mirror of
https://github.com/SheffieldML/GPy.git
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Fixed lots of examples
This commit is contained in:
Alan Saul
parent
f65e92228d
commit
1cf4ad1ff4
11 changed files with 22 additions and 699 deletions
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@ -8,5 +8,4 @@ from parameterization.observable_array import ObsAr
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from gp import GP
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from sparse_gp import SparseGP
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from svigp import SVIGP
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from mapping import *
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@ -1,434 +0,0 @@
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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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from ..util.linalg import pdinv, mdot, tdot, dpotrs, dtrtrs, jitchol, backsub_both_sides
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from gp import GP
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import time
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import sys
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class SVIGP(GP):
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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 sqehd 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, Y, kernel, Z, q_u=None, batchsize=10):
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raise NotImplementedError, "This is a work in progress, see github issue "
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GP.__init__(self, X, Y, kernel)
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self.batchsize=batchsize
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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 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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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._param_grad_helper(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._param_grad_helper(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.Y_batch 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.Y_batch = self.Y[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 = np.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
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the other (See Hensman et al 2012 Fast Variational inference in the
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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(self) # Change this to callback()
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time.sleep(0.01)
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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 = 0.02
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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 = 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
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self.hbar_t = (1-1/self.tau_t)*self.hbar_t + 1/self.tau_t * np.dot(g_t1.T, g_t2)
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self.vb_steplength = np.dot(self.gbar_t1.T, self.gbar_t2) / self.hbar_t
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self.vb_steplength *= decr_factor
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self.tau_t = self.tau_t*(1-self.vb_steplength) + 1
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def _raw_predict(self, X_new, X_variance_new=None, which_parts='all',full_cov=False):
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"""Internal helper function for making predictions, does not account for normalization"""
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#TODO: make this more efficient!
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self.Kmmi, self.Lm, self.Lmi, self.Kmm_logdet = pdinv(self.Kmm)
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tmp = self.Kmmi- mdot(self.Kmmi,self.q_u_cov,self.Kmmi)
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if X_variance_new is None:
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Kx = self.kern.K(X_new,self.Z)
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mu = np.dot(Kx,self.Kmmi_m)
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if full_cov:
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Kxx = self.kern.K(X_new)
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var = Kxx - mdot(Kx,tmp,Kx.T)
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else:
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Kxx = self.kern.Kdiag(X_new)
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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, *args, **kwargs):
|
||||
"""
|
||||
See GPy.plotting.matplot_dep.svig_plots.plot
|
||||
"""
|
||||
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
|
||||
from ..plotting.matplot_dep import svig_plots
|
||||
svig_plots.plot(self,*args,**kwargs)
|
||||
|
||||
|
||||
def plot_traces(self):
|
||||
"""
|
||||
See GPy.plotting.matplot_dep.svig_plots.plot_traces
|
||||
"""
|
||||
assert "matplotlib" in sys.modules, "matplotlib package has not been imported."
|
||||
from ..plotting.matplot_dep import svig_plots
|
||||
svig_plots.plot_traces(self)
|
||||
|
|
@ -4,6 +4,4 @@
|
|||
import classification
|
||||
import regression
|
||||
import dimensionality_reduction
|
||||
import tutorials
|
||||
import stochastic
|
||||
import non_gaussian
|
||||
|
|
|
|||
|
|
@ -28,13 +28,13 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True):
|
|||
m = GPy.models.SparseGPClassification(X, Y, kernel=kernel, num_inducing=num_inducing)
|
||||
|
||||
# Contrain all parameters to be positive
|
||||
m.tie_params('.*len')
|
||||
#m.tie_params('.*len')
|
||||
m['.*len'] = 10.
