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new ssrbf implementation
This commit is contained in:
Zhenwen Dai
parent
c7d0bd2204
commit
22d30d9d39
1 changed files with 380 additions and 181 deletions
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@ -7,193 +7,392 @@ The package for the psi statistics computation
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import numpy as np
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import numpy as np
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def psicomputations(variance, lengthscale, Z, variational_posterior):
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try:
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"""
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from scipy import weave
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Z - MxQ
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mu - NxQ
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi0, psi1 and psi2
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# Produced intermediate results:
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# _psi1 NxM
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mu = variational_posterior.mean
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S = variational_posterior.variance
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gamma = variational_posterior.binary_prob
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psi0 = np.empty(mu.shape[0])
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def _psicomputations(variance, lengthscale, Z, variational_posterior):
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psi0[:] = variance
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"""
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psi1 = _psi1computations(variance, lengthscale, Z, mu, S, gamma)
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Z - MxQ
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psi2 = _psi2computations(variance, lengthscale, Z, mu, S, gamma)
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mu - NxQ
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return psi0, psi1, psi2
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi0, psi1 and psi2
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# Produced intermediate results:
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# _psi1 NxM
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mu = variational_posterior.mean
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S = variational_posterior.variance
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gamma = variational_posterior.binary_prob
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def _psi1computations(variance, lengthscale, Z, mu, S, gamma):
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N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1]
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"""
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l2 = np.square(lengthscale)
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Z - MxQ
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log_denom1 = np.log(S/l2+1)
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mu - NxQ
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log_denom2 = np.log(2*S/l2+1)
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S - NxQ
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log_gamma = np.log(gamma)
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gamma - NxQ
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log_gamma1 = np.log(1.-gamma)
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"""
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variance = float(variance)
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# here are the "statistics" for psi1
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psi0 = np.empty(N)
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# Produced intermediate results:
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psi0[:] = variance
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# _psi1 NxM
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psi1 = np.empty((N,M))
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psi2n = np.empty((N,M,M))
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lengthscale2 = np.square(lengthscale)
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from ....util.misc import param_to_array
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S = param_to_array(S)
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mu = param_to_array(mu)
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gamma = param_to_array(gamma)
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Z = param_to_array(Z)
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# psi1
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support_code = """
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_psi1_denom = S[:, None, :] / lengthscale2 + 1. # Nx1xQ
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#include <math.h>
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_psi1_denom_sqrt = np.sqrt(_psi1_denom) #Nx1xQ
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"""
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_psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ
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code = """
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_psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom) # NxMxQ
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for(int n=0; n<N; n++) {
