Source code for gpflow.kernels.linears

# Copyright 2017-2020 The GPflow Contributors. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
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# http://www.apache.org/licenses/LICENSE-2.0
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from typing import Optional

import tensorflow as tf
from check_shapes import check_shapes, inherit_check_shapes

from ..base import Parameter, TensorType
from ..utilities import positive
from .base import ActiveDims, Kernel


[docs] class Linear(Kernel): """ The linear kernel. Functions drawn from a GP with this kernel are linear, i.e. f(x) = cx. The kernel equation is k(x, y) = σ²xy where σ² is the variance parameter. """ @check_shapes( "variance: [broadcast n_active_dims]", ) def __init__( self, variance: TensorType = 1.0, active_dims: Optional[ActiveDims] = None ) -> None: """ :param variance: the (initial) value for the variance parameter(s), to induce ARD behaviour this must be initialised as an array the same length as the the number of active dimensions e.g. [1., 1., 1.] :param active_dims: a slice or list specifying which columns of X are used """ super().__init__(active_dims) self.variance = Parameter(variance, transform=positive()) self._validate_ard_active_dims(self.variance) @property def ard(self) -> bool: """ Whether ARD behaviour is active. """ ndims: int = self.variance.shape.ndims return ndims > 0 @inherit_check_shapes def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor: if X2 is None: return tf.matmul(X * self.variance, X, transpose_b=True) else: return tf.tensordot(X * self.variance, X2, [[-1], [-1]]) @inherit_check_shapes def K_diag(self, X: TensorType) -> tf.Tensor: return tf.reduce_sum(tf.square(X) * self.variance, axis=-1)
[docs] class Polynomial(Linear): """ The Polynomial kernel. Functions drawn from a GP with this kernel are polynomials of degree `d`. The kernel equation is k(x, y) = (σ²xy + γ)ᵈ where: σ² is the variance parameter, γ is the offset parameter, d is the degree parameter. """ @check_shapes( "variance: [broadcast n_active_dims]", ) def __init__( self, degree: TensorType = 3.0, variance: TensorType = 1.0, offset: TensorType = 1.0, active_dims: Optional[ActiveDims] = None, ) -> None: """ :param degree: the degree of the polynomial :param variance: the (initial) value for the variance parameter(s), to induce ARD behaviour this must be initialised as an array the same length as the the number of active dimensions e.g. [1., 1., 1.] :param offset: the offset of the polynomial :param active_dims: a slice or list specifying which columns of X are used """ super().__init__(variance, active_dims) self.degree = degree self.offset = Parameter(offset, transform=positive()) @inherit_check_shapes def K(self, X: TensorType, X2: Optional[TensorType] = None) -> tf.Tensor: return (super().K(X, X2) + self.offset) ** self.degree @inherit_check_shapes def K_diag(self, X: TensorType) -> tf.Tensor: return (super().K_diag(X) + self.offset) ** self.degree