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

stationaries.py

```
import numpy as np
import tensorflow as tf
from ..base import Parameter
from ..utilities import positive
from ..utilities.ops import square_distance
from .base import Kernel
class Stationary(Kernel):
"""
Base class for kernels that are stationary, that is, they only depend on
r = || x - x' ||
This class handles 'ard' behaviour, which stands for 'Automatic Relevance
Determination'. This means that the kernel has one lengthscale per
dimension, otherwise the kernel is isotropic (has a single lengthscale).
"""
def __init__(self, variance=1.0, lengthscale=1.0, **kwargs):
"""
:param variance: the (initial) value for the variance parameter
:param lengthscale: the (initial) value for the lengthscale 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 kwargs: accepts `name` and `active_dims`, which is a list of
length input_dim which controls which columns of X are used
"""
for kwarg in kwargs:
if kwarg not in {'name', 'active_dims'}:
raise TypeError('Unknown keyword argument:', kwarg)
super().__init__(**kwargs)
self.variance = Parameter(variance, transform=positive())
self.lengthscale = Parameter(lengthscale, transform=positive())
self._validate_ard_active_dims(self.lengthscale)
@property
def ard(self) -> bool:
"""
Whether ARD behaviour is active.
"""
return self.lengthscale.shape.ndims > 0
def scaled_squared_euclid_dist(self, X, X2=None):
"""
Returns ||(X - X2ᵀ) / ℓ||² i.e. squared L2-norm.
"""
X_scaled = X / self.lengthscale
X2_scaled = X2 / self.lengthscale if X2 is not None else X2
return square_distance(X_scaled, X2_scaled)
def K(self, X, X2=None, presliced=False):
if not presliced:
X, X2 = self.slice(X, X2)
r2 = self.scaled_squared_euclid_dist(X, X2)
return self.K_r2(r2)
def K_diag(self, X, presliced=False):
return tf.fill(tf.shape(X)[:-1], tf.squeeze(self.variance))
def K_r2(self, r2):
"""
Returns the kernel evaluated on r² (`r2`), which is the squared scaled Euclidean distance
Should operate element-wise on r²
"""
if hasattr(self, "K_r"):
# Clipping around the (single) float precision which is ~1e-45.
r = tf.sqrt(tf.maximum(r2, 1e-40))
return self.K_r(r) # pylint: disable=no-member
raise NotImplementedError
class SquaredExponential(Stationary):
"""
The radial basis function (RBF) or squared exponential kernel. The kernel equation is
k(r) = σ² exp{-½ r²}
where:
r is the Euclidean distance between the input points, scaled by the lengthscale parameter ℓ.
σ² is the variance parameter
Functions drawn from a GP with this kernel are infinitely differentiable!
"""
def K_r2(self, r2):
return self.variance * tf.exp(-0.5 * r2)
class RationalQuadratic(Stationary):
"""
Rational Quadratic kernel,
k(r) = σ² (1 + r² / 2αℓ²)^(-α)
σ² : variance
ℓ : lengthscale
α : alpha, determines relative weighting of small-scale and large-scale fluctuations
For α → ∞, the RQ kernel becomes equivalent to the squared exponential.
"""
def __init__(self, variance=1.0, lengthscale=1.0, alpha=1.0, active_dims=None):
super().__init__(variance=variance, lengthscale=lengthscale, active_dims=active_dims)
self.alpha = Parameter(alpha, transform=positive())
def K_r2(self, r2):
return self.variance * (1 + 0.5 * r2 / self.alpha) ** (-self.alpha)
class Exponential(Stationary):
"""
The Exponential kernel. It is equivalent to a Matern12 kernel with doubled lengthscales.
"""
def K_r(self, r):
return self.variance * tf.exp(-0.5 * r)
class Matern12(Stationary):
"""
The Matern 1/2 kernel. Functions drawn from a GP with this kernel are not
differentiable anywhere. The kernel equation is
k(r) = σ² exp{-r}
where:
r is the Euclidean distance between the input points, scaled by the lengthscale parameter ℓ.
σ² is the variance parameter
"""
def K_r(self, r):
return self.variance * tf.exp(-r)
class Matern32(Stationary):
"""
The Matern 3/2 kernel. Functions drawn from a GP with this kernel are once
differentiable. The kernel equation is
k(r) = σ² (1 + √3r) exp{-√3 r}
where:
r is the Euclidean distance between the input points, scaled by the lengthscale parameter ℓ,
σ² is the variance parameter.
"""
def K_r(self, r):
sqrt3 = np.sqrt(3.)
return self.variance * (1. + sqrt3 * r) * tf.exp(-sqrt3 * r)
class Matern52(Stationary):
"""
The Matern 5/2 kernel. Functions drawn from a GP with this kernel are twice
differentiable. The kernel equation is
k(r) = σ² (1 + √5r + 5/3r²) exp{-√5 r}
where:
r is the Euclidean distance between the input points, scaled by the lengthscale parameter ℓ,
σ² is the variance parameter.
"""
def K_r(self, r):
sqrt5 = np.sqrt(5.)
return self.variance * (1.0 + sqrt5 * r + 5.0 / 3.0 * tf.square(r)) * tf.exp(-sqrt5 * r)
class Cosine(Stationary):
"""
The Cosine kernel. Functions drawn from a GP with this kernel are sinusoids
(with a random phase). The kernel equation is
k(r) = σ² cos{r}
where:
r is the Euclidean distance between the input points, scaled by the lengthscale parameter ℓ,
σ² is the variance parameter.
"""
def K_r(self, r):
return self.variance * tf.cos(r)
```

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