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_psi1_common = gamma[:,None,:] / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #Nx1xQ
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for(int m1=0;m1<M;m1++) {
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_psi1_exponent1 = np.log(gamma[:,None,:]) - (_psi1_dist_sq + np.log(_psi1_denom))/2. # NxMxQ
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double log_psi1=0;
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_psi1_exponent2 = np.log(1.-gamma[:,None,:]) - (np.square(Z[None,:,:])/lengthscale2)/2. # NxMxQ
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for(int m2=0;m2<=m1;m2++) {
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_psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)
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double log_psi2_n=0;
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_psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ
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for(int q=0;q<Q;q++) {
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_psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM
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double Snq = S(n,q);
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_psi1 = variance * np.exp(_psi1_exp_sum) # NxM
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double lq = l2(q);
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double Zm1q = Z(m1,q);
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double Zm2q = Z(m2,q);
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return _psi1
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if(m2==0) {
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// Compute Psi_1
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double muZ = mu(n,q)-Z(m1,q);
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def _psi2computations(variance, lengthscale, Z, mu, S, gamma):
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double psi1_exp1 = log_gamma(n,q) - (muZ*muZ/(Snq+lq) +log_denom1(n,q))/2.;
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"""
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double psi1_exp2 = log_gamma1(n,q) -Zm1q*Zm1q/(2.*lq);
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Z - MxQ
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log_psi1 += (psi1_exp1>psi1_exp2)?psi1_exp1+log1p(exp(psi1_exp2-psi1_exp1)):psi1_exp2+log1p(exp(psi1_exp1-psi1_exp2));
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mu - NxQ
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}
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S - NxQ
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// Compute Psi_2
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gamma - NxQ
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double muZhat = mu(n,q) - (Zm1q+Zm2q)/2.;
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"""
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double Z2 = Zm1q*Zm1q+ Zm2q*Zm2q;
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# here are the "statistics" for psi2
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double dZ = Zm1q - Zm2q;
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# Produced intermediate results:
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# _psi2 MxM
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lengthscale2 = np.square(lengthscale)
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double psi2_exp1 = dZ*dZ/(-4.*lq)-muZhat*muZhat/(2.*Snq+lq) - log_denom2(n,q)/2. + log_gamma(n,q);
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double psi2_exp2 = log_gamma1(n,q) - Z2/(2.*lq);
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log_psi2_n += (psi2_exp1>psi2_exp2)?psi2_exp1+log1p(exp(psi2_exp2-psi2_exp1)):psi2_exp2+log1p(exp(psi2_exp1-psi2_exp2));
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}
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double exp_psi2_n = exp(log_psi2_n);
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psi2n(n,m1,m2) = variance*variance*exp_psi2_n;
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if(m1!=m2) { psi2n(n,m2,m1) = variance*variance*exp_psi2_n;}
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}
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psi1(n,m1) = variance*exp(log_psi1);
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}
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}
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"""
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weave.inline(code, support_code=support_code, arg_names=['psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','log_denom1','log_denom2','log_gamma','log_gamma1'], type_converters=weave.converters.blitz)
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_psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
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psi2 = psi2n.sum(axis=0)
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_psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
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return psi0,psi1,psi2,psi2n
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_psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q
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_psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ
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# psi2
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from GPy.util.caching import Cacher
