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models.py
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models.py
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import objax
import jax.numpy as np
from jax import vmap
from .utils import diag, cho_factor, cho_solve, softplus, softplus_inv, transpose
from .basemodels import (
GaussianProcess,
SparseGaussianProcess,
MarkovGaussianProcess,
SparseMarkovGaussianProcess,
MarkovMeanFieldGaussianProcess,
SparseMarkovMeanFieldGaussianProcess,
InfiniteHorizonGaussianProcess,
SparseInfiniteHorizonGaussianProcess
)
from .inference import (
Newton,
VariationalInference,
ExpectationPropagation,
PosteriorLinearisation,
PosteriorLinearisation2ndOrder,
PosteriorLinearisation2ndOrderGaussNewton,
PosteriorLinearisation2ndOrderQuasiNewton,
Taylor,
GaussNewton,
VariationalGaussNewton,
QuasiNewton,
VariationalQuasiNewton,
ExpectationPropagationQuasiNewton,
# PosteriorLinearisationQuasiNewton,
NewtonRiemann,
VariationalInferenceRiemann,
ExpectationPropagationRiemann,
PosteriorLinearisation2ndOrderRiemann
)
from .kernels import Independent
# ############ Syntactic sugar adding the inference method functionality to the models ################
# note: re-declaring the inputs here is not strictly necessary, but creates nice documentation
# ##### Variational Inference #####
class VariationalGP(VariationalInference, GaussianProcess):
"""
Variational Gaussian process [1], adapted to use conjugate computation VI [2]
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
[1] Opper, Archambeau: The Variational Gaussian Approximation Revisited, Neural Computation, 2009
[2] Khan, Lin: Conugate-Computation Variational Inference - Converting Inference in Non-Conjugate Models in to
Inference in Conjugate Models, AISTATS 2017
"""
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
class VariationalRiemannGP(VariationalInferenceRiemann, GaussianProcess):
"""
Variational Gaussian process [1], adapted to use conjugate computation VI [2] with PSD guarantees [3].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
[1] Opper, Archambeau: The Variational Gaussian Approximation Revisited, Neural Computation, 2009
[2] Khan, Lin: Conugate-Computation Variational Inference - Converting Inference in Non-Conjugate Models in to
Inference in Conjugate Models, AISTATS 2017
[3] Lin, Schmidt & Khan: Handling the Positive-Definite Constraint in the Bayesian Learning Rule, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
class SparseVariationalGP(VariationalInference, SparseGaussianProcess):
"""
Sparse variational Gaussian process (SVGP) [1], adapted to use conjugate computation VI [2]
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param Z: inducing inputs
:param opt_z: boolean determining whether to optimise the inducing input locations
[1] Hensman, Matthews, Ghahramani: Scalable Variational Gaussian Process Classification, AISTATS 2015
[2] Khan, Lin: Conugate-Computation Variational Inference - Converting Inference in Non-Conjugate Models in to
Inference in Conjugate Models, AISTATS 2017
"""
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z)
class SparseVariationalRiemannGP(VariationalInferenceRiemann, SparseGaussianProcess):
"""
Sparse variational Gaussian process (SVGP) [1], adapted to use conjugate computation VI [2] with PSD guarantees [3].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param Z: inducing inputs
:param opt_z: boolean determining whether to optimise the inducing input locations
[1] Hensman, Matthews, Ghahramani: Scalable Variational Gaussian Process Classification, AISTATS 2015
[2] Khan, Lin: Conugate-Computation Variational Inference - Converting Inference in Non-Conjugate Models in to
Inference in Conjugate Models, AISTATS 2017
[3] Lin, Schmidt & Khan: Handling the Positive-Definite Constraint in the Bayesian Learning Rule, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z)
SVGP = SparseVariationalGP
class MarkovVariationalGP(VariationalInference, MarkovGaussianProcess):
"""
Markov variational Gaussian process: a VGP where the posterior is computed via
(spatio-temporal) filtering and smoothing [1]
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
[1] Chang, Wilkinson, Khan, Solin: Fast Variational Learning in State Space Gaussian Process Models, MLSP 2020
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class SparseMarkovVariationalGP(VariationalInference, SparseMarkovGaussianProcess):
"""
Sparse Markov variational Gaussian process: a sparse VGP with inducing states, where the posterior is computed via
(spatio-temporal) filtering and smoothing [1, 2].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
:param Z: inducing inputs
[1] Adam, Eleftheriadis, Durrande, Artemev, Hensman: Doubly Sparse Variational Gaussian Processes, AISTATS 2020
[2] Wilkinson, Solin, Adam: Sparse Algorithms for Markovian Gaussian Processes, AISTATS 2021
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, Z=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel, Z=Z)
class MarkovVariationalMeanFieldGP(VariationalInference, MarkovMeanFieldGaussianProcess):
pass
class SparseMarkovVariationalMeanFieldGP(VariationalInference, SparseMarkovMeanFieldGaussianProcess):
pass
class InfiniteHorizonVariationalGP(VariationalInference, InfiniteHorizonGaussianProcess):
"""
Infinite-horizon GP [1] with variational inference.
