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https://github.com/SheffieldML/GPy.git
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began to merege the SVIGP code into GPy.
Example is implemented, but the step length is a bit crazy!
This commit is contained in:
James Hensman
parent
5d28333582
commit
b452e3eebc
7 changed files with 557 additions and 2 deletions
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@ -4,6 +4,7 @@
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from model import *
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from parameterised import *
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import priors
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from GPy.core.gp import GP
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from GPy.core.sparse_gp import SparseGP
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from gp import GP
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from sparse_gp import SparseGP
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from fitc import FITC
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from svigp import SVIGP
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@ -29,6 +29,7 @@ class GPBase(Model):
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self._Xscale = np.ones((1, self.input_dim))
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super(GPBase, self).__init__()
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#Model.__init__(self)
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# All leaf nodes should call self._set_params(self._get_params()) at
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# the end
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466
GPy/core/svigp.py
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466
GPy/core/svigp.py
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@ -0,0 +1,466 @@
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# Copyright (c) 2012, James Hensman and Nicolo' Fusi
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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import pylab as pb
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from .. import kern
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from ..util.linalg import pdinv, mdot, tdot, dpotrs, dtrtrs, jitchol, backsub_both_sides
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from ..likelihoods import EP
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from gp_base import GPBase
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from model import Model
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import time
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import sys
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class SVIGP(GPBase):
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"""
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Stochastic Variational inference in a Gaussian Process
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:param X: inputs
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:type X: np.ndarray (N x Q)
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:param Y: observed data
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:type Y: np.ndarray of observations (N x D)
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:param batchsize: the size of a h
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Additional kwargs are used as for a sparse GP. They include
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:param q_u: canonical parameters of the distribution squasehd into a 1D array
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:type q_u: np.ndarray
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:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
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:type M: int
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:param kernel : the kernel/covariance function. See link kernels
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:type kernel: a GPy kernel
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:param Z: inducing inputs (optional, see note)
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:type Z: np.ndarray (M x Q) | None
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:param X_uncertainty: The uncertainty in the measurements of X (Gaussian variance)
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:type X_uncertainty: np.ndarray (N x Q) | None
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:param Zslices: slices for the inducing inputs (see slicing TODO: link)
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:param M : Number of inducing points (optional, default 10. Ignored if Z is not None)
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:type M: int
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:param beta: noise precision. TODO> ignore beta if doing EP
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:type beta: float
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:param normalize_(X|Y) : whether to normalize the data before computing (predictions will be in original scales)
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:type normalize_(X|Y): bool
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"""
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def __init__(self, X, likelihood, kernel, Z, q_u=None, batchsize=10, X_variance=None):
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GPBase.__init__(self, X, likelihood, kernel, normalize_X=False)
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self.batchsize=batchsize
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self.Y = self.likelihood.Y.copy()
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self.Z = Z
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self.num_inducing = Z.shape[0]
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self.batchcounter = 0
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self.epochs = 0
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self.iterations = 0
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self.vb_steplength = 0.05
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self.param_steplength = 1e-5
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self.momentum = 0.9
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if X_variance is None:
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self.has_uncertain_inputs = False
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else:
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self.has_uncertain_inputs = True
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self.X_variance = X_variance
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if q_u is None:
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q_u = np.hstack((np.random.randn(self.num_inducing*self.output_dim),-.5*np.eye(self.num_inducing).flatten()))
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self.set_vb_param(q_u)
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self._permutation = np.random.permutation(self.num_data)
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self.load_batch()
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self._param_trace = []
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self._ll_trace = []
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self._grad_trace = []
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#set the adaptive steplength parameters
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self.hbar_t = 0.0
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self.tau_t = 100.0
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self.gbar_t = 0.0
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self.gbar_t1 = 0.0
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self.gbar_t2 = 0.0