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_psi2_denom = 2.*S[:, None, None, :] / lengthscale2 + 1. # Nx1x1xQ
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psicomputations = Cacher(_psicomputations, limit=1)
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_psi2_denom_sqrt = np.sqrt(_psi2_denom)
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_psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q
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_psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom)
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_psi2_common = gamma[:,None,None,:]/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # Nx1x1xQ
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_psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom)+np.log(gamma[:,None,None,:]) #N,M,M,Q
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_psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ
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_psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)
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_psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))
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_psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM
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_psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM
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return _psi2
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def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
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ARD = (len(lengthscale)!=1)
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def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
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_,psi1,_,psi2n = psicomputations(variance, lengthscale, Z, variational_posterior)
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ARD = (len(lengthscale)!=1)
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dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
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mu = variational_posterior.mean
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dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
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S = variational_posterior.variance
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gamma = variational_posterior.binary_prob
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N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1]
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l2 = np.square(lengthscale)
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log_denom1 = np.log(S/l2+1)
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log_denom2 = np.log(2*S/l2+1)
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log_gamma = np.log(gamma)
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log_gamma1 = np.log(1.-gamma)
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variance = float(variance)
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dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2
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dvar = np.zeros(1)
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dmu = np.zeros((N,Q))
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dS = np.zeros((N,Q))
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dgamma = np.zeros((N,Q))
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dl = np.zeros(Q)
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dZ = np.zeros((M,Q))
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dvar += np.sum(dL_dpsi0)
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dL_dlengscale = dl_psi1 + dl_psi2
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from ....util.misc import param_to_array
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if not ARD:
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S = param_to_array(S)
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dL_dlengscale = dL_dlengscale.sum()
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mu = param_to_array(mu)
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gamma = param_to_array(gamma)
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Z = param_to_array(Z)
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dL_dgamma = dgamma_psi1 + dgamma_psi2
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support_code = """
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dL_dmu = dmu_psi1 + dmu_psi2
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#include <math.h>
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dL_dS = dS_psi1 + dS_psi2
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"""
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dL_dZ = dZ_psi1 + dZ_psi2
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code = """
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for(int n=0; n<N; n++) {
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for(int m1=0;m1<M;m1++) {
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double log_psi1=0;
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for(int m2=0;m2<M;m2++) {
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double log_psi2_n=0;
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for(int q=0;q<Q;q++) {
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double Snq = S(n,q);
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double lq = l2(q);
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double Zm1q = Z(m1,q);