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param dare_iters: number of iterations to run the DARE solver for
[1] Solin, Hensman, Turner: Infinite-Horizon Gaussian Processes, NeurIPS 2018
"""
def __init__(self, kernel, likelihood, X, Y, R=None, dare_iters=20, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, dare_iters=dare_iters, parallel=parallel)
class SparseInfiniteHorizonVariationalGP(VariationalInference, SparseInfiniteHorizonGaussianProcess):
pass
# ##### Expectation Propagation #####
class ExpectationPropagationGP(ExpectationPropagation, GaussianProcess):
"""
Expectation propagation Gaussian process (EPGP).
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
[1] Minka: A Family of Algorithms for Approximate Bayesian Inference, Ph. D thesis 2000
"""
def __init__(self, kernel, likelihood, X, Y, power=1.):
self.power = power
super().__init__(kernel, likelihood, X, Y)
class SparseExpectationPropagationGP(ExpectationPropagation, SparseGaussianProcess):
"""
Sparse expectation propagation Gaussian process (SEPGP) [1].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param Z: inducing inputs
:param opt_z: boolean determining whether to optimise the inducing input locations
[1] Csato, Opper: Sparse on-line Gaussian processes, Neural Computation 2002
[2] Bui, Yan, Turner: A Unifying Framework for Gaussian Process Pseudo Point Approximations Using
Power Expectation Propagation, JMLR 2017
"""
def __init__(self, kernel, likelihood, X, Y, Z, power=1., opt_z=False):
self.power = power
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
class MarkovExpectationPropagationGP(ExpectationPropagation, MarkovGaussianProcess):
"""
Markov EP Gaussian process: an EPGP where the posterior is computed via
(spatio-temporal) filtering and smoothing [1].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
[1] Wilkinson, Chang, Riis Andersen, Solin: State Space Expectation Propagation, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y, R=None, power=1., parallel=None):
self.power = power
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class SparseMarkovExpectationPropagationGP(ExpectationPropagation, SparseMarkovGaussianProcess):
"""
Sparse Markov EP Gaussian process: a sparse EPGP with inducing states, where the posterior is computed via
(spatio-temporal) filtering and smoothing [1].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
:param Z: inducing inputs
[1] Wilkinson, Solin, Adam: Sparse Algorithms for Markovian Gaussian Processes, AISTATS 2021
"""
def __init__(self, kernel, likelihood, X, Y, R=None, power=1., parallel=None, Z=None):
self.power = power
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel, Z=Z)
class MarkovExpectationPropagationMeanFieldGP(ExpectationPropagation, MarkovMeanFieldGaussianProcess):
pass
class SparseMarkovExpectationPropagationMeanFieldGP(ExpectationPropagation, SparseMarkovMeanFieldGaussianProcess):
pass
class InfiniteHorizonExpectationPropagationGP(ExpectationPropagation, InfiniteHorizonGaussianProcess):
"""
Infinite-horizon GP [1] with expectation propagation.