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self.hbar_tp = 0.0
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self.tau_tp = 10000.0
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self.gbar_tp = 0.0
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self.adapt_param_steplength = True
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self.adapt_vb_steplength = True
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self._param_steplength_trace = []
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self._vb_steplength_trace = []
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def _compute_kernel_matrices(self):
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# kernel computations, using BGPLVM notation
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self.Kmm = self.kern.K(self.Z)
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if self.has_uncertain_inputs:
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self.psi0 = self.kern.psi0(self.Z, self.X_batch, self.X_variance_batch)
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self.psi1 = self.kern.psi1(self.Z, self.X_batch, self.X_variance_batch)
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self.psi2 = self.kern.psi2(self.Z, self.X_batch, self.X_variance_batch)
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else:
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self.psi0 = self.kern.Kdiag(self.X_batch)
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self.psi1 = self.kern.K(self.X_batch, self.Z)
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self.psi2 = None
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def dL_dtheta(self):
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dL_dtheta = self.kern.dK_dtheta(self.dL_dKmm, self.Z)
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if self.has_uncertain_inputs:
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dL_dtheta += self.kern.dpsi0_dtheta(self.dL_dpsi0, self.Z, self.X_batch, self.X_variance_batch)
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dL_dtheta += self.kern.dpsi1_dtheta(self.dL_dpsi1, self.Z, self.X_batch, self.X_variance_batch)
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dL_dtheta += self.kern.dpsi2_dtheta(self.dL_dpsi2, self.Z, self.X_batch, self.X_variance_batch)
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else:
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dL_dtheta += self.kern.dK_dtheta(self.dL_dpsi1, self.X_batch, self.Z)
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dL_dtheta += self.kern.dKdiag_dtheta(self.dL_dpsi0, self.X_batch)
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return dL_dtheta
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def _set_params(self, p, computations=True):
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self.kern._set_params_transformed(p[:self.kern.num_params])
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self.likelihood._set_params(p[self.kern.num_params:])
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if computations:
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self._compute_kernel_matrices()
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self._computations()
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def _get_params(self):
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return np.hstack((self.kern._get_params_transformed() , self.likelihood._get_params()))
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def _get_param_names(self):
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return self.kern._get_param_names_transformed() + self.likelihood._get_param_names()
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def load_batch(self):
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"""
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load a batch of data (set self.X_batch and self.likelihood.Y from self.X, self.Y)
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"""
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#if we've seen all the data, start again with them in a new random order
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if self.batchcounter+self.batchsize > self.num_data:
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self.batchcounter = 0
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self.epochs += 1
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self._permutation = np.random.permutation(self.num_data)
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this_perm = self._permutation[self.batchcounter:self.batchcounter+self.batchsize]
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self.X_batch = self.X[this_perm]
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self.likelihood.set_data(self.Y[this_perm])
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if self.has_uncertain_inputs:
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self.X_variance_batch = self.X_variance[this_perm]
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self.batchcounter += self.batchsize
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self.data_prop = float(self.batchsize)/self.num_data
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self._compute_kernel_matrices()
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self._computations()
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def _computations(self,do_Kmm=True, do_Kmm_grad=True):
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"""
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All of the computations needed. Some are optional, see kwargs.
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"""
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if do_Kmm:
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self.Lm = jitchol(self.Kmm)
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# The rather complex computations of self.A
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if self.has_uncertain_inputs:
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if self.likelihood.is_heteroscedastic:
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psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.batchsize, 1, 1))).sum(0)
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else:
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psi2_beta = self.psi2.sum(0) * self.likelihood.precision
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evals, evecs = linalg.eigh(psi2_beta)
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clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
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tmp = evecs * np.sqrt(clipped_evals)
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else:
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if self.likelihood.is_heteroscedastic:
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tmp = self.psi1.T * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.batchsize)))
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else:
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tmp = self.psi1.T * (np.sqrt(self.likelihood.precision))
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tmp, _ = dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
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self.A = tdot(tmp)
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self.V = self.likelihood.precision*self.likelihood.Y
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self.VmT = np.dot(self.V,self.q_u_expectation[0].T)
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self.psi1V = np.dot(self.psi1.T, self.V)
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self.B = np.eye(self.num_inducing)*self.data_prop + self.A
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self.Lambda = backsub_both_sides(self.Lm, self.B.T)