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double Zm2q = Z(m2,q);
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double gnq = gamma(n,q);
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double mu_nq = mu(n,q);
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return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma
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if(m2==0) {
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// Compute Psi_1
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double lpsi1 = psi1(n,m1)*dL_dpsi1(n,m1);
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if(q==0) {dvar(0) += lpsi1/variance;}
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def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S, gamma):
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double Zmu = Zm1q - mu_nq;
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"""
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double denom = Snq+lq;
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dL_dpsi1 - NxM
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double Zmu2_denom = Zmu*Zmu/denom;
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Z - MxQ
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mu - NxQ
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S - NxQ
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gamma - NxQ
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"""
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# here are the "statistics" for psi1
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# Produced intermediate results: dL_dparams w.r.t. psi1
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# _dL_dvariance 1
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# _dL_dlengthscale Q
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# _dL_dZ MxQ
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# _dL_dgamma NxQ
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# _dL_dmu NxQ
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# _dL_dS NxQ
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lengthscale2 = np.square(lengthscale)
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double exp1 = log_gamma(n,q)-(Zmu*Zmu/(Snq+lq)+log_denom1(n,q))/(2.);
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double exp2 = log_gamma1(n,q)-Zm1q*Zm1q/(2.*lq);
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double d_exp1,d_exp2;
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if(exp1>exp2) {
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d_exp1 = 1.;
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d_exp2 = exp(exp2-exp1);
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} else {
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d_exp1 = exp(exp1-exp2);
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d_exp2 = 1.;
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}
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double exp_sum = d_exp1+d_exp2;
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# psi1
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dmu(n,q) += lpsi1*Zmu*d_exp1/(denom*exp_sum);
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_psi1_denom = S / lengthscale2 + 1. # NxQ
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dS(n,q) += lpsi1*(Zmu2_denom-1.)*d_exp1/(denom*exp_sum)/2.;
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_psi1_denom_sqrt = np.sqrt(_psi1_denom) #NxQ
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dgamma(n,q) += lpsi1*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum;
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_psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ
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dl(q) += lpsi1*((Zmu2_denom+Snq/lq)/denom*d_exp1+Zm1q*Zm1q/(lq*lq)*d_exp2)/(2.*exp_sum);
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_psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom[:,None,:]) # NxMxQ
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dZ(m1,q) += lpsi1*(-Zmu/denom*d_exp1-Zm1q/lq*d_exp2)/exp_sum;
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_psi1_common = gamma / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #NxQ
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}
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_psi1_exponent1 = np.log(gamma[:,None,:]) -0.5 * (_psi1_dist_sq + np.log(_psi1_denom[:, None,:])) # NxMxQ
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// Compute Psi_2
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_psi1_exponent2 = np.log(1.-gamma[:,None,:]) -0.5 * (np.square(Z[None,:,:])/lengthscale2) # NxMxQ
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double lpsi2 = psi2n(n,m1,m2)*dL_dpsi2(m1,m2);
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_psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)
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if(q==0) {dvar(0) += lpsi2*2/variance;}
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_psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ
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_psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM
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_psi1_exp_dist_sq = np.exp(-0.5*_psi1_dist_sq) # NxMxQ
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_psi1_exp_Z = np.exp(-0.5*np.square(Z[None,:,:])/lengthscale2) # 1xMxQ
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_psi1_q = variance * np.exp(_psi1_exp_sum[:,:,None] - _psi1_exponent) # NxMxQ