|
||||
m.update_likelihood_approximation()
|
||||
|
||||
# Optimize
|
||||
if optimize:
|
||||
m.optimize(max_iters=max_iters)
|
||||
for _ in range(5):
|
||||
m.optimize(max_iters=int(max_iters/5))
|
||||
print(m)
|
||||
|
||||
#Test
|
||||
|
|
@ -150,7 +150,7 @@ def sparse_toy_linear_1d_classification(num_inducing=10, seed=default_seed, opti
|
|||
print m
|
||||
return m
|
||||
|
||||
def toy_heaviside(seed=default_seed, optimize=True, plot=True):
|
||||
def toy_heaviside(seed=default_seed, max_iters=100, optimize=True, plot=True):
|
||||
"""
|
||||
Simple 1D classification example using a heavy side gp transformation
|
||||
|
||||
|
|
@ -166,16 +166,18 @@ def toy_heaviside(seed=default_seed, optimize=True, plot=True):
|
|||
Y[Y.flatten() == -1] = 0
|
||||
|
||||
# Model definition
|
||||
noise_model = GPy.likelihoods.bernoulli(GPy.likelihoods.noise_models.gp_transformations.Heaviside())
|
||||
likelihood = GPy.likelihoods.EP(Y, noise_model)
|
||||
m = GPy.models.GPClassification(data['X'], likelihood=likelihood)
|
||||
kernel = GPy.kern.RBF(1)
|
||||
likelihood = GPy.likelihoods.Bernoulli(gp_link=GPy.likelihoods.link_functions.Heaviside())
|
||||
ep = GPy.inference.latent_function_inference.expectation_propagation.EP()
|
||||
m = GPy.core.GP(X=data['X'], Y=Y, kernel=kernel, likelihood=likelihood, inference_method=ep, name='gp_classification_heaviside')
|
||||
#m = GPy.models.GPClassification(data['X'], likelihood=likelihood)
|
||||
|
||||
# Optimize
|
||||
if optimize:
|
||||
m.update_likelihood_approximation()
|
||||
# Parameters optimization:
|
||||
m.optimize()
|
||||
#m.pseudo_EM()
|
||||
for _ in range(5):
|
||||
m.optimize(max_iters=int(max_iters/5))
|
||||
print m
|
||||
|
||||
# Plot
|
||||
if plot:
|
||||
|
|
|
|||
|
|
@ -59,7 +59,7 @@ def student_t_approx(optimize=True, plot=True):
|
|||
t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
|
||||
laplace_inf = GPy.inference.latent_function_inference.Laplace()
|
||||
m3 = GPy.core.GP(X, Y.copy(), kernel3, likelihood=t_distribution, inference_method=laplace_inf)
|
||||
m3['.*t_noise'].constrain_bounded(1e-6, 10.)
|
||||
m3['.*t_scale2'].constrain_bounded(1e-6, 10.)
|
||||
m3['.*white'].constrain_fixed(1e-5)
|
||||
m3.randomize()
|
||||
|
||||
|
|
@ -67,7 +67,7 @@ def student_t_approx(optimize=True, plot=True):
|
|||
t_distribution = GPy.likelihoods.StudentT(deg_free=deg_free, sigma2=edited_real_sd)
|
||||
laplace_inf = GPy.inference.latent_function_inference.Laplace()
|
||||
m4 = GPy.core.GP(X, Yc.copy(), kernel4, likelihood=t_distribution, inference_method=laplace_inf)
|
||||
m4['.*t_noise'].constrain_bounded(1e-6, 10.)
|
||||
m4['.*t_scale2'].constrain_bounded(1e-6, 10.)
|
||||
m4['.*white'].constrain_fixed(1e-5)
|
||||
m4.randomize()
|
||||
print m4
|
||||
|
|
@ -124,6 +124,7 @@ def student_t_approx(optimize=True, plot=True):
|
|||
return m1, m2, m3, m4
|
||||
|
||||
def boston_example(optimize=True, plot=True):
|
||||
raise NotImplementedError("Needs updating")
|
||||
import sklearn
|
||||
from sklearn.cross_validation import KFold
|
||||
optimizer='bfgs'
|
||||
|
|
@ -152,8 +153,8 @@ def boston_example(optimize=True, plot=True):
|
|||
noise = 1e-1 #np.exp(-2)
|
||||
rbf_len = 0.5
|
||||
data_axis_plot = 4
|
||||
kernelstu = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
||||
kernelgp = GPy.kern.rbf(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
||||
kernelstu = GPy.kern.RBF(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
||||
kernelgp = GPy.kern.RBF(X.shape[1]) + GPy.kern.white(X.shape[1]) + GPy.kern.bias(X.shape[1])
|
||||
|
||||
#Baseline
|
||||
score_folds[0, n] = rmse(Y_test, np.mean(Y_train))
|
||||
|
|
@ -162,8 +163,8 @@ def boston_example(optimize=True, plot=True):
|
|||
print "Gauss GP"
|
||||
mgp = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelgp.copy())
|
||||
mgp.constrain_fixed('.*white', 1e-5)
|
||||
mgp['rbf_len'] = rbf_len
|
||||
mgp['noise'] = noise
|
||||