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self.LQL = backsub_both_sides(self.Lm,self.q_u_expectation[1].T,transpose='right')
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self.trace_K = self.psi0.sum() - np.trace(self.A)/self.likelihood.precision
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self.Kmmi_m, _ = dpotrs(self.Lm, self.q_u_expectation[0], lower=1)
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self.projected_mean = np.dot(self.psi1,self.Kmmi_m)
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# Compute dL_dpsi
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self.dL_dpsi0 = - 0.5 * self.output_dim * self.likelihood.precision * np.ones(self.batchsize)
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self.dL_dpsi1, _ = dpotrs(self.Lm,np.asfortranarray(self.VmT.T),lower=1)
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self.dL_dpsi1 = self.dL_dpsi1.T
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dL_dpsi2 = -0.5 * self.likelihood.precision * backsub_both_sides(self.Lm, self.LQL - self.output_dim * np.eye(self.num_inducing))
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if self.has_uncertain_inputs:
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self.dL_dpsi2 = np.repeat(dL_dpsi2[None,:,:],self.batchsize,axis=0)
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else:
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self.dL_dpsi1 += 2.*np.dot(dL_dpsi2,self.psi1.T).T
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self.dL_dpsi2 = None
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# Compute dL_dKmm
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if do_Kmm_grad:
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tmp = np.dot(self.LQL,self.A) - backsub_both_sides(self.Lm,np.dot(self.q_u_expectation[0],self.psi1V.T),transpose='right')
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tmp += tmp.T
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tmp += -self.output_dim*self.B
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tmp += self.data_prop*self.LQL
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self.dL_dKmm = 0.5*backsub_both_sides(self.Lm,tmp)
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#Compute the gradient of the log likelihood wrt noise variance
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self.partial_for_likelihood = -0.5*(self.batchsize*self.output_dim - np.sum(self.A*self.LQL))*self.likelihood.precision
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self.partial_for_likelihood += (0.5*self.output_dim*self.trace_K + 0.5 * self.likelihood.trYYT - np.sum(self.likelihood.Y*self.projected_mean))*self.likelihood.precision**2
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def log_likelihood(self):
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"""
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As for uncollapsed sparse GP, but account for the proportion of data we're looking at right now.
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NB. self.batchsize is the size of the batch, not the size of X_all
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"""
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assert not self.likelihood.is_heteroscedastic
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A = -0.5*self.batchsize*self.output_dim*(np.log(2.*np.pi) - np.log(self.likelihood.precision))
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B = -0.5*self.likelihood.precision*self.output_dim*self.trace_K
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Kmm_logdet = 2.*np.sum(np.log(np.diag(self.Lm)))
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C = -0.5*self.output_dim*self.data_prop*(Kmm_logdet-self.q_u_logdet - self.num_inducing)
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C += -0.5*np.sum(self.LQL * self.B)
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D = -0.5*self.likelihood.precision*self.likelihood.trYYT
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E = np.sum(self.V*self.projected_mean)
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return (A+B+C+D+E)/self.data_prop
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def _log_likelihood_gradients(self):
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return np.hstack((self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))/self.data_prop
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def vb_grad_natgrad(self):
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"""
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Compute the gradients of the lower bound wrt the canonical and
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Expectation parameters of u.
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Note that the natural gradient in either is given by the gradient in the other (See Hensman et al 2012 Fast Variational inference in the conjugate exponential Family)
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"""
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# Gradient for eta
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dL_dmmT_S = -0.5*self.Lambda/self.data_prop + 0.5*self.q_u_prec
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Kmmipsi1V,_ = dpotrs(self.Lm,self.psi1V,lower=1)
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dL_dm = (Kmmipsi1V - np.dot(self.Lambda,self.q_u_mean))/self.data_prop
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# Gradients for theta
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S = self.q_u_cov
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Si = self.q_u_prec
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m = self.q_u_mean
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dL_dSi = -mdot(S,dL_dmmT_S, S)
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dL_dmhSi = -2*dL_dSi
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dL_dSim = np.dot(dL_dSi,m) + np.dot(Si, dL_dm)
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return np.hstack((dL_dm.flatten(),dL_dmmT_S.flatten())) , np.hstack((dL_dSim.flatten(), dL_dmhSi.flatten()))
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def optimize(self, iterations, print_interval=10, callback=lambda:None, callback_interval=5):
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param_step = 0.
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#Iterate!
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for i in range(iterations):
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#store the current configuration for plotting later
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self._param_trace.append(self._get_params())
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self._ll_trace.append(self.log_likelihood() + self.log_prior())
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#load a batch
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self.load_batch()
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#compute the (stochastic) gradient
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natgrads = self.vb_grad_natgrad()
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grads = self._transform_gradients(self._log_likelihood_gradients() + self._log_prior_gradients())
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self._grad_trace.append(grads)
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#compute the steps in all parameters
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vb_step = self.vb_steplength*natgrads[0]
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if (self.epochs>=1):#only move the parameters after the first epoch
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param_step = self.momentum*param_step + self.param_steplength*grads
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else:
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param_step = 0.
