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from ..base import Base
import numpy as np
import multiprocessing as mp
from GPy.kern import Matern32, Matern52, RBF, ExpQuad
from scipy.optimize import least_squares
class NSGP(Base):
"""
A class to learn Nott and Dunsmuir's non-stationary kernel. For more information, refer to
https://academic.oup.com/biomet/article-abstract/89/4/819/242307
Parameters
------------
N : int, default=10
Number of nearby points to learn each kernel locally
eta : int, default=1
A hyperparameter used in weight function
loc_kernel : str, default='m32', ('m32', 'm52' or 'rbf')
type of kernel to be used
"""
def __init__(self, N=10, eta=1, kernel_name="m32", verbose=True):
super().__init__()
self.__N = N + 1 # Number of datapoints for local kernel learning
self.__eta = eta # Eta hyperparameter for weighting function
self.__kernel_name = kernel_name
self.__param_dict = {
"N": self.__N,
"eta": self.__eta,
"kernel_name": self.__kernel_name,
}
self._KX_inv = None
def get_all_params(self):
"""
Returns class parameters
"""
return self.__param_dict
def get_param(self, param):
"""
Returns the value of a parameter
"""
return self.__param_dict[param]
def __calculate_dmat(self):
self.__dmat = np.zeros((self._X.shape[0], self._X.shape[0]))
for i in range(self._X.shape[0]):
for j in range(i, self._X.shape[0]):
self.__dmat[i, j] = np.linalg.norm(self._X[i] - self._X[j])
self.__dmat[j, i] = self.__dmat[i, j]
def __get_close_locs(self):
self.__calculate_dmat() # Distance matrix
return [
self.__dmat[i].argsort()[: self.__N]
for i in range(self._X.shape[0])
]
def __weight_func(self, S):
return np.exp(-(1 / self.__eta) * ((S - self._X) ** 2).sum(axis=1))
def _model(self, loc):
def __D_z(sj):
return self._Gamma[np.ix_(sj, sj)]
def __obfunc(x):
kernel = kern_dict[self.__kernel_name]
kernel.variance = x[0]
kernel.lengthscale = x[1:]
kern_vals = kernel.K(self._X[self.__close_locs[loc]])
term = (__D_z(self.__close_locs[loc]) - kern_vals) / kern_vals
return np.sum(term**2)
# ARD can be added
kern_dict = {
"m32": Matern32(
input_dim=self._X.shape[1],
active_dims=list(range(self._X.shape[1])),
ARD=True,
),
"m52": Matern52(
input_dim=self._X.shape[1],
active_dims=list(range(self._X.shape[1])),
ARD=True,
),
"rbf": RBF(
input_dim=self._X.shape[1],
active_dims=list(range(self._X.shape[1])),
ARD=True,
),
"expqd": ExpQuad(
input_dim=self._X.shape[1],
active_dims=list(range(self._X.shape[1])),
ARD=True,
),
}
kernel = kern_dict[self.__kernel_name]
params = least_squares(__obfunc, np.ones((self._X.shape[1] + 1))).x
kernel.variance = params[0]
kernel.lengthscale = params[1:]
return kernel.K
def _c_inv(self, kern_func):
return np.linalg.pinv(kern_func(self._X))
def __learnLocal(self):
# self._verbose_print('Training local kernels. This may take a few moments')
job = mp.Pool()
self.__kernels = job.map(self._model, list(range(self._X.shape[0])))
self.__C_inv = job.map(self._c_inv, self.__kernels)
job.close()
# self._verbose_print('Training complete')
def _Kernel(self, S1, S2=None):
"""
This function is for the NSGP Class.
This is not expected to be called directly.
