statics.py
``````import tensorflow as tf
from ..base import Parameter, positive
from .base import Kernel

class Static(Kernel):
"""
Kernels who don't depend on the value of the inputs are 'Static'.  The only
parameter is a variance, σ².
"""

def __init__(self, variance=1.0, active_dims=None):
super().__init__(active_dims)
self.variance = Parameter(variance, transform=positive())

def K_diag(self, X, presliced=False):
return tf.fill((X.shape[0], ), tf.squeeze(self.variance))

class White(Static):
"""
The White kernel: this kernel produces 'white noise'. The kernel equation is

k(x_n, x_m) = δ(n, m) σ²

where:
δ(.,.) is the Kronecker delta,
σ²  is the variance parameter.
"""

def K(self, X, X2=None, presliced=False):
if X2 is None:
d = tf.fill((X.shape[0], ), tf.squeeze(self.variance))
return tf.linalg.diag(d)
else:
shape = [X.shape[0], X2.shape[0]]
return tf.zeros(shape, dtype=X.dtype)

class Constant(Static):
"""
The Constant (aka Bias) kernel. Functions drawn from a GP with this kernel
are constant, i.e. f(x) = c, with c ~ N(0, σ^2). The kernel equation is

k(x, y) = σ²

where:
σ²  is the variance parameter.
"""

def K(self, X, X2=None, presliced=False):
if X2 is None:
shape = tf.stack([X.shape[0], X.shape[0]])
else:
shape = tf.stack([X.shape[0], X2.shape[0]])
return tf.fill(shape, tf.squeeze(self.variance))
``````