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param dare_iters: number of iterations to run the DARE solver for
[1] Solin, Hensman, Turner: Infinite-Horizon Gaussian Processes, NeurIPS 2018
"""
def __init__(self, kernel, likelihood, X, Y, R=None, power=1., dare_iters=20, parallel=None):
self.power = power
super().__init__(kernel, likelihood, X, Y, R=R, dare_iters=dare_iters, parallel=parallel)
class SparseInfiniteHorizonExpectationPropagationGP(ExpectationPropagation, SparseInfiniteHorizonGaussianProcess):
pass
# ##### Newton / Laplace #####
class NewtonGP(Newton, GaussianProcess):
"""
[1] Rasmussen, Williams: Gaussian Processes for Machine Learning, 2006
"""
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
class SparseNewtonGP(Newton, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
class MarkovNewtonGP(Newton, MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class SparseMarkovNewtonGP(Newton, SparseMarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, Z=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel, Z=Z)
class MarkovNewtonMeanFieldGP(Newton, MarkovMeanFieldGaussianProcess):
pass
class SparseMarkovNewtonMeanFieldGP(Newton, SparseMarkovMeanFieldGaussianProcess):
pass
class InfiniteHorizonNewtonGP(Newton, InfiniteHorizonGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, dare_iters=20, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, dare_iters=dare_iters, parallel=parallel)
class SparseInfiniteHorizonNewtonGP(Newton, SparseInfiniteHorizonGaussianProcess):
pass
LaplaceGP = NewtonGP
SparseLaplaceGP = SparseNewtonGP
MarkovLaplaceGP = MarkovNewtonGP
SparseMarkovLaplaceGP = SparseMarkovNewtonGP
MarkovLaplaceGPMeanField = MarkovNewtonMeanFieldGP
SparseMarkovLaplaceGPMeanField = SparseMarkovNewtonMeanFieldGP
InfiniteHorizonLaplaceGP = InfiniteHorizonNewtonGP
SparseInfiniteHorizonLaplaceGP = SparseInfiniteHorizonNewtonGP
# ##### Posterior Linearisation #####
class PosteriorLinearisationGP(PosteriorLinearisation, GaussianProcess):
"""
[1] Garcia-Fernandez, Tronarp, Sarkka: Gaussian Process Classification
Using Posterior Linearization, IEEE Signal Processing 2019
"""
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
# class PosteriorLinearisationNewtonGP(PosteriorLinearisationNewton, GaussianProcess):
# pass
class SparsePosteriorLinearisationGP(PosteriorLinearisation, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
class MarkovPosteriorLinearisationGP(PosteriorLinearisation, MarkovGaussianProcess):
"""
[1] Garcia-Fernandez, Svensson, Sarkka: Iterated Posterior Linearization Smoother, IEEE Automatic Control 2016
[2] Wilkinson, Chang, Riis Andersen, Solin: State Space Expectation Propagation, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class SparseMarkovPosteriorLinearisationGP(PosteriorLinearisation, SparseMarkovGaussianProcess):
"""
[1] Wilkinson, Solin, Adam: Sparse Algorithms for Markovian Gaussian Processes, AISTATS 2021
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, Z=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel, Z=Z)
class MarkovPosteriorLinearisationMeanFieldGP(PosteriorLinearisation, MarkovMeanFieldGaussianProcess):
pass
class SparseMarkovPosteriorLinearisationMeanFieldGP(PosteriorLinearisation, SparseMarkovMeanFieldGaussianProcess):
pass
class InfiniteHorizonPosteriorLinearisationGP(PosteriorLinearisation, InfiniteHorizonGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, dare_iters=20, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, dare_iters=dare_iters, parallel=parallel)
class SparseInfiniteHorizonPosteriorLinearisationGP(PosteriorLinearisation, SparseInfiniteHorizonGaussianProcess):
pass
# ##### Taylor #####
class TaylorGP(Taylor, GaussianProcess):
"""
[1] Steinberg, Bonilla: Extended and Unscented Gaussian Processes, NeurIPS 2014
"""
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
class SparseTaylorGP(Taylor, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
class MarkovTaylorGP(Taylor, MarkovGaussianProcess):
"""
[1] Bell: The Iterated Kalman Smoother as a Gauss-Newton method, SIAM Journal on Optimization 1994
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class SparseMarkovTaylorGP(Taylor, SparseMarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, Z=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel, Z=Z)
class MarkovTaylorMeanFieldGP(Taylor, MarkovMeanFieldGaussianProcess):
pass
class SparseMarkovTaylorMeanFieldGP(Taylor, SparseMarkovMeanFieldGaussianProcess):
pass
class InfiniteHorizonTaylorGP(Taylor, InfiniteHorizonGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, dare_iters=20, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, dare_iters=dare_iters, parallel=parallel)