"""
S2exists = True
if np.all(S1 == S2) or S2 is None:
S2exists = False
S2 = S1
assert S1.shape[1] == self._X.shape[1]
assert S2.shape[1] == self._X.shape[1]
# Calculating Weights & c_mats
self.__v_s1 = np.zeros((S1.shape[0], self._X.shape[0]))
self.__v_s2 = np.zeros((S2.shape[0], self._X.shape[0]))
self.__c_mat_s1 = np.zeros(
(self._X.shape[0], S1.shape[0], self._X.shape[0])
)
self.__c_mat_s2 = np.zeros(
(self._X.shape[0], self._X.shape[0], S2.shape[0])
)
self.__c_mat_s1s2 = np.zeros(
(self._X.shape[0], S1.shape[0], S2.shape[0])
)
for s1i, s1 in enumerate(S1):
s_vec = self.__weight_func(s1)
self.__v_s1[s1i, :] = s_vec / s_vec.sum()
if S2exists:
for s2i, s2 in enumerate(S2):
s_vec = self.__weight_func(s2)
self.__v_s2[s2i, :] = s_vec / s_vec.sum()
for i in range(self._X.shape[0]):
self.__c_mat_s1[i, :, :] = self.__kernels[i](S1, self._X)
self.__c_mat_s2[i, :, :] = self.__kernels[i](self._X, S2)
self.__c_mat_s1s2[i, :, :] = self.__kernels[i](S1, S2)
else:
self.__v_s2 = self.__v_s1
for i in range(self._X.shape[0]):
self.__c_mat_s1[i, :, :] = self.__kernels[i](S1, self._X)
self.__c_mat_s2[i, :, :] = self.__c_mat_s1[i, :, :].T
self.__c_mat_s1s2[i, :, :] = self.__kernels[i](S1)
# Calculating main covariance function
first_term = np.zeros((S1.shape[0], S2.shape[0]), dtype="float64")
for i in range(self._X.shape[0]):
for j in range(self._X.shape[0]):
first_term += (
self.__c_mat_s1[i, :, :]
.dot(self.__C_inv[i])
.dot(self._Gamma)
.dot(self.__C_inv[j])
.dot(self.__c_mat_s2[j, :, :])
) * (
self.__v_s1[:, i]
.reshape(-1, 1)
.dot(self.__v_s2[:, j].reshape(1, -1))
)
second_term = np.zeros((S1.shape[0], S2.shape[0]))
for i in range(self._X.shape[0]):
second_term += np.sqrt(
self.__v_s1[:, i]
.reshape(-1, 1)
.dot(self.__v_s2[:, i].reshape(1, -1))
) * (
self.__c_mat_s1s2[i, :, :]
- self.__c_mat_s1[i, :, :]
.dot(self.__C_inv[i])
.dot(self.__c_mat_s2[i, :, :])
)
return first_term + second_term
def _fit(self, X, y, ECM):
"""
This function is for the NSGP Class.
This is not expected to be called directly.
"""
self._Gamma = ECM # Empirical Covariance Matrix
assert type(self._Gamma) == type(
np.zeros((1, 1))
), "ECM must be a numpy array"
assert self._Gamma.shape[0] == self._Gamma.shape[1] == X.shape[0], (
"ECM must have ("
+ str(X.shape[0])
+ ", "
+ str(X.shape[0])
+ ") shape"
)
self._X = X # training fetures
self._y = y # Training values
self.__param_dict["X"] = X
self.__param_dict["y"] = y
self.__param_dict["ECM"] = self._Gamma
# Get closest N locations for each train location
self.__close_locs = self.__get_close_locs()
self.__learnLocal() # Learning local kernels
return self
def _predict(self, X, return_cov=False):
"""
This function is for the NSGP Class.
This is not expected to be called directly.
"""
if self._KX_inv is None:
self._KX_inv = np.linalg.pinv(self._Kernel(self._X, self._X))
KX_test = self._Kernel(X, self._X)
pred_mean = (
KX_test.dot(self._KX_inv).dot(self._y - self._y.mean())
+ self._y.mean()
)
if return_cov:
pred_var = self._Kernel(X, X) - KX_test.dot(self._KX_inv).dot(
KX_test.T
)
return (pred_mean, pred_var)
return pred_mean
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