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_psi1 = variance * np.exp(_psi1_exp_sum) # NxM
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_dL_dvariance = np.einsum('nm,nm->',dL_dpsi1, _psi1)/variance # 1
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_dL_dgamma = np.einsum('nm,nmq,nmq->nq',dL_dpsi1, _psi1_q, (_psi1_exp_dist_sq/_psi1_denom_sqrt[:,None,:]-_psi1_exp_Z)) # NxQ
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_dL_dmu = np.einsum('nm, nmq, nmq, nmq, nq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_dist,_psi1_common) # NxQ
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_dL_dS = np.einsum('nm,nmq,nmq,nq,nmq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_common,(_psi1_dist_sq-1.))/2. # NxQ
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_dL_dZ = np.einsum('nm,nmq,nmq->mq',dL_dpsi1,_psi1_q, (- _psi1_common[:,None,:] * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z))
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_dL_dlengthscale = lengthscale* np.einsum('nm,nmq,nmq->q',dL_dpsi1,_psi1_q,(_psi1_common[:,None,:]*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + (1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z))
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return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
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double dZm1m2 = Zm1q - Zm2q;
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double Z2 = Zm1q*Zm1q+Zm2q*Zm2q;
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double muZhat = mu_nq - (Zm1q + Zm2q)/2.;
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double denom = 2.*Snq+lq;
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double muZhat2_denom = muZhat*muZhat/denom;
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def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S, gamma):
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double exp1 = dZm1m2*dZm1m2/(-4.*lq)-muZhat*muZhat/(2.*Snq+lq) - log_denom2(n,q)/2. + log_gamma(n,q);
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"""
|
double exp2 = log_gamma1(n,q) - Z2/(2.*lq);
|
||||||
Z - MxQ
|
double d_exp1,d_exp2;
|
||||||
mu - NxQ
|
if(exp1>exp2) {
|
||||||
S - NxQ
|
d_exp1 = 1.;
|
||||||
gamma - NxQ
|
d_exp2 = exp(exp2-exp1);
|
||||||
dL_dpsi2 - MxM
|
} else {
|
||||||
"""
|
d_exp1 = exp(exp1-exp2);
|
||||||
# here are the "statistics" for psi2
|
d_exp2 = 1.;
|
||||||
# Produced the derivatives w.r.t. psi2:
|
}
|
||||||
# _dL_dvariance 1
|
double exp_sum = d_exp1+d_exp2;
|
||||||
# _dL_dlengthscale Q
|
|
||||||
# _dL_dZ MxQ
|
|
||||||
# _dL_dgamma NxQ
|
|
||||||
# _dL_dmu NxQ
|
|
||||||
# _dL_dS NxQ
|
|
||||||
|
|
||||||
lengthscale2 = np.square(lengthscale)
|
dmu(n,q) += -2.*lpsi2*muZhat/denom*d_exp1/exp_sum;
|
||||||
|
dS(n,q) += lpsi2*(2.*muZhat2_denom-1.)/denom*d_exp1/exp_sum;
|
||||||
|
dgamma(n,q) += lpsi2*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum;
|
||||||
|
dl(q) += lpsi2*(((Snq/lq+muZhat2_denom)/denom+dZm1m2*dZm1m2/(4.*lq*lq))*d_exp1+Z2/(2.*lq*lq)*d_exp2)/exp_sum;
|
||||||
|
dZ(m1,q) += 2.*lpsi2*((muZhat/denom-dZm1m2/(2*lq))*d_exp1-Zm1q/lq*d_exp2)/exp_sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
"""
|
||||||
|
weave.inline(code, support_code=support_code, arg_names=['dL_dpsi1','dL_dpsi2','psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','log_denom1','log_denom2','log_gamma','log_gamma1','dvar','dl','dmu','dS','dgamma','dZ'], type_converters=weave.converters.blitz)
|
||||||
|
|
||||||
_psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
|
dl *= 2.*lengthscale
|
||||||
_psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
|
if not ARD:
|
||||||
_psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q
|
dl = dl.sum()
|
||||||
_psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ
|
|
||||||
|
|
||||||
# psi2
|
return dvar, dl, dZ, dmu, dS, dgamma
|
||||||
_psi2_denom = 2.*S / lengthscale2 + 1. # NxQ
|
|
||||||
_psi2_denom_sqrt = np.sqrt(_psi2_denom)
|
|
||||||
_psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q
|
|
||||||
_psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom[:,None,None,:])
|
|
||||||
_psi2_common = gamma/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # NxQ
|
|
||||||
_psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom[:,None,None,:])+np.log(gamma[:,None,None,:]) #N,M,M,Q
|
|
||||||
_psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ
|
|
||||||
_psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)
|
|
||||||
_psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))
|
|
||||||
_psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM
|
|
||||||
_psi2_q = variance*variance * np.exp(_psi2_exp_sum[:,:,:,None]-_psi2_exponent) # NxMxMxQ
|
|
||||||
_psi2_exp_dist_sq = np.exp(-_psi2_Zdist_sq -_psi2_mudist_sq) # NxMxMxQ
|
|
||||||
_psi2_exp_Z = np.exp(-0.5*_psi2_Z_sq_sum) # MxMxQ
|
|
||||||
_psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM
|
|
||||||
_dL_dvariance = np.einsum('mo,mo->',dL_dpsi2,_psi2)*2./variance
|
|
||||||
_dL_dgamma = np.einsum('mo,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,(_psi2_exp_dist_sq/_psi2_denom_sqrt[:,None,None,:] - _psi2_exp_Z))
|
|
||||||
_dL_dmu = -2.*np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,_psi2_common,_psi2_mudist,_psi2_exp_dist_sq)
|
|
||||||
_dL_dS = np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q, _psi2_common, (2.*_psi2_mudist_sq-1.), _psi2_exp_dist_sq)
|
|
||||||
_dL_dZ = 2.*np.einsum('mo,nmoq,nmoq->mq',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(-_psi2_Zdist*_psi2_denom[:,None,None,:]+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z))