class SparseInfiniteHorizonTaylorGP(Taylor, SparseInfiniteHorizonGaussianProcess):
pass
# Extensions to posterior linearisation
class MarkovPosteriorLinearisation2ndOrderGP(PosteriorLinearisation2ndOrder, MarkovGaussianProcess):
pass
class MarkovPosteriorLinearisation2ndOrderGaussNewtonGP(PosteriorLinearisation2ndOrderGaussNewton,
MarkovGaussianProcess):
pass
class MarkovPosteriorLinearisation2ndOrderRiemannGP(PosteriorLinearisation2ndOrderRiemann, MarkovGaussianProcess):
pass
# Gauss-Newton approximations
class GaussNewtonGP(GaussNewton, GaussianProcess):
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
LaplaceGaussNewtonGP = GaussNewtonGP
class MarkovGaussNewtonGP(GaussNewton, MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
MarkovLaplaceGaussNewtonGP = MarkovGaussNewtonGP
class SparseGaussNewtonGP(GaussNewton, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z)
SparseLaplaceGaussNewtonGP = SparseGaussNewtonGP
class VariationalGaussNewtonGP(VariationalGaussNewton, GaussianProcess):
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
class MarkovVariationalGaussNewtonGP(VariationalGaussNewton, MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class SparseVariationalGaussNewtonGP(VariationalGaussNewton, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z)
# Quasi-Newton approximations
# --- quasi-Newton ---
class QuasiNewtonGP(QuasiNewton, GaussianProcess):
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
self.mean_prev = objax.StateVar(self.pseudo_likelihood.mean)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(self.func_dim), [self.num_data, 1, 1]))
LaplaceQuasiNewtonGP = QuasiNewtonGP
class VariationalQuasiNewtonGP(VariationalQuasiNewton, GaussianProcess):
def __init__(self, kernel, likelihood, X, Y, fullcov=True):
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
class ExpectationPropagationQuasiNewtonGP(ExpectationPropagationQuasiNewton, GaussianProcess):
def __init__(self, kernel, likelihood, X, Y, power=1., fullcov=True):
self.power = power
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
# class PosteriorLinearisationQuasiNewtonGP(PosteriorLinearisationQuasiNewton, GaussianProcess):
# def __init__(self, kernel, likelihood, X, Y, fullcov=True):
# self.fullcov = fullcov
# super().__init__(kernel, likelihood, X, Y)
# if fullcov:
# self.mean_prev = objax.StateVar(
# np.concatenate([self.pseudo_likelihood.mean,
# np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
# axis=1)
# )
# dim = self.mean_prev.value.shape[1]
# self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
# self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
# else:
# self.mean_prev = objax.StateVar(
# np.concatenate([self.pseudo_likelihood.mean,
# diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
# )
# self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
# self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
class PosteriorLinearisation2ndOrderQuasiNewtonGP(PosteriorLinearisation2ndOrderQuasiNewton, GaussianProcess):
def __init__(self, kernel, likelihood, X, Y, fullcov=True):
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
# --- Sparse Quasi-Newton ---
class SparseQuasiNewtonGP(QuasiNewton, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False):
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
self.mean_prev = objax.StateVar(self.pseudo_likelihood.mean)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(self.func_dim), [self.num_data, 1, 1]))
SparseLaplaceQuasiNewtonGP = SparseQuasiNewtonGP
class SparseVariationalQuasiNewtonGP(VariationalQuasiNewton, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False, fullcov=True):
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
class SparseExpectationPropagationQuasiNewtonGP(ExpectationPropagationQuasiNewton, SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, power=1., opt_z=False, fullcov=True):
self.power = power
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
# class SparsePosteriorLinearisationQuasiNewtonGP(PosteriorLinearisationQuasiNewton, SparseGaussianProcess):
# def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False, fullcov=True):
# self.fullcov = fullcov
# super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
# if fullcov:
# self.mean_prev = objax.StateVar(
# np.concatenate([self.pseudo_likelihood.mean,
# np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
# axis=1)
# )
# dim = self.mean_prev.value.shape[1]
# self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
# self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
# else:
# self.mean_prev = objax.StateVar(
# np.concatenate([self.pseudo_likelihood.mean,
# diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
# )
# self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
# self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
class SparsePosteriorLinearisation2ndOrderQuasiNewtonGP(PosteriorLinearisation2ndOrderQuasiNewton,
SparseGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, Z, opt_z=False, fullcov=True):
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y, Z, opt_z=opt_z)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
# --- Markov quasi-Newton ---
class MarkovQuasiNewtonGP(QuasiNewton, MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
self.mean_prev = objax.StateVar(self.pseudo_likelihood.mean)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(self.func_dim), [self.num_data, 1, 1]))
MarkovLaplaceQuasiNewtonGP = MarkovQuasiNewtonGP
class MarkovVariationalQuasiNewtonGP(VariationalQuasiNewton, MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, fullcov=True):
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
class MarkovExpectationPropagationQuasiNewtonGP(ExpectationPropagationQuasiNewton, MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, power=1., parallel=None, fullcov=True):
self.power = power
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
# class MarkovPosteriorLinearisationQuasiNewtonGP(PosteriorLinearisationQuasiNewton, MarkovGaussianProcess):
# def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, fullcov=True):
# self.fullcov = fullcov
# super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
# if fullcov:
# self.mean_prev = objax.StateVar(
# np.concatenate([self.pseudo_likelihood.mean,
# np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
# axis=1)
# )
# dim = self.mean_prev.value.shape[1]
# self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
# self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
# else:
# self.mean_prev = objax.StateVar(
# np.concatenate([self.pseudo_likelihood.mean,
# diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
# )
# self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
# self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
class MarkovPosteriorLinearisation2ndOrderQuasiNewtonGP(PosteriorLinearisation2ndOrderQuasiNewton,
MarkovGaussianProcess):
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None, fullcov=True):
self.fullcov = fullcov
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
if fullcov:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
np.reshape(self.pseudo_likelihood.covariance, (self.num_data, -1, 1))],
axis=1)
)
dim = self.mean_prev.value.shape[1]
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(dim), [self.num_data, 1, 1]))
else:
self.mean_prev = objax.StateVar(
np.concatenate([self.pseudo_likelihood.mean,
diag(self.pseudo_likelihood.covariance)[..., None]], axis=1)
)
self.jacobian_prev = objax.StateVar(np.zeros([self.num_data, 2 * self.func_dim, 1]))
self.hessian_approx = objax.StateVar(-1e2 * np.tile(np.eye(2 * self.func_dim), [self.num_data, 1, 1]))
# PSD constraints via Riemannian gradients
class MarkovVariationalRiemannGP(VariationalInferenceRiemann, MarkovGaussianProcess):
"""
Markov variational Gaussian process: a VGP where the posterior is computed via
(spatio-temporal) filtering and smoothing [1] with PSD constraints via Riemannian gradients [2].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
[1] Chang, Wilkinson, Khan, Solin: Fast Variational Learning in State Space Gaussian Process Models, MLSP 2020
[2] Lin, Schmidt, Khan: Handling the Positive-Definite Constraint in the Bayesian Learning Rule, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class MarkovExpectationPropagationRiemannGP(ExpectationPropagationRiemann, MarkovGaussianProcess):
"""
Markov EP Gaussian process: an EPGP where the posterior is computed via
(spatio-temporal) filtering and smoothing [1] with PSD constraints via Riemannian gradients [2].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
[1] Wilkinson, Chang, Riis Andersen, Solin: State Space Expectation Propagation, ICML 2020
[2] Lin, Schmidt, Khan: Handling the Positive-Definite Constraint in the Bayesian Learning Rule, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y, R=None, power=1., parallel=None):
self.power = power
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
class MarkovNewtonRiemannGP(NewtonRiemann, MarkovGaussianProcess):
"""
Markov Laplace Gaussian process with PSD constraints via Riemannian gradients [1].
