Machine learning

Fundamentals

Inference

Inference algorithms.

Computing the posterior distribution $p(\theta |\mathcal{D})$, where $\theta$ represents the unknown variables, and $\mathcal{D}$ represents the known variables.

Prediction

Models for prediction.

Conditional distributions of the form $p(\mathbf{y}|\mathbf{x})$, where $\mathbf{x}\in \mathcal{X}$ is some input (often high dimensional), and $\mathbf{y}\in \mathcal{Y}$ is the desired output (often low dimensional).

Generation

Models for generation.

Distributions of the form $p(\mathbf{x})$ or $p(\mathbf{x}|\mathbf{c})$, where $\mathbf{c}$ are optional conditioning inputs, and where there may be multiple valid inputs.

Discovery

Latent variable models.

Joint models of the form $p(\mathbf{z},\mathbf{x})=p(\mathbf{z})p(\mathbf{x}|\mathbf{z})$, where $\mathbf{z}$ is the hidden state, and $\mathbf{x}$ are the observations that are assumed to be generated from $\mathbf{z}$.

Action

Models and algorithms which can be used to make decisions under uncertainty.