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self.set_vb_param(self.get_vb_param() + vb_step)
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#Note: don't recompute everything here, wait until the next iteration when we have a new batch
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self._set_params(self._untransform_params(self._get_params_transformed() + param_step), computations=False)
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#print messages if desired
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if i and (not i%print_interval):
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print i, np.mean(self._ll_trace[-print_interval:]) #, self.log_likelihood()
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print np.round(np.mean(self._grad_trace[-print_interval:],0),3)
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sys.stdout.flush()
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#callback
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if i and not i%callback_interval:
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callback()
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time.sleep(0.1)
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if self.epochs > 10:
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self._adapt_steplength()
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self.iterations += 1
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def _adapt_steplength(self):
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if self.adapt_vb_steplength:
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# self._adaptive_vb_steplength()
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self._adaptive_vb_steplength_KL()
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self._vb_steplength_trace.append(self.vb_steplength)
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assert self.vb_steplength > 0
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if self.adapt_param_steplength:
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# self._adaptive_param_steplength()
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# self._adaptive_param_steplength_log()
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self._adaptive_param_steplength_from_vb()
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self._param_steplength_trace.append(self.param_steplength)
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def _adaptive_param_steplength(self):
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decr_factor = 0.1
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g_tp = self._transform_gradients(self._log_likelihood_gradients())
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self.gbar_tp = (1-1/self.tau_tp)*self.gbar_tp + 1/self.tau_tp * g_tp
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self.hbar_tp = (1-1/self.tau_tp)*self.hbar_tp + 1/self.tau_tp * np.dot(g_tp.T, g_tp)
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new_param_steplength = np.dot(self.gbar_tp.T, self.gbar_tp) / self.hbar_tp
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#- hack
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new_param_steplength *= decr_factor
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self.param_steplength = (self.param_steplength + new_param_steplength)/2
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#-
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self.tau_tp = self.tau_tp*(1-self.param_steplength) + 1
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def _adaptive_param_steplength_log(self):
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stp = np.logspace(np.log(0.0001), np.log(1e-6), base=np.e, num=18000)
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self.param_steplength = stp[self.iterations]
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def _adaptive_param_steplength_log2(self):
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self.param_steplength = (self.iterations + 0.001)**-0.5
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def _adaptive_param_steplength_from_vb(self):
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self.param_steplength = self.vb_steplength * 0.01
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def _adaptive_vb_steplength(self):
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decr_factor = 0.1
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g_t = self.vb_grad_natgrad()[0]
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self.gbar_t = (1-1/self.tau_t)*self.gbar_t + 1/self.tau_t * g_t
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self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t.T, g_t)
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new_vb_steplength = np.dot(self.gbar_t.T, self.gbar_t) / self.hbar_t
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#- hack
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new_vb_steplength *= decr_factor
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self.vb_steplength = (self.vb_steplength + new_vb_steplength)/2
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#-
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self.tau_t = self.tau_t*(1-self.vb_steplength) + 1
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def _adaptive_vb_steplength_KL(self):
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decr_factor = 1 #0.1
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natgrad = self.vb_grad_natgrad()
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g_t1 = natgrad[0]
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g_t2 = natgrad[1]
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self.gbar_t1 = (1-1/self.tau_t)*self.gbar_t1 + 1/self.tau_t * g_t1
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||||
self.gbar_t2 = (1-1/self.tau_t)*self.gbar_t2 + 1/self.tau_t * g_t2
|
||||
self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t1.T, g_t2)
|
||||
self.vb_steplength = np.dot(self.gbar_t1.T, self.gbar_t2) / self.hbar_t
|
||||
self.vb_steplength *= decr_factor
|
||||
self.tau_t = self.tau_t*(1-self.vb_steplength) + 1
|
||||
|
||||
def _raw_predict(self, X_new, X_variance_new=None, which_parts='all',full_cov=False):
|
||||
"""Internal helper function for making predictions, does not account for normalization"""
|
||||
|
||||
#TODO: make this more efficient!