:param kernel: a kernel object
:param likelihood: a likelihood object
:param X: inputs
:param Y: observations
:param R: spatial inputs
:param parallel: boolean determining whether to run parallel filtering
[1] Lin, Schmidt, Khan: Handling the Positive-Definite Constraint in the Bayesian Learning Rule, ICML 2020
"""
def __init__(self, kernel, likelihood, X, Y, R=None, parallel=None):
super().__init__(kernel, likelihood, X, Y, R=R, parallel=parallel)
MarkovLaplaceRiemannGP = MarkovNewtonRiemannGP
class TrainableDiagonalGaussianDistribution(objax.Module):
def __init__(self, mean, variance):
self.mean_ = objax.TrainVar(mean)
self.transformed_variance = objax.TrainVar(vmap(softplus_inv)(variance))
def __call__(self):
return self.mean, self.covariance
@property
def mean(self):
return self.mean_.value
@property
def variance(self):
return softplus(self.transformed_variance.value)
@property
def covariance(self):
return vmap(np.diag)(self.variance)
@property
def nat1(self):
chol = cho_factor(self.covariance, lower=True)
return cho_solve(chol, self.mean)
@property
def nat2(self):
chol = cho_factor(self.covariance, lower=True)
return cho_solve(chol, np.tile(np.eye(self.covariance.shape[1]), [self.covariance.shape[0], 1, 1]))
class TrainableGaussianDistribution(objax.Module):
def __init__(self, mean, covariance):
self.dim = mean.shape[1]
cholcov, _ = cho_factor(covariance, lower=True)
self.mean_ = objax.TrainVar(mean)
self.transformed_covariance = objax.TrainVar(vmap(self.get_tril, [0, None])(cholcov, self.dim))
def __call__(self):
return self.mean, self.covariance
@staticmethod
def get_tril(chol, dim):
return chol[np.tril_indices(dim)]
def fill_lower_tri(self, v):
idx = np.tril_indices(self.dim)
return np.zeros((self.dim, self.dim), dtype=v.dtype).at[idx].set(v)
@property
def mean(self):
return self.mean_.value
@property
def covariance(self):
chol_low = vmap(self.fill_lower_tri)(self.transformed_covariance.value)
return transpose(chol_low) @ chol_low
@property
def nat1(self):
chol = cho_factor(self.covariance, lower=True)
return cho_solve(chol, self.mean)
@property
def nat2(self):
chol = cho_factor(self.covariance, lower=True)
return cho_solve(chol, np.tile(np.eye(self.covariance.shape[1]), [self.covariance.shape[0], 1, 1]))
class FirstOrderVariationalGP(VariationalGP):
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
if isinstance(self.kernel, Independent):
pseudo_lik_size = self.func_dim # the multi-latent case
else:
pseudo_lik_size = self.obs_dim
# self.pseudo_likelihood = TrainableDiagonalGaussianDistribution(
# mean=np.zeros([self.num_data, pseudo_lik_size, 1]),
# variance=1e2 * np.ones([self.num_data, pseudo_lik_size])
# )
self.pseudo_likelihood = TrainableGaussianDistribution(
mean=np.zeros([self.num_data, pseudo_lik_size, 1]),
covariance=1e2 * np.tile(np.eye(pseudo_lik_size), [self.num_data, 1, 1])
)
def energy(self, **kwargs):
"""
"""
self.update_posterior()
return super().energy(**kwargs)
class FirstOrderMarkovVariationalGP(MarkovVariationalGP):
def __init__(self, kernel, likelihood, X, Y):
super().__init__(kernel, likelihood, X, Y)
if isinstance(self.kernel, Independent):
pseudo_lik_size = self.func_dim # the multi-latent case
else:
pseudo_lik_size = self.obs_dim
self.pseudo_likelihood = TrainableGaussianDistribution(
mean=np.zeros([self.num_data, pseudo_lik_size, 1]),
covariance=1e2 * np.tile(np.eye(pseudo_lik_size), [self.num_data, 1, 1])
)
def energy(self, **kwargs):
"""
"""
self.update_posterior()
return super().energy(**kwargs)