GPy/GPy/kern/_src/coregionalize.py

# Copyright (c) 2012, James Hensman and Ricardo Andrade
# Licensed under the BSD 3-clause license (see LICENSE.txt)

from kern import Kern
import numpy as np
from scipy import weave
from ...core.parameterization import Param

class Coregionalize(Kern):
    """
    Covariance function for intrinsic/linear coregionalization models

    This covariance has the form:
    .. math::
       \mathbf{B} = \mathbf{W}\mathbf{W}^\top + \text{diag}(kappa)

    An intrinsic/linear coregionalization covariance function of the form:
    .. math::

       k_2(x, y)=\mathbf{B} k(x, y)

    it is obtained as the tensor product between a covariance function
    k(x,y) and B.

    :param output_dim: number of outputs to coregionalize
    :type output_dim: int
    :param rank: number of columns of the W matrix (this parameter is ignored if parameter W is not None)
    :type rank: int
    :param W: a low rank matrix that determines the correlations between the different outputs, together with kappa it forms the coregionalization matrix B
    :type W: numpy array of dimensionality (num_outpus, W_columns)
    :param kappa: a vector which allows the outputs to behave independently
    :type kappa: numpy array of dimensionality  (output_dim,)

    .. note: see coregionalization examples in GPy.examples.regression for some usage.
    """
    def __init__(self, output_dim, rank=1, W=None, kappa=None, name='coregion'):
        super(Coregionalize, self).__init__(input_dim=1, name=name)
        self.output_dim = output_dim
        self.rank = rank
        if self.rank>output_dim-1:
            print("Warning: Unusual choice of rank, it should normally be less than the output_dim.")
        if W is None:
            W = 0.5*np.random.randn(self.output_dim,self.rank)/np.sqrt(self.rank)
        else:
            assert W.shape==(self.output_dim,self.rank)
        self.W = Param('W',W)
        if kappa is None:
            kappa = 0.5*np.ones(self.output_dim)
        else:
            assert kappa.shape==(self.output_dim,)
        self.kappa = Param('kappa', kappa)
        self.add_parameters(self.W, self.kappa)
        self.parameters_changed()


    def parameters_changed(self):
        self.B = np.dot(self.W, self.W.T) + np.diag(self.kappa)

    def K(self,index,index2,target):
        index = np.asarray(index,dtype=np.int)

        #here's the old code (numpy)
        #if index2 is None:
            #index2 = index
        #else:
            #index2 = np.asarray(index2,dtype=np.int)
        #false_target = target.copy()
        #ii,jj = np.meshgrid(index,index2)
        #ii,jj = ii.T, jj.T
        #false_target += self.B[ii,jj]

        if index2 is None:
            code="""
            for(int i=0;i<N; i++){
              target[i+i*N] += B[index[i]+output_dim*index[i]];
              for(int j=0; j<i; j++){
                  target[j+i*N] += B[index[i]+output_dim*index[j]];
                  target[i+j*N] += target[j+i*N];
                }
              }
            """
            N,B,output_dim = index.size, self.B, self.output_dim
            weave.inline(code,['target','index','N','B','output_dim'])
        else:
            index2 = np.asarray(index2,dtype=np.int)
            code="""
            for(int i=0;i<num_inducing; i++){
              for(int j=0; j<N; j++){
                  target[i+j*num_inducing] += B[output_dim*index[j]+index2[i]];
                }
              }
            """
            N,num_inducing,B,output_dim = index.size,index2.size, self.B, self.output_dim
            weave.inline(code,['target','index','index2','N','num_inducing','B','output_dim'])


    def Kdiag(self,index,target):
        target += np.diag(self.B)[np.asarray(index,dtype=np.int).flatten()]

    def update_gradients_full(self,dL_dK, index, index2=None):
        index = np.asarray(index,dtype=np.int)
        dL_dK_small = np.zeros_like(self.B)
        if index2 is None:
            index2 = index
        else:
            index2 = np.asarray(index2,dtype=np.int)

        code="""
        for(int i=0; i<num_inducing; i++){
          for(int j=0; j<N; j++){
            dL_dK_small[index[j] + output_dim*index2[i]] += dL_dK[i+j*num_inducing];
          }
        }
        """
        N, num_inducing, output_dim = index.size, index2.size, self.output_dim
        weave.inline(code, ['N','num_inducing','output_dim','dL_dK','dL_dK_small','index','index2'])

        dkappa = np.diag(dL_dK_small)
        dL_dK_small += dL_dK_small.T
        dW = (self.W[:,None,:]*dL_dK_small[:,:,None]).sum(0)

        self.W.gradient = dW
        self.kappa.gradient = dkappa

    def update_gradients_sparse(self, dL_dKmm, dL_dKnm, dL_dKdiag, X, Z):
        raise NotImplementedError, "some code below"
    #def dKdiag_dtheta(self,dL_dKdiag,index,target):
        #index = np.asarray(index,dtype=np.int).flatten()
        #dL_dKdiag_small = np.zeros(self.output_dim)
        #for i in range(self.output_dim):
            #dL_dKdiag_small[i] += np.sum(dL_dKdiag[index==i])
        #dW = 2.*self.W*dL_dKdiag_small[:,None]
        #dkappa = dL_dKdiag_small
        #target += np.hstack([dW.flatten(),dkappa])

    def gradients_X(self,dL_dK,X,X2):
        if X2 is None:
            return np.zeros((X.shape[0], X.shape[0]))
        else:
            return np.zeros((X.shape[0], X2.shape[0]))