|
||||
self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
|
||||
tmp = self.Kmmi- mdot(self.Kmmi,self.q_u_cov,self.Kmmi)
|
||||
|
||||
if X_variance_new is None:
|
||||
Kx = self.kern.K(X_new,self.Z)
|
||||
mu = np.dot(Kx,self.Kmmi_m)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(X_new)
|
||||
var = Kxx - mdot(Kx,tmp,Kx.T)
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(X_new)
|
||||
var = (Kxx - np.sum(Kx*np.dot(Kx,tmp),1))[:,None]
|
||||
return mu, var
|
||||
else:
|
||||
assert X_variance_new.shape == X_new.shape
|
||||
Kx = self.kern.psi1(self.Z,X_new, X_variance_new)
|
||||
mu = np.dot(Kx,self.Kmmi_m)
|
||||
Kxx = self.kern.psi0(self.Z,X_new,X_variance_new)
|
||||
psi2 = self.kern.psi2(self.Z,X_new,X_variance_new)
|
||||
diag_var = Kxx - np.sum(np.sum(psi2*tmp[None,:,:],1),1)
|
||||
if full_cov:
|
||||
raise NotImplementedError
|
||||
else:
|
||||
return mu, diag_var[:,None]
|
||||
|
||||
def predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
|
||||
# normalize X values
|
||||
Xnew = (Xnew.copy() - self._Xoffset) / self._Xscale
|
||||
if X_variance_new is not None:
|
||||
X_variance_new = X_variance_new / self._Xscale ** 2
|
||||
|
||||
# here's the actual prediction by the GP model
|
||||
mu, var = self._raw_predict(Xnew, X_variance_new, full_cov=full_cov, which_parts=which_parts)
|
||||
|
||||
# now push through likelihood
|
||||
mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov)
|
||||
|
||||
return mean, var, _025pm, _975pm
|
||||
|
||||
|
||||
def set_vb_param(self,vb_param):
|
||||
"""set the distribution q(u) from the canonical parameters"""
|
||||
self.q_u_canonical_flat = vb_param.copy()
|
||||
self.q_u_canonical = self.q_u_canonical_flat[:self.num_inducing*self.output_dim].reshape(self.num_inducing,self.output_dim),self.q_u_canonical_flat[self.num_inducing*self.output_dim:].reshape(self.num_inducing,self.num_inducing)
|
||||
|
||||
self.q_u_prec = -2.*self.q_u_canonical[1]
|
||||
self.q_u_cov, q_u_Li, q_u_L, tmp = pdinv(self.q_u_prec)
|
||||
self.q_u_Li = q_u_Li
|
||||
self.q_u_logdet = -tmp
|
||||
self.q_u_mean, _ = dpotrs(q_u_Li, np.asfortranarray(self.q_u_canonical[0]),lower=1)
|
||||
|
||||
self.q_u_expectation = (self.q_u_mean, np.dot(self.q_u_mean,self.q_u_mean.T)+self.q_u_cov*self.output_dim)
|
||||
|
||||
|
||||
def get_vb_param(self):
|
||||
"""
|
||||
Return the canonical parameters of the distribution q(u)
|
||||
"""
|
||||
return self.q_u_canonical_flat
|
||||
|
||||
|
||||
def plot(self, ax=None, fignum=None, Z_height=None, **kwargs):
|
||||
|
||||
if ax is None:
|
||||
fig = pb.figure(num=fignum)
|
||||
ax = fig.add_subplot(111)
|
||||
|
||||
#horrible hack here:
|
||||
data = self.likelihood.data.copy()
|
||||
self.likelihood.data = self.Y
|
||||
GPBase.plot(self, ax=ax, **kwargs)
|
||||
self.likelihood.data = data
|
||||
|
||||
Zu = self.Z * self._Xscale + self._Xoffset
|
||||
if self.input_dim==1:
|
||||
ax.plot(self.X_batch, self.likelihood.data, 'gx',mew=2)
|
||||
if Z_height is None:
|
||||
Z_height = ax.get_ylim()[0]
|
||||
ax.plot(Zu, np.zeros_like(Zu) + Z_height, 'r|', mew=1.5, markersize=12)
|
||||
|
||||
if self.input_dim==2:
|
||||
ax.scatter(self.X_all[:,0], self.X_all[:,1], 20., self.Y[:,0], linewidth=0, cmap=pb.cm.jet)
|
||||
ax.plot(Zu[:,0], Zu[:,1], 'w^')
|
||||
|
||||
def plot_traces(self):
|
||||
pb.figure()
|
||||
t = np.array(self._param_trace)
|
||||
pb.subplot(2,1,1)
|
||||
for l,ti in zip(self._get_param_names(),t.T):
|
||||
if not l[:3]=='iip':
|
||||
pb.plot(ti,label=l)
|
||||
pb.legend(loc=0)
|
||||
|
||||
pb.subplot(2,1,2)
|
||||
pb.plot(np.asarray(self._ll_trace),label='stochastic likelihood')
|
||||
pb.legend(loc=0)
|
||||
|
|
@ -5,3 +5,4 @@ import classification
|
|||
import regression
|
||||
import dimensionality_reduction
|
||||
import tutorials
|
||||
import stochastic
|
||||
|
|
|
|||
41
GPy/examples/stochastic.py
Normal file
41
GPy/examples/stochastic.py
Normal file
|
|
@ -0,0 +1,41 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
import pylab as pb
|
||||
import numpy as np
|
||||
import GPy
|
||||
|
||||
def toy_1d():
|
||||
N = 2000
|
||||
M = 20
|
||||
|
||||
#create data
|
||||
X = np.linspace(0,32,N)[:,None]
|
||||
Z = np.linspace(0,32,M)[:,None]
|
||||
Y = np.sin(X) + np.cos(0.3*X) + np.random.randn(*X.shape)/np.sqrt(50.)
