Source code for GPy.models.gp_offset_regression

# Copyright (c) 2012 - 2014 the GPy Austhors (see AUTHORS.txt)
# Licensed under the BSD 3-clause license (see LICENSE.txt)
# Written by Mike Smith.

import numpy as np
from ..core import GP
from .. import likelihoods
from .. import kern
from ..core import Param

[docs]class GPOffsetRegression(GP): """ Gaussian Process model for offset regression :param X: input observations, we assume for this class that this has one dimension of actual inputs and the last dimension should be the index of the cluster (so X should be Nx2) :param Y: observed values (Nx1?) :param kernel: a GPy kernel, defaults to rbf :param Norm normalizer: [False] :param noise_var: the noise variance for Gaussian likelhood, defaults to 1. Normalize Y with the norm given. If normalizer is False, no normalization will be done If it is None, we use GaussianNorm(alization) .. Note:: Multiple independent outputs are allowed using columns of Y """ def __init__(self, X, Y, kernel=None, Y_metadata=None, normalizer=None, noise_var=1., mean_function=None): assert X.shape[1]>1, "Need at least two input dimensions, as last dimension is the label of the cluster" if kernel is None: kernel = kern.RBF(X.shape[1]-1) #self._log_marginal_likelihood = np.nan #todo likelihood = likelihoods.Gaussian(variance=noise_var) self.X_fixed = X[:,:-1] self.selected = np.array([int(x) for x in X[:,-1]]) super(GPOffsetRegression, self).__init__(X, Y, kernel, likelihood, name='GP offset regression', Y_metadata=Y_metadata, normalizer=normalizer, mean_function=mean_function) maxcluster = np.max(self.selected) self.offset = Param('offset', np.zeros(maxcluster)) #self.offset.set_prior(...) self.link_parameter(self.offset) #def dr_doffset(self, X, sel): #how much r changes wrt the offset hyperparameters #def dL_doffset(self, X, sel): # dL_dr = self.dK_dr_via_X(X, X) * dL_dK
[docs] def dr_doffset(self,X,sel,delta): #given an input matrix, X and the offsets (delta) #finds dr/dDelta #returns them as a list, one for each offset (delta). #get the input values #a matrix G represents the effect of increasing the offset on the radius passed to the kernel for each input. For example #what effect will increasing offset 4 have on the kernel output of inputs 5 and 8? Answer: Gs[4][5,8]... (positive or negative) Gs = [] for i,d in enumerate(delta): #X[sel==(i+1)]-=d G = np.repeat(np.array(sel==(i+1))[:,None]*1,len(X),axis=1) - np.repeat(np.array(sel==(i+1))[None,:]*1,len(X),axis=0) Gs.append(G) #does subtracting the two Xs end up positive or negative (if negative we need to flip the sign in G). w = np.repeat(X,len(X),axis=1) - np.repeat(X.T,len(X),axis=0) dr_doffsets = [] for i,d in enumerate(delta): dr_doffset = np.sign(w * Gs[i]) #print "dr_doffset %d" % i #print dr_doffset #print Gs[i] #print w dr_doffsets.append(dr_doffset) #lastly we need to divide by the lengthscale: So far we've found d(X_i - X_j)/dOffsets #we want dr/dOffsets. (X_i - X_j)/lengthscale = r dr_doffsets /= self.kern.lengthscale return dr_doffsets
[docs] def parameters_changed(self): offsets = np.hstack([0.0,self.offset.values])[:,None] self.X = self.X_fixed - offsets[self.selected] super(GPOffsetRegression, self).parameters_changed() dL_dr = self.kern.dK_dr_via_X(self.X, self.X) * self.grad_dict['dL_dK'] dr_doff = self.dr_doffset(self.X,self.selected,self.offset.values) for i in range(len(dr_doff)): dL_doff = dL_dr * dr_doff[i] self.offset.gradient[i] = -np.sum(dL_doff)