|
|
||||||
_dL_dlengthscale = 2.*lengthscale* np.einsum('mo,nmoq,nmoq->q',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom[:,None,None,:]+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z))
|
|
||||||
|
|
||||||
return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
|
except:
|
||||||
|
|
||||||
|
def psicomputations(variance, lengthscale, Z, variational_posterior):
|
||||||
|
"""
|
||||||
|
Z - MxQ
|
||||||
|
mu - NxQ
|
||||||
|
S - NxQ
|
||||||
|
gamma - NxQ
|
||||||
|
"""
|
||||||
|
# here are the "statistics" for psi0, psi1 and psi2
|
||||||
|
# Produced intermediate results:
|
||||||
|
# _psi1 NxM
|
||||||
|
mu = variational_posterior.mean
|
||||||
|
S = variational_posterior.variance
|
||||||
|
gamma = variational_posterior.binary_prob
|
||||||
|
|
||||||
|
psi0 = np.empty(mu.shape[0])
|
||||||
|
psi0[:] = variance
|
||||||
|
psi1 = _psi1computations(variance, lengthscale, Z, mu, S, gamma)
|
||||||
|
psi2 = _psi2computations(variance, lengthscale, Z, mu, S, gamma)
|
||||||
|
return psi0, psi1, psi2
|
||||||
|
|
||||||
|
def _psi1computations(variance, lengthscale, Z, mu, S, gamma):
|
||||||
|
"""
|
||||||
|
Z - MxQ
|
||||||
|
mu - NxQ
|
||||||
|
S - NxQ
|
||||||
|
gamma - NxQ
|
||||||
|
"""
|
||||||
|
# here are the "statistics" for psi1
|
||||||
|
# Produced intermediate results:
|
||||||
|
# _psi1 NxM
|
||||||
|
|
||||||
|
lengthscale2 = np.square(lengthscale)
|
||||||
|
|
||||||
|
# psi1
|
||||||
|
_psi1_denom = S[:, None, :] / lengthscale2 + 1. # Nx1xQ
|
||||||
|
_psi1_denom_sqrt = np.sqrt(_psi1_denom) #Nx1xQ
|
||||||
|
_psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ
|
||||||
|
_psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom) # NxMxQ
|
||||||
|
_psi1_common = gamma[:,None,:] / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #Nx1xQ
|
||||||
|
_psi1_exponent1 = np.log(gamma[:,None,:]) - (_psi1_dist_sq + np.log(_psi1_denom))/2. # NxMxQ
|
||||||
|
_psi1_exponent2 = np.log(1.-gamma[:,None,:]) - (np.square(Z[None,:,:])/lengthscale2)/2. # NxMxQ
|
||||||
|
_psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)
|
||||||
|
_psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ
|
||||||
|
_psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM
|
||||||
|
_psi1 = variance * np.exp(_psi1_exp_sum) # NxM
|
||||||
|
|
||||||
|
return _psi1
|
||||||
|
|
||||||
|
def _psi2computations(variance, lengthscale, Z, mu, S, gamma):
|
||||||
|
"""
|
||||||
|
Z - MxQ
|
||||||
|
mu - NxQ
|
||||||
|
S - NxQ
|
||||||
|
gamma - NxQ
|
||||||
|
"""
|
||||||
|
# here are the "statistics" for psi2
|
||||||
|
# Produced intermediate results:
|
||||||
|
# _psi2 MxM
|
||||||
|
|
||||||
|
lengthscale2 = np.square(lengthscale)
|
||||||
|
|
||||||
|
_psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
|
||||||
|
_psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
|
||||||
|
_psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q
|
||||||
|
_psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ
|
||||||
|
|
||||||
|
# psi2
|
||||||
|
_psi2_denom = 2.*S[:, None, None, :] / lengthscale2 + 1. # Nx1x1xQ
|
||||||
|
_psi2_denom_sqrt = np.sqrt(_psi2_denom)
|
||||||
|
_psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q
|
||||||
|
_psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom)
|
||||||
|
_psi2_common = gamma[:,None,None,:]/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # Nx1x1xQ
|
||||||
|
_psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom)+np.log(gamma[:,None,None,:]) #N,M,M,Q
|
||||||
|
_psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ
|
||||||
|
_psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)
|
||||||
|
_psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))
|
||||||
|
_psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM
|
||||||
|
_psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM
|
||||||
|
|
||||||
|
return _psi2
|
||||||
|
|
||||||
|
def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):
|
||||||
|
ARD = (len(lengthscale)!=1)
|
||||||
|
|
||||||
|
dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||||
|
dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
|
||||||
|
|
||||||
|
dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2
|
||||||
|
|
||||||
|
dL_dlengscale = dl_psi1 + dl_psi2
|
||||||
|
if not ARD:
|
||||||
|
dL_dlengscale = dL_dlengscale.sum()
|
||||||
|
|
||||||
|
dL_dgamma = dgamma_psi1 + dgamma_psi2
|
||||||
|
dL_dmu = dmu_psi1 + dmu_psi2
|
||||||
|
dL_dS = dS_psi1 + dS_psi2
|
||||||
|
dL_dZ = dZ_psi1 + dZ_psi2
|
||||||
|
|
||||||
|
return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma
|
||||||
|
|
||||||
|
def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S, gamma):
|
||||||
|
"""
|
||||||
|
dL_dpsi1 - NxM
|
||||||
|
Z - MxQ
|
||||||
|
mu - NxQ
|
||||||
|
S - NxQ
|
||||||
|
gamma - NxQ
|
||||||
|
"""
|
||||||
|
# here are the "statistics" for psi1
|
||||||
|
# Produced intermediate results: dL_dparams w.r.t. psi1
|
||||||
|
# _dL_dvariance 1
|
||||||
|
# _dL_dlengthscale Q
|
||||||
|
# _dL_dZ MxQ
|
||||||
|
# _dL_dgamma NxQ
|
||||||
|
# _dL_dmu NxQ
|
||||||
|
# _dL_dS NxQ
|
||||||
|
|
||||||
|
lengthscale2 = np.square(lengthscale)
|
||||||
|
|
||||||
|
# psi1
|
||||||
|
_psi1_denom = S / lengthscale2 + 1. # NxQ
|
||||||
|
_psi1_denom_sqrt = np.sqrt(_psi1_denom) #NxQ
|
||||||
|
_psi1_dist = Z[None, :, :] - mu[:, None, :] # NxMxQ
|
||||||
|
_psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom[:,None,:]) # NxMxQ
|
||||||
|
_psi1_common = gamma / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #NxQ