|
||||
|
||||
m = GPy.models.SVIGPRegression(X,Y, batchsize=10, Z=Z)
|
||||
m.ensure_default_constraints()
|
||||
m.constrain_bounded('noise_variance',1e-3,1e-1)
|
||||
|
||||
m.param_steplength = 1e-4
|
||||
|
||||
fig = pb.figure()
|
||||
ax = fig.add_subplot(111)
|
||||
def cb():
|
||||
ax.cla()
|
||||
m.plot(ax=ax,Z_height=-3)
|
||||
ax.set_ylim(-3,3)
|
||||
fig.canvas.draw()
|
||||
|
||||
m.optimize(500, callback=cb, callback_interval=1)
|
||||
|
||||
m.plot_traces()
|
||||
return m
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -4,6 +4,7 @@
|
|||
from gp_regression import GPRegression
|
||||
from gp_classification import GPClassification
|
||||
from sparse_gp_regression import SparseGPRegression
|
||||
from svigp_regression import SVIGPRegression
|
||||
from sparse_gp_classification import SparseGPClassification
|
||||
from fitc_classification import FITCClassification
|
||||
from gplvm import GPLVM
|
||||
|
|
|
|||
44
GPy/models/svigp_regression.py
Normal file
44
GPy/models/svigp_regression.py
Normal file
|
|
@ -0,0 +1,44 @@
|
|||
# Copyright (c) 2012, James Hensman
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
import numpy as np
|
||||
from ..core import SVIGP
|
||||
from .. import likelihoods
|
||||
from .. import kern
|
||||
|
||||
class SVIGPRegression(SVIGP):
|
||||
"""
|
||||
Gaussian Process model for regression
|
||||
|
||||
This is a thin wrapper around the SVIGP class, with a set of sensible defalts
|
||||
|
||||
:param X: input observations
|
||||
:param Y: observed values
|
||||
:param kernel: a GPy kernel, defaults to rbf+white
|
||||
:param normalize_X: whether to normalize the input data before computing (predictions will be in original scales)
|
||||
:type normalize_X: False|True
|
||||
:param normalize_Y: whether to normalize the input data before computing (predictions will be in original scales)
|
||||
:type normalize_Y: False|True
|
||||
:rtype: model object
|
||||
|
||||
.. Note:: Multiple independent outputs are allowed using columns of Y
|
||||
|
||||
"""
|
||||
|
||||
def __init__(self, X, Y, kernel=None, Z=None, num_inducing=10, q_u=None, batchsize=10):
|
||||
# kern defaults to rbf (plus white for stability)
|
||||
if kernel is None:
|
||||
kernel = kern.rbf(X.shape[1], variance=1., lengthscale=4.) + kern.white(X.shape[1], 1e-3)
|
||||
|
||||
# Z defaults to a subset of the data
|
||||
if Z is None:
|
||||
i = np.random.permutation(X.shape[0])[:num_inducing]
|
||||
Z = X[i].copy()
|
||||
else:
|
||||
assert Z.shape[1] == X.shape[1]
|
||||
|
||||
# likelihood defaults to Gaussian
|
||||
likelihood = likelihoods.Gaussian(Y, normalize=False)
|
||||
|
||||
SVIGP.__init__(self, X, likelihood, kernel, Z, q_u=q_u, batchsize=batchsize)
|
||||
self.load_batch()
|
||||
Loading…
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Reference in a new issue