Matern
Matern kernel.
The class of Matern kernels is a generalization of the RBF. It has an additional parameter \(\nu\) which controls the smoothness of the resulting function. The smaller \(\nu\), the less smooth the approximated function is. As \(\nu\rightarrow\infty\), the kernel becomes equivalent to the RBF kernel. When \(\nu = 1/2\), the Matérn kernel becomes identical to the absolute exponential kernel. Important intermediate values are \(\nu=1.5\) (once differentiable functions) and \(\nu=2.5\) (twice differentiable functions).
The kernel is given by:
Python Reference (opens in a new tab)
Constructors
constructor()
Signature
new Matern(opts?: object): Matern;Parameters
| Name | Type | Description |
|---|---|---|
opts? | object | - |
opts.length_scale? | number | ArrayLike | The length scale of the kernel. If a float, an isotropic kernel is used. If an array, an anisotropic kernel is used where each dimension of l defines the length-scale of the respective feature dimension. Default Value 1 |
opts.length_scale_bounds? | "fixed" | The lower and upper bound on ‘length_scale’. If set to “fixed”, ‘length_scale’ cannot be changed during hyperparameter tuning. |
opts.nu? | number | The parameter nu controlling the smoothness of the learned function. The smaller nu, the less smooth the approximated function is. For nu=inf, the kernel becomes equivalent to the RBF kernel and for nu=0.5 to the absolute exponential kernel. Important intermediate values are nu=1.5 (once differentiable functions) and nu=2.5 (twice differentiable functions). Note that values of nu not in [0.5, 1.5, 2.5, inf] incur a considerably higher computational cost (appr. 10 times higher) since they require to evaluate the modified Bessel function. Furthermore, in contrast to l, nu is kept fixed to its initial value and not optimized. Default Value 1.5 |
Returns
Defined in: generated/gaussian_process/kernels/Matern.ts:25 (opens in a new tab)
Methods
__call__()
Return the kernel k(X, Y) and optionally its gradient.
Signature
__call__(opts: object): Promise<ArrayLike[]>;Parameters
| Name | Type | Description |
|---|---|---|
opts | object | - |
opts.X? | ArrayLike[] | Left argument of the returned kernel k(X, Y) |
opts.Y? | ArrayLike[] | Right argument of the returned kernel k(X, Y). If undefined, k(X, X) if evaluated instead. |
opts.eval_gradient? | boolean | Determines whether the gradient with respect to the log of the kernel hyperparameter is computed. Only supported when Y is undefined. Default Value false |
Returns
Promise<ArrayLike[]>
Defined in: generated/gaussian_process/kernels/Matern.ts:122 (opens in a new tab)
clone_with_theta()
Returns a clone of self with given hyperparameters theta.
Signature
clone_with_theta(opts: object): Promise<any>;Parameters
| Name | Type | Description |
|---|---|---|
opts | object | - |
opts.theta? | ArrayLike | The hyperparameters |
Returns
Promise<any>
Defined in: generated/gaussian_process/kernels/Matern.ts:171 (opens in a new tab)
diag()
Returns the diagonal of the kernel k(X, X).
The result of this method is identical to np.diag(self(X)); however, it can be evaluated more efficiently since only the diagonal is evaluated.
Signature
diag(opts: object): Promise<ArrayLike>;Parameters
| Name | Type | Description |
|---|---|---|
opts | object | - |
opts.X? | ArrayLike[] | Left argument of the returned kernel k(X, Y) |
Returns
Promise<ArrayLike>
Defined in: generated/gaussian_process/kernels/Matern.ts:206 (opens in a new tab)
dispose()
Disposes of the underlying Python resources.
Once dispose() is called, the instance is no longer usable.
Signature
dispose(): Promise<void>;Returns
Promise<void>
Defined in: generated/gaussian_process/kernels/Matern.ts:105 (opens in a new tab)
init()
Initializes the underlying Python resources.
This instance is not usable until the Promise returned by init() resolves.
Signature
init(py: PythonBridge): Promise<void>;Parameters
| Name | Type |
|---|---|
py | PythonBridge |
Returns
Promise<void>
Defined in: generated/gaussian_process/kernels/Matern.ts:62 (opens in a new tab)
is_stationary()
Returns whether the kernel is stationary.
Signature
is_stationary(opts: object): Promise<any>;Parameters
| Name | Type |
|---|---|
opts | object |
Returns
Promise<any>
Defined in: generated/gaussian_process/kernels/Matern.ts:239 (opens in a new tab)
Properties
_isDisposed
boolean=false
Defined in: generated/gaussian_process/kernels/Matern.ts:23 (opens in a new tab)
_isInitialized
boolean=false
Defined in: generated/gaussian_process/kernels/Matern.ts:22 (opens in a new tab)
_py
PythonBridge
Defined in: generated/gaussian_process/kernels/Matern.ts:21 (opens in a new tab)
id
string
Defined in: generated/gaussian_process/kernels/Matern.ts:18 (opens in a new tab)
opts
any
Defined in: generated/gaussian_process/kernels/Matern.ts:19 (opens in a new tab)
Accessors
anisotropic
Signature
anisotropic(): Promise<any>;Returns
Promise<any>
Defined in: generated/gaussian_process/kernels/Matern.ts:262 (opens in a new tab)
hyperparameter_length_scale
Signature
hyperparameter_length_scale(): Promise<any>;Returns
Promise<any>
Defined in: generated/gaussian_process/kernels/Matern.ts:282 (opens in a new tab)
py
Signature
py(): PythonBridge;Returns
PythonBridge
Defined in: generated/gaussian_process/kernels/Matern.ts:49 (opens in a new tab)
Signature
py(pythonBridge: PythonBridge): void;Parameters
| Name | Type |
|---|---|
pythonBridge | PythonBridge |
Returns
void
Defined in: generated/gaussian_process/kernels/Matern.ts:53 (opens in a new tab)