A short introduction about machine learning.

# Type of machine learning (ML)

## Predictive/ supervised learning

**Goal**: learn a mapping from inputs $x$ to outputs $y$, given a labeled set of input-output pairs , a.k.a.**training set**.**Conditional density estimation**, i.e. build models for### Classification

a.k.a. pattern recognition.- Binary classification
- Multi-class classification
- Multi-label classification (viewed as doing multiple binary predictions)

The **mode** of the distribution , a.k.a. **MAP (maximum a posteriori) estimate**:

- Given a probabilistic output, compute the “best guess” as to the “true label”:

### Regression

## Descriptive/ unsupervised learning

**Goal**: Only given inputs , find “interesting patterns” in the data (a.k.a.*knowledge discovery*).**Unconditional density estimation**, i.e. build models for

Popular deep unsupervised generative models:

- GANs
- VAEs
- Fully visible belief networks (FVBN)

### Discovering clusters

**Dimension reduction**: Clustering data into groups. Let $K$ denote the number of clusters, we estimate the distribution over the number of clusters, $P(K|\mathscr{D})$, which tells us if there are subpopulations within the data.

### Discovering latent factors

Reduce the dimensionality by projecting the data to a lower dimensional subspace which captures the “essence” of the data.

### Discovering graph structure

Measure a set of correlated variables, discover which ones are most correlated with which others. We learn the graph structure from the data, i.e. compute .

### Matrix completion

Missing data (**NaN**, “not a number”) completion.

#### Image inpainting

“Fill in” holes in an image with realistic texture. This can be tackled by building a joint probability model of the pixels, given a set of clean images, and then inferring the unknown variables (pixels) given the known variables (pixels).

#### Collaborative filtering

Key idea: the prediction is not based on features of the movie or user (although it could be), but merely on a ratings matrix $\mathbf{X}(m,u)$ with user $u$ of movie $m$.

#### Market basket analysis

## Reinforcement learning

**Goal**: learn how to act / behave when given occasional reward or punishment signals (e.g. how a baby learns to walk).

# Basic ML concepts

## Parametric v.s. non-parametric models

### Parametric models

- Models have a fixed number of parameters.
- Cons: strong assumptions about the nature of the data distributions.

### Non-parametric models

- The number of model parameters grow with the amount of training set.
- Example: $K$-nearest neighbor classifier
- The
**curse of dimensionality**