# -*- coding:utf-8 -*-
import numpy as np
from scipy import spatial
from ._src.enhance_gauss import grad_width64
[docs]class gauss:
"""gaussian kernel"""
def __init__(
self,
num_dim,
width=3,
scale=1,
ard=False,
max_width=1e6,
min_width=1e-6,
max_scale=1e6,
min_scale=1e-6,
):
"""
Parameters
----------
num_dim: int
width: float
scale: float
ard: bool
flag to use Automatic Relevance Determination (ARD).
max_width: float
Maximum value of width
min_width: float
Minimum value of width
max_scale: float
Maximum value of scale
min_scale: float
Minimum value of scale
"""
self.ard = ard
self.num_dim = num_dim
self.scale = scale
self.max_ln_width = np.log(max_width)
self.min_ln_width = np.log(min_width)
self.max_ln_scale = np.log(max_scale)
self.min_ln_scale = np.log(min_scale)
if self.ard:
# with ARD
self.num_params = num_dim + 1
if isinstance(width, np.ndarray) and len(width) == self.num_dim:
self.width = width
else:
self.width = width * np.ones(self.num_dim)
else:
# without ARD
self.width = width
self.num_params = 2
params = self.cat_params(self.width, self.scale)
self.set_params(params)
[docs] def print_params(self):
"""
show the current kernel parameters
"""
print(" Parameters of Gaussian kernel \n ")
print(" width = ", +self.width)
print(" scale = ", +self.scale)
print(" scale2 = ", +self.scale**2)
print(" \n")
[docs] def prepare(self, params=None):
"""
Setting parameters
Parameters
----------
params: numpy.ndarray
parameters
Returns
-------
params: numpy.ndarray
width: int
scale: int
"""
if params is None:
params = self.params
width = self.width
scale = self.scale
else:
params = self.supp_params(params)
width, scale = self.decomp_params(params)
return params, width, scale
[docs] def get_grad(self, X, params=None):
"""
Getting gradiant values of X
Parameters
----------
X: numpy.ndarray
N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate.
params: numpy.ndarray
Returns
-------
grad: numpy.ndarray
"""
num_data = X.shape[0]
params, width, scale = self.prepare(params)
G = self.get_cov(X, params=params)
grad = np.zeros((self.num_params, num_data, num_data))
if self.ard:
grad[0 : self.num_params - 1, :, :] = grad_width64(X, width, G)
else:
pairwise_dists = spatial.distance.pdist(X / width, "euclidean")
grad[0, :, :] = G * spatial.distance.squareform(pairwise_dists**2)
grad[-1, :, :] = 2 * G
return grad
[docs] def get_cov(self, X, Z=None, params=None, diag=False):
"""
compute the covariant matrix
Parameters
----------
X: numpy.ndarray
N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate.
Z: numpy.ndarray
N x d dimensional matrix. Each row of Z denotes the d-dimensional feature vector of search candidate.
params: numpy.ndarray
Parameters
diag: bool
If X is the diagonalization matrix, true.
Returns
-------
G: numpy.ndarray
covariant matrix
"""
params, width, scale = self.prepare(params)
scale2 = scale**2
if Z is None:
if diag:
G = scale2 * np.ones(X.shape[0])
else:
pairwise_dists = spatial.distance.squareform(
spatial.distance.pdist(X / width, "euclidean") ** 2
)
G = np.exp(-0.5 * pairwise_dists) * scale2
else:
pairwise_dists = (
spatial.distance.cdist(X / width, Z / width, "euclidean") ** 2
)
G = np.exp(-0.5 * pairwise_dists) * scale2
return G
[docs] def set_params(self, params):
"""
set kernel parameters
Parameters
----------
params: numpy.ndarray
Parameters for optimization.
"""
params = self.supp_params(params)
self.params = params
self.width, self.scale = self.decomp_params(params)
[docs] def supp_params(self, params):
"""
Set maximum (minimum) values for parameters when the parameter is greater(less) than this value.
Parameters
----------
params: numpy.ndarray
Parameters for optimization.
Array of real elements of size (n,), where ‘n’ is the number of independent variables.