mgp['.*len'] = rbf_len
|
||||
mgp['.*noise'] = noise
|
||||
print mgp
|
||||
if optimize:
|
||||
mgp.optimize(optimizer=optimizer, messages=messages)
|
||||
|
|
@ -198,9 +199,9 @@ def boston_example(optimize=True, plot=True):
|
|||
stu_t_likelihood = GPy.likelihoods.Laplace(Y_train.copy(), t_distribution)
|
||||
mstu_t = GPy.models.GPRegression(X_train.copy(), Y_train.copy(), kernel=kernelstu.copy(), likelihood=stu_t_likelihood)
|
||||
mstu_t.constrain_fixed('.*white', 1e-5)
|
||||
mstu_t.constrain_bounded('.*t_noise', 0.0001, 1000)
|
||||
mstu_t.constrain_bounded('.*t_scale2', 0.0001, 1000)
|
||||
mstu_t['rbf_len'] = rbf_len
|
||||
mstu_t['.*t_noise'] = noise
|
||||
mstu_t['.*t_scale2'] = noise
|
||||
print mstu_t
|
||||
if optimize:
|
||||
mstu_t.optimize(optimizer=optimizer, messages=messages)
|
||||
|
|
|
|||
|
|
@ -1,40 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
try:
|
||||
import pylab as pb
|
||||
except:
|
||||
pass
|
||||
import numpy as np
|
||||
import GPy
|
||||
|
||||
def toy_1d(optimize=True, plot=True):
|
||||
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.constrain_bounded('noise_variance',1e-3,1e-1)
|
||||
m.constrain_bounded('white_variance',1e-3,1e-1)
|
||||
|
||||
m.param_steplength = 1e-4
|
||||
|
||||
if plot:
|
||||
fig = pb.figure()
|
||||
ax = fig.add_subplot(111)
|
||||
def cb(foo):
|
||||
ax.cla()
|
||||
m.plot(ax=ax,Z_height=-3)
|
||||
ax.set_ylim(-3,3)
|
||||
fig.canvas.draw()
|
||||
|
||||
if optimize:
|
||||
m.optimize(500, callback=cb, callback_interval=1)
|
||||
|
||||
if plot:
|
||||
m.plot_traces()
|
||||
return m
|
||||
|
|
@ -1,156 +0,0 @@
|
|||
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
||||
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
||||
|
||||
|
||||
"""
|
||||
Code of Tutorials
|
||||
"""
|
||||
|
||||
try:
|
||||
import pylab as pb
|
||||
pb.ion()
|
||||
except:
|
||||
pass
|
||||
import numpy as np
|
||||
import GPy
|
||||
|
||||
def tuto_GP_regression(optimize=True, plot=True):
|
||||
"""The detailed explanations of the commands used in this file can be found in the tutorial section"""
|
||||
|
||||
X = np.random.uniform(-3.,3.,(20,1))
|
||||
Y = np.sin(X) + np.random.randn(20,1)*0.05
|
||||
|
||||
kernel = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
|
||||
|
||||
m = GPy.models.GPRegression(X, Y, kernel)
|
||||
|
||||
print m
|
||||
if plot:
|
||||
m.plot()
|
||||
|
||||
m.constrain_positive('')
|
||||
|
||||
m.unconstrain('') # may be used to remove the previous constrains
|
||||
m.constrain_positive('.*rbf_variance')
|
||||
m.constrain_bounded('.*lengthscale',1.,10. )
|
||||
m.constrain_fixed('.*noise',0.0025)
|
||||
|
||||
if optimize:
|
||||
m.optimize()
|
||||
m.optimize_restarts(num_restarts = 10)
|
||||
|
||||
#######################################################
|
||||
#######################################################
|
||||
# sample inputs and outputs
|
||||
X = np.random.uniform(-3.,3.,(50,2))
|
||||
Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(50,1)*0.05
|
||||
|
||||
# define kernel
|
||||
ker = GPy.kern.Matern52(2,ARD=True) + GPy.kern.white(2)
|
||||
|
||||
# create simple GP model
|
||||
m = GPy.models.GPRegression(X, Y, ker)
|
||||
|
||||
# contrain all parameters to be positive
|
||||
m.constrain_positive('')
|
||||
|
||||
# optimize and plot
|
||||
if optimize:
|
||||
m.optimize('tnc', max_f_eval = 1000)
|
||||
if plot:
|
||||
m.plot()
|
||||
|
||||
print m
|
||||
return(m)
|
||||
|
||||
def tuto_kernel_overview(optimize=True, plot=True):
|
||||
"""The detailed explanations of the commands used in this file can be found in the tutorial section"""
|
||||
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
|
||||
ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.)
|
||||
ker3 = GPy.kern.rbf(1, .5, .5)
|
||||
|
||||
print ker2
|
||||
|
||||
if plot:
|
||||
ker1.plot()
|
||||
ker2.plot()
|
||||
ker3.plot()
|
||||
|
||||
k1 = GPy.kern.rbf(1,1.,2.)
