(x) = \mathbf{w}^\top x : \mathbf{w} \in \mathbb{R}^n\}$ .

Cost (objective) function: measures how well a hypothesis fits the training data. Using squared loss as an example:

J(h) = \frac{1}{n} \sum_{(x_i, y_i) \in \mathcal{D}_\text{train}} \bigl(h(x_i) - y_i\bigr)^2

Training (learning): find the best hypothesis in $\mathcal{H}$ by minimizing the cost on the training set (optimization):

h^* = \arg\min_{h \in \mathcal{H}} \frac{1}{n} \sum_{(x_i, y_i) \in \mathcal{D}_\text{train}} \bigl(h(x_i) - y_i\bigr)^2

Testing (evaluation): assess the performance of the learned model $h^*$ on the test set:

\text{Test error} = \frac{1}{m} \sum_{(x_i, y_i) \in \mathcal{D}_\text{test}} \bigl(h^*(x_i) - y_i\bigr)^2

Data collection: gather relevant historical data.
Data preprocessing: handle missing values, outliers, and data quality issues.
Model design: choose the hypothesis space $\mathcal{H}$ , objective function $J$ , and optimization method.
Training: learn model parameters from training data.
Testing: evaluate performance on unseen test data.
Model improvement: refine the model, features, or data to improve performance.

Paradigm	Description
Reinforcement Learning (RL)	An agent interacts with an environment over time, taking actions to maximize expected cumulative reward. At each step $t$ : observe state $s_t$ , take action $a_t$ , receive reward $r_t$ , transition to $s_{t+1}$ .
Semi-supervised learning	Learning from a mixture of labeled and unlabeled data, typically when labeled data is scarce.
Ensemble learning	Combining predictions from multiple models to obtain a final decision, often improving robustness and accuracy.
Transfer learning	Leveraging knowledge learned from a source domain to improve learning in a target domain, especially when target data is limited.
Federated learning	Training models across distributed clients using local data, sharing only model updates (not raw data) — privacy-preserving.
Machine unlearning	Removing the influence of specific training samples from a trained model, motivated by privacy and regulatory requirements.