Returns
-------
params: numpy.ndarray
"""
index = np.where(params[0:-1] > self.max_ln_width)
params[index[0]] = self.max_ln_width
index = np.where(params[0:-1] < self.min_ln_width)
params[index[0]] = self.min_ln_width
if params[-1] > self.max_ln_scale:
params[-1] = self.max_ln_scale
if params[-1] < self.min_ln_scale:
params[-1] = self.min_ln_scale
return params
[docs] def decomp_params(self, params):
"""
decompose the parameters defined on the log region
into width and scale parameters
Parameters
----------
params: numpy.ndarray
parameters
Returns
-------
width: float
scale: float
"""
width = np.exp(params[0:-1])
scale = np.exp(params[-1])
return width, scale
[docs] def save(self, file_name):
"""
save the gaussian kernel
Parameters
----------
file_name: str
file name to save the information of the kernel
"""
kwarg = {
"name": "gauss",
"params": self.params,
"ard": self.ard,
"num_dim": self.num_dim,
"max_ln_scale": self.max_ln_scale,
"min_ln_scale": self.min_ln_scale,
"max_ln_width": self.max_ln_width,
"min_ln_width": self.min_ln_width,
"num_params": self.num_params,
}
with open(file_name, "wb") as f:
np.savez(f, **kwarg)
[docs] def load(self, file_name):
"""
Recovering the Gaussian kernel from file
Parameters
----------
file_name: str
file name to load the information of the kernel
"""
temp = np.load(file_name)
self.num_dim = temp["num_dim"]
self.ard = temp["ard"]
self.max_ln_scale = temp["max_ln_scale"]
self.min_ln_scale = temp["min_ln_scale"]
self.max_ln_width = temp["max_ln_width"]
self.min_ln_width = temp["min_ln_width"]
params = temp["params"]
self.set_params(params)
[docs] def get_params_bound(self):
"""
Getting boundary array.
Returns
-------
bound: list
A num_params-dimensional array with the tuple (min_params, max_params).
"""
if self.ard:
bound = [
(self.min_ln_width, self.max_ln_width) for i in range(0, self.num_dim)
]
else:
bound = [(self.min_ln_width, self.max_ln_width)]
bound.append((self.min_ln_scale, self.max_ln_scale))
return bound
[docs] def cat_params(self, width, scale):
"""
Taking the logarithm of width and scale parameters
and concatinate them into one ndarray
Parameters
----------
width: int
scale: int
Returns
-------
params: numpy.ndarray
Parameters
"""
params = np.zeros(self.num_params)
params[0:-1] = np.log(width)
params[-1] = np.log(scale)
return params
[docs] def rand_expans(self, num_basis, params=None):
"""
Kernel Expansion
Parameters
----------
num_basis: int
total number of basis
params: numpy.ndarray
Parameters
Returns
-------
tupple (W, b, amp)
"""
params, width, scale = self.prepare(params)
scale2 = scale**2
amp = np.sqrt((2 * scale2) / num_basis)
W = np.random.randn(num_basis, self.num_dim) / width
b = np.random.rand(num_basis) * 2 * np.pi
return (W, b, amp)
[docs] def get_cand_params(self, X, t):
"""
Getting candidate parameters.
Parameters
----------
X: numpy.ndarray
N x d dimensional matrix. Each row of X denotes the d-dimensional feature vector of search candidate.
t: numpy.ndarray
N dimensional array.
The negative energy of each search candidate (value of the objective function to be optimized).
Returns
-------
params: numpy.ndarray
"""
if self.ard:
# with ARD
width = np.zeros(self.num_dim)
scale = np.std(t)
u = np.random.uniform(0.4, 0.8)
width = u * (np.max(X, 0) - np.min(X, 0)) * np.sqrt(self.num_dim)
index = np.where(np.abs(width) < 1e-6)
width[index[0]] = 1e-6
params = np.append(np.log(width), np.log(scale))
else:
# without ARD
num_data = X.shape[0]
M = max(2000, int(np.floor(num_data / 5)))
dist = np.zeros(M)
for m in range(M):
a = np.random.randint(0, X.shape[0], 2)
dist[m] = np.linalg.norm(X[a[0], :] - X[a[1], :])
dist = np.sort(dist)
tmp = int(np.floor(M / 10))
n = np.random.randint(0, 5)
width = dist[(2 * n + 1) * tmp]
scale = np.std(t)
params = np.append(np.log(width + 1e-8), np.log(scale))
return params