# gizai:ml/linear

linear models.

```gizlang
import * as Linear from "gizai:ml/linear";
```

## Types

### `Sgd`

```gizlang
type Sgd = { loss: string; rate: string; alpha: f64; l2: bool; eta0: f64; power: f64; cost: f64; epsilon: f64; maxIter: i64; tol: f64; patience: i64; }
```

Stochastic gradient descent as scikit-learn's _plain_sgd. loss: squared_error, hinge, perceptron,
epsilon_insensitive; rate: optimal, invscaling, constant, pa1 (passive-aggressive). y is ±1 for classification.

- `loss`: `string`
- `rate`: `string`
- `alpha`: `f64`
- `l2`: `bool`
- `eta0`: `f64`
- `power`: `f64`
- `cost`: `f64`
- `epsilon`: `f64`
- `maxIter`: `i64`
- `tol`: `f64`
- `patience`: `i64`

### `SgdState`

```gizlang
type SgdState = { w: Vec<f64>; b: f64; scale: f64; t: f64; init: f64; }
```

One SGD model as it learns: the weights (times `scale`), the intercept, the step count and the start of the optimal
rate.

- `w`: `Vec<f64>`
- `b`: `f64`
- `scale`: `f64`
- `t`: `f64`
- `init`: `f64`

## Functions

### `ridge`

```gizlang
function ridge(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, t: i64, alpha: f64, center: bool): Vec<f64>
```

Least squares (ridge when alpha > 0) of t targets: the minimum-norm solution, as LAPACK's lstsq gives it.

Effects: fail.

### `enetFit`

```gizlang
function enetFit(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, t: i64, alpha: f64, l1: f64, maxIter: i64, tol: f64): Vec<f64>
```

Elastic net coefficients (d by t, row-major) for the `t` targets of the centered data, one coordinate descent per target.

Effects: fail.

### `omp`

```gizlang
function omp(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, t: i64, atoms: i64): Vec<f64>
```

Orthogonal matching pursuit: the atom most correlated with the residual, then least squares on the chosen atoms.

Effects: fail.

### `bayesianRidge`

```gizlang
function bayesianRidge(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, maxIter: i64, tol: f64, a1: f64, a2: f64, l1: f64, l2: f64): Vec<f64>
```

Bayesian ridge regression (scikit-learn's evidence maximization in the eigenbasis of XᵀX).

Effects: fail.

### `ard`

```gizlang
function ard(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, maxIter: i64, tol: f64, threshold: f64, a1: f64, a2: f64, l1: f64, l2: f64): Vec<f64>
```

Automatic relevance determination (scikit-learn's ARDRegression).

Effects: fail.

### `sgdState`

```gizlang
function sgdState(s: Sgd, d: i64): SgdState
```

The starting state of SGD model `s` over `d` features: zero weights and its first learning rate.

Effects: fail.

### `sgdPass`

```gizlang
function sgdPass(s: Sgd, st: mut SgdState, x: Vec<f64>, d: i64, y: Vec<f64>, order: Vec<i64>): f64
```

One pass of SGD over rows `order` of x: the sum of their losses.

Effects: fail.

### `sgdWeights`

```gizlang
function sgdWeights(st: SgdState, d: i64): Vec<f64>
```

The `d` weights of state `st`, scaled, followed by its intercept.

Effects: fail.

### `sgd`

```gizlang
function sgd(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, s: Sgd, rng: mut Random): Vec<f64>
```

The weights then intercept that SGD model `s` learns from the `n` by `d` rows `x` and targets `y`, in `rng`'s order.

Effects: fail.

### `ransac`

```gizlang
function ransac(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, t: i64, trials0: i64, rng: mut Random): Vec<f64> throws string
```

RANSAC around least squares: the consensus of the most inliers within the median absolute deviation of y.

Effects: fail.

### `theilSen`

```gizlang
function theilSen(x: Vec<f64>, n: i64, d: i64, y: Vec<f64>, population: i64, maxIter: i64, tol: f64, rng: mut Random): Vec<f64>
```

Theil-Sen: the spatial median (modified Weiszfeld) of the exact fits of subsets of d + 1 rows.

Effects: fail.