|
||||
k2 = GPy.kern.Matern32(1, 0.5, 0.2)
|
||||
|
||||
# Product of kernels
|
||||
k_prod = k1.prod(k2) # By default, tensor=False
|
||||
k_prodtens = k1.prod(k2,tensor=True)
|
||||
|
||||
# Sum of kernels
|
||||
k_add = k1.add(k2) # By default, tensor=False
|
||||
k_addtens = k1.add(k2,tensor=True)
|
||||
|
||||
k1 = GPy.kern.rbf(1,1.,2)
|
||||
k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
|
||||
|
||||
k = k1 * k2 # equivalent to k = k1.prod(k2)
|
||||
print k
|
||||
|
||||
# Simulate sample paths
|
||||
X = np.linspace(-5,5,501)[:,None]
|
||||
Y = np.random.multivariate_normal(np.zeros(501),k.K(X),1)
|
||||
|
||||
k1 = GPy.kern.rbf(1)
|
||||
k2 = GPy.kern.Matern32(1)
|
||||
k3 = GPy.kern.white(1)
|
||||
|
||||
k = k1 + k2 + k3
|
||||
print k
|
||||
|
||||
k.constrain_positive('.*var')
|
||||
k.constrain_fixed(np.array([1]),1.75)
|
||||
k.tie_params('.*len')
|
||||
k.unconstrain('white')
|
||||
k.constrain_bounded('white',lower=1e-5,upper=.5)
|
||||
print k
|
||||
|
||||
k_cst = GPy.kern.bias(1,variance=1.)
|
||||
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
|
||||
Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True)
|
||||
print Kanova
|
||||
|
||||
# sample inputs and outputs
|
||||
X = np.random.uniform(-3.,3.,(40,2))
|
||||
Y = 0.5*X[:,:1] + 0.5*X[:,1:] + 2*np.sin(X[:,:1]) * np.sin(X[:,1:])
|
||||
|
||||
# Create GP regression model
|
||||
m = GPy.models.GPRegression(X, Y, Kanova)
|
||||
|
||||
if plot:
|
||||
fig = pb.figure(figsize=(5,5))
|
||||
ax = fig.add_subplot(111)
|
||||
m.plot(ax=ax)
|
||||
|
||||
pb.figure(figsize=(20,3))
|
||||
pb.subplots_adjust(wspace=0.5)
|
||||
axs = pb.subplot(1,5,1)
|
||||
m.plot(ax=axs)
|
||||
pb.subplot(1,5,2)
|
||||
pb.ylabel("= ",rotation='horizontal',fontsize='30')
|
||||
axs = pb.subplot(1,5,3)
|
||||
m.plot(ax=axs, which_parts=[False,True,False,False])
|
||||
pb.ylabel("cst +",rotation='horizontal',fontsize='30')
|
||||
axs = pb.subplot(1,5,4)
|
||||
m.plot(ax=axs, which_parts=[False,False,True,False])
|
||||
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
|
||||
axs = pb.subplot(1,5,5)
|
||||
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
|
||||
m.plot(ax=axs, which_parts=[False,False,False,True])
|
||||
|
||||
return(m)
|
||||
|
||||
|
||||
def model_interaction(optimize=True, plot=True):
|
||||
X = np.random.randn(20,1)
|
||||
Y = np.sin(X) + np.random.randn(*X.shape)*0.01 + 5.
|
||||
k = GPy.kern.RBF(1) + GPy.kern.Bias(1)
|
||||
m = GPy.models.GPRegression(X, Y, kernel=k)
|
||||
return m
|
||||
|
||||
|
|
@ -4,7 +4,6 @@
|
|||
from gp_regression import GPRegression
|
||||
from gp_classification import GPClassification
|
||||
from sparse_gp_regression import SparseGPRegression, SparseGPRegressionUncertainInput
|
||||
from svigp_regression import SVIGPRegression
|
||||
from sparse_gp_classification import SparseGPClassification
|
||||
from gplvm import GPLVM
|
||||
from bcgplvm import BCGPLVM
|
||||
|
|
|
|||
|
|
@ -1,45 +0,0 @@
|
|||
# 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, normalize_Y=False):
|
||||
# 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=normalize_Y)
|
||||
|
||||
SVIGP.__init__(self, X, likelihood, kernel, Z, q_u=q_u, batchsize=batchsize)
|
||||
self.load_batch()
|
||||
|
||||
|
|
@ -6,7 +6,6 @@ import models_plots
|
|||
import priors_plots
|
||||
import variational_plots
|
||||
import kernel_plots
|
||||
import svig_plots
|
||||
import dim_reduction_plots
|
||||
import mapping_plots
|
||||
import Tango
|
||||
|
|
|
|||
|
|
@ -36,7 +36,7 @@ def flatten_nested(lst):
|
|||
result.append(element)
|
||||
return result
|
||||
|
||||
#@nottest
|
||||
@nottest
|
||||
def test_models():
|
||||
optimize=False
|
||||
plot=True
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue