GaussianProcessRegressor

Defined in: ml/estimators/GaussianProcessRegressor.js:246

Extends

• Regressor

Constructors

Constructor

new GaussianProcessRegressor(opts?): GaussianProcessRegressor

Defined in: ml/estimators/GaussianProcessRegressor.js:264

Parameters

opts?

Options

alpha

number | number[]

KNOWN observation noise added to the diagonal of K (default: 1e-10). A scalar applies the same noise to every point (homoscedastic); an array of length n gives a per-observation noise variance (heteroscedastic). Never tuned by optimize — to LEARN a noise level, add a WhiteKernel to the kernel instead. Same split as scikit-learn. Can also be supplied per-fit via fit(X, y, { alpha }).

kernel

string | Kernel

Kernel instance or type (‘rbf’, ‘periodic’, ‘rational_quadratic’)

lengthScale

number

Length scale for kernel (default: 1.0)

noiseLevel

number | number[]

Alias for alpha

normalizeY

boolean

Standardize the target (center + scale to unit variance) before fitting; predictions, std, covariance and posterior samples are back-transformed. Alias: normalize_y (default: false)

period

number

Period for periodic kernel

variance

number

Signal variance (default: 1.0)

Returns

GaussianProcessRegressor

Overrides

Regressor.constructor

Properties

_alphaDiag

_alphaDiag: number[]

Defined in: ml/estimators/GaussianProcessRegressor.js:336

---

_alphaVector

_alphaVector: number[] | number[][]

Defined in: ml/estimators/GaussianProcessRegressor.js:333

---

_L

_L: Matrix

Defined in: ml/estimators/GaussianProcessRegressor.js:332

---

_predictAD

_predictAD: object

Defined in: ml/estimators/GaussianProcessRegressor.js:440

meanFn

meanFn: any

stdFn

stdFn: any

---

_seed

_seed: any

Defined in: ml/estimators/GaussianProcessRegressor.js:327

---

_state

_state: object

Defined in: core/estimators/estimator.js:27

Inherited from

Regressor._state

---

_warnings

_warnings: any[]

Defined in: core/estimators/estimator.js:29

Inherited from

Regressor._warnings

---

_XTrain

_XTrain: Matrix

Defined in: ml/estimators/GaussianProcessRegressor.js:330

---

_yMean

_yMean: number

Defined in: ml/estimators/GaussianProcessRegressor.js:315

---

_yStd

_yStd: number

Defined in: ml/estimators/GaussianProcessRegressor.js:316

---

_yTrain

_yTrain: any[] | number[]

Defined in: ml/estimators/GaussianProcessRegressor.js:331

---

alpha

alpha: number | number[]

Defined in: ml/estimators/GaussianProcessRegressor.js:307

---

fitted

fitted: boolean

Defined in: core/estimators/estimator.js:25

Inherited from

Regressor.fitted

---

kernel

kernel: RBF | Kernel | Periodic | RationalQuadratic | Matern | ConstantKernel

Defined in: ml/estimators/GaussianProcessRegressor.js:269

---

logMarginalLikelihood_

logMarginalLikelihood_: number

Defined in: ml/estimators/GaussianProcessRegressor.js:337

---

normalizeY

normalizeY: any

Defined in: ml/estimators/GaussianProcessRegressor.js:314

---

nRestarts

nRestarts: any

Defined in: ml/estimators/GaussianProcessRegressor.js:326

---

optimize

optimize: boolean

Defined in: ml/estimators/GaussianProcessRegressor.js:323

---

params

params: any

Defined in: core/estimators/estimator.js:24

Inherited from

Regressor.params

Methods

_computePosteriorCovariance()

_computePosteriorCovariance(XTest, KStar): object

Defined in: ml/estimators/GaussianProcessRegressor.js:974

Parameters

XTest

any

KStar

any

Returns

object

covarianceMatrix

covarianceMatrix: any

diag

diag: any[]

---

_prepareArgsForFit()

_prepareArgsForFit(args?): { columns?: undefined; columnsX: any[]; prepared: boolean; raw?: undefined; rows: any[]; X: any[][]; y: any[]; } | { columns: any[]; columnsX?: undefined; prepared: boolean; raw?: undefined; rows: any[]; X: any[][]; y?: undefined; } | { columns?: undefined; columnsX?: undefined; prepared?: undefined; raw: any[]; rows?: undefined; X?: undefined; y?: undefined; }

Defined in: core/estimators/estimator.js:367

Convenience helper: parse arguments passed to fit/predict/transform.

Supports declarative table-style inputs:

• fit({ X, y, data, omit_missing })
• fit({ data, columns, … })

Returns an object { X, y, prepared, rows } where X/y are numeric arrays if preparation was required, otherwise returns the original values.

Note: this helper only prepares numeric matrices/vectors using core table utilities; it does not perform encoding of categorical predictors.

Parameters

args?

any[] = []

Returns

{ columns?: undefined; columnsX: any[]; prepared: boolean; raw?: undefined; rows: any[]; X: any[][]; y: any[]; } | { columns: any[]; columnsX?: undefined; prepared: boolean; raw?: undefined; rows: any[]; X: any[][]; y?: undefined; } | { columns?: undefined; columnsX?: undefined; prepared?: undefined; raw: any[]; rows?: undefined; X?: undefined; y?: undefined; }

Inherited from

Regressor._prepareArgsForFit

---

_r2()

_r2(yTrue, yPred): number

Defined in: core/estimators/estimator.js:489

Parameters

yTrue

any

yPred

any

Returns

number

Inherited from

Regressor._r2

---

_repr_html_()

_repr_html_(): string

Defined in: core/estimators/estimator.js:201

Observable/Jupyter HTML representation

Returns

string

HTML representation

Inherited from

Regressor._repr_html_

---

clearWarnings()

clearWarnings(): void

Defined in: core/estimators/estimator.js:139

Clear all warnings

Returns

void

Inherited from

Regressor.clearWarnings

---

fit()

fit(X, y?, opts?): GaussianProcessRegressor

Defined in: ml/estimators/GaussianProcessRegressor.js:356

Fit the GP to training data

Parameters

X

any

Training inputs (n samples × d features), or a declarative spec { X, columns, y, data, omit_missing, alpha }

y?

number[] = null

Training targets (n)

opts?

Options

alpha?

number | number[]

Known observation noise, overriding the constructor’s. A scalar is added uniformly to the diagonal of K; an array of length n gives each observation its own noise variance (heteroscedastic regression), matching sklearn’s array-valued alpha. Use it for measurements of unequal reliability — a poll’s sampling variance, a sensor’s per-reading error — instead of pretending they all carry the same noise. It is never tuned by optimize; for a noise level to be learned, put a WhiteKernel in the kernel instead.

Returns

GaussianProcessRegressor

The fitted estimator (for chaining)

Overrides

Regressor.fit

---

getMemoryUsage()

getMemoryUsage(): string

Defined in: core/estimators/estimator.js:97

Get memory usage in human-readable format

Returns

string

Memory usage string (e.g., “2.3 MB” or “145 KB”)

Inherited from

Regressor.getMemoryUsage

---

getParams()

getParams(): any

Defined in: core/estimators/estimator.js:294

Get a shallow copy of parameters.

Returns

any

Inherited from

Regressor.getParams

---

getState()

getState(): any

Defined in: core/estimators/estimator.js:65

Get comprehensive model state

Returns

any

State information including fitted status, memory estimate, warnings

Inherited from

Regressor.getState

---

getWarnings()

getWarnings(): any[]

Defined in: core/estimators/estimator.js:124

Get all warnings

Returns

any[]

Array of warning objects

Inherited from

Regressor.getWarnings

---

getWarningsByType()

getWarningsByType(type): any[]

Defined in: core/estimators/estimator.js:148

Get warnings of a specific type

Parameters

type

string

Warning type

Returns

any[]

Filtered warnings

Inherited from

Regressor.getWarningsByType

---

hasWarnings()

hasWarnings(): boolean

Defined in: core/estimators/estimator.js:132

Check if model has warnings

Returns

boolean

Inherited from

Regressor.hasWarnings

---

isFitted()

isFitted(): boolean

Defined in: core/estimators/estimator.js:36

Check if model is fitted

Returns

boolean

Inherited from

Regressor.isFitted

---

logMarginalLikelihood()

logMarginalLikelihood(): number

Defined in: ml/estimators/GaussianProcessRegressor.js:457

Log marginal likelihood of the training data under the current hyperparameters: log p(y|X) = -½ yᵀK⁻¹y - ½ log|K| - n/2 log(2π). Requires the model to have seen training data (via fit).

Returns

number

---

predict()

predict(X, opts?): number[] | { covariance?: number[][]; mean: number[]; std?: number[]; }

Defined in: ml/estimators/GaussianProcessRegressor.js:787

Predict at test points

Parameters

X

number[][]

Test inputs (m samples × d features)

opts?

Options

returnCov?

boolean

Return the full posterior covariance

returnStd?

boolean

Return per-point standard deviations

Returns

number[] | { covariance?: number[][]; mean: number[]; std?: number[]; }

Predicted means, or an object with mean and std/covariance when requested

Overrides

Regressor.predict

---

predictGradient()

predictGradient(x): object

Defined in: ml/estimators/GaussianProcessRegressor.js:849

The predictive mean and standard deviation at ONE input, with their gradients with respect to that input.

What a gradient-based search over the input space needs, where predict gives the value only. Maximizing a lower confidence bound over an ionome, say, is a smooth problem in a dozen dimensions; a quasi-Newton method with this gradient converges in tens of evaluations where a derivative-free simplex needs thousands and grows unreliable past ten dimensions.

The mean is k(x, X)·α and the variance k(x, x) − ‖L⁻¹k(x, X)‖²; both are written in @tangent.to/grad ops with x as the variable and everything the fit produced as constants, compiled once per fit and replayed per call. Stationary kernels only (RBF, Matérn, White, Constant and sums), so that k(x, x) is a constant. normalizeY is undone as in predict.

Parameters

x

number[]

one input, length d

Returns

object

mean

mean: number

meanGradient

meanGradient: number[]

std

std: number

stdGradient

stdGradient: number[]

---

sample()

sample(X, nSamples?, seed?): any[][]

Defined in: ml/estimators/GaussianProcessRegressor.js:886

Sample from the posterior distribution

Parameters

X

any[]

Test inputs

nSamples?

number = 1

Number of samples

seed?

number = null

Random seed for reproducibility

Returns

any[][]

Array of samples

---

samplePrior()

samplePrior(X, nSamples?, seed?): any[][]

Defined in: ml/estimators/GaussianProcessRegressor.js:923

Sample from the prior (unfitted GP)

Parameters

X

any[]

Input points

nSamples?

number = 1

Number of samples

seed?

number = null

Random seed for reproducibility

Returns

any[][]

Array of samples

---

save()

save(): string

Defined in: core/estimators/estimator.js:329

Save model to JSON string

Returns

string

JSON representation of the model

Inherited from

Regressor.save

---

score()

score(yTrueOrOpts, yPred, _opts?, …args?): number

Defined in: core/estimators/estimator.js:461

Default R^2 scoring implementation: 1 - SS_res / SS_tot

Accepts either:

• arrays: score(yTrue, yPred)
• table-style: score({ X, y, data }) where predict will be called internally

Parameters

yTrueOrOpts

any

yPred

any

_opts?

args?

…any[] = {}

Returns

number

Inherited from

Regressor.score

---

setParams()

setParams(params?): GaussianProcessRegressor

Defined in: core/estimators/estimator.js:285

Set parameters (mutates instance).

Parameters

params?

any = {}

Returns

GaussianProcessRegressor

Inherited from

Regressor.setParams

---

toJSON()

toJSON(): object

Defined in: ml/estimators/GaussianProcessRegressor.js:1037

Serialize minimal model metadata. Subclasses may override to include learned parameters.

Returns

object

alpha

alpha: number | number[]

alphaVector

alphaVector: number[] | number[][]

fitted

fitted: boolean

kernel

kernel: object

kernel.params

params: any

kernel.type

type: string

L

L: any

normalizeY

normalizeY: any

type

type: string = 'GaussianProcessRegressor'

XTrain

XTrain: any

yMean

yMean: number

yStd

yStd: number

yTrain

yTrain: any[] | number[]

Overrides

Regressor.toJSON

---

transform()

transform(): void

Defined in: core/estimators/estimator.js:431

Transform should be implemented by transformers.

Returns

void

Inherited from

Regressor.transform

---

fromJSON()

static fromJSON(json): GaussianProcessRegressor

Defined in: ml/estimators/GaussianProcessRegressor.js:1058

Basic deserialization. Subclasses should override if they need to restore learned arrays / matrices.

Parameters

json

any

Returns

GaussianProcessRegressor

Overrides

Regressor.fromJSON

---

load()

static load(jsonString): Estimator

Defined in: core/estimators/estimator.js:346

Load model from JSON string

Parameters

jsonString

string

JSON representation

Returns

Estimator

Reconstructed estimator instance

Inherited from

Regressor.load