https://github.com/GPflow/GPflow
Tip revision: f3c511060ce62072a34a50319237d28b82d10448 authored by Vincent Dutordoir on 27 August 2020, 11:22:49 UTC
Release 2.1.0 (#1552)
Release 2.1.0 (#1552)
Tip revision: f3c5110
linears.py
import tensorflow as tf
from ..base import Parameter
from ..utilities import positive
from .base import Kernel
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.
"""
def __init__(self, variance=1.0, active_dims=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.
"""
return self.variance.shape.ndims > 0
def K(self, X, X2=None):
if X2 is None:
return tf.matmul(X * self.variance, X, transpose_b=True)
else:
return tf.tensordot(X * self.variance, X2, [[-1], [-1]])
def K_diag(self, X):
return tf.reduce_sum(tf.square(X) * self.variance, axis=-1)
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.
"""
def __init__(self, degree=3.0, variance=1.0, offset=1.0, active_dims=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())
def K(self, X, X2=None):
return (super().K(X, X2) + self.offset) ** self.degree
def K_diag(self, X):
return (super().K_diag(X) + self.offset) ** self.degree