Revision

**291ae6c7dbfcbded27c604f136982a5067d14b8e**authored by thevincentadam on**20 January 2020, 12:17:20 UTC**, committed by thevincentadam on**20 January 2020, 12:17:20 UTC****1 parent**5dc31b8

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, presliced=False):
if not presliced:
X, X2 = self.slice(X, X2)
if X2 is None:
return tf.linalg.matmul(X * self.variance, X, transpose_b=True)
return tf.linalg.matmul(X * self.variance, X2, transpose_b=True)
def K_diag(self, X, presliced=False):
if not presliced:
X, _ = self.slice(X, None)
return tf.reduce_sum(tf.square(X) * self.variance, 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, presliced=False):
return (super().K(X, X2, presliced=presliced) + self.offset)**self.degree
def K_diag(self, X, presliced=False):
return (super().K_diag(X, presliced=presliced) + self.offset)**self.degree
```

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