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Arccosine

ArcCosine 

ArcCosine(active_dims=None, order=0, variance=1.0, weight_variance=1.0, bias_variance=1.0, n_dims=None, compute_engine=DenseKernelComputation())

Bases: AbstractKernel

The ArCosine kernel.

This kernel is non-stationary and resembles the behavior of neural networks. See Section 3.1 of Cho and Saul (2011) for additional details.

Parameters:

  • active_dims (Union[list[int], slice, None], default: None ) –

    The indices of the input dimensions that the kernel operates on.

  • order (Literal[0, 1, 2], default: 0 ) –

    The order of the kernel. Must be 0, 1 or 2.

  • variance (Union[ScalarFloat, Variable[ScalarArray]], default: 1.0 ) –

    The variance of the kernel Οƒ.

  • weight_variance (Union[WeightVarianceCompatible, Variable[WeightVariance]], default: 1.0 ) –

    The weight variance of the kernel.

  • bias_variance (Union[ScalarFloat, Variable[ScalarArray]], default: 1.0 ) –

    The bias variance of the kernel.

  • n_dims (Union[int, None], default: None ) –

    The number of input dimensions. If lengthscale is an array, this argument is ignored.

  • compute_engine (AbstractKernelComputation, default: DenseKernelComputation() ) –

    The computation engine that the kernel uses to compute the covariance matrix.

cross_covariance 

cross_covariance(x, y)

Compute the cross-covariance matrix of the kernel.

Parameters:

  • x (Num[Array, 'N D']) –

    the first input matrix of shape (N, D).

  • y (Num[Array, 'M D']) –

    the second input matrix of shape (M, D).

Returns:

  • Float[Array, 'N M'] –

    The cross-covariance matrix of the kernel of shape (N, M).

gram 

gram(x)

Compute the gram matrix of the kernel.

Parameters:

  • x (Num[Array, 'N D']) –

    the input matrix of shape (N, D).

Returns:

  • LinearOperator –

    The gram matrix of the kernel of shape (N, N).

diagonal 

diagonal(x)

Compute the diagonal of the gram matrix of the kernel.

Parameters:

  • x (Num[Array, 'N D']) –

    the input matrix of shape (N, D).

Returns:

  • Float[Array, ' N'] –

    The diagonal of the gram matrix of the kernel of shape (N,).

slice_input 

slice_input(x)

Slice out the relevant columns of the input matrix.

Select the relevant columns of the supplied matrix to be used within the kernel's evaluation.

Parameters:

  • x (Float[Array, '... D']) –

    the matrix or vector that is to be sliced.

Returns:

  • Float[Array, '... Q'] –

    The sliced form of the input matrix.

__add__ 

__add__(other)

Add two kernels together. Args: other (AbstractKernel): The kernel to be added to the current kernel.

Returns:

  • AbstractKernel ( AbstractKernel ) –

    A new kernel that is the sum of the two kernels.

__mul__ 

__mul__(other)

Multiply two kernels together.

Parameters:

  • other (AbstractKernel) –

    The kernel to be multiplied with the current kernel.

Returns:

  • AbstractKernel ( AbstractKernel ) –

    A new kernel that is the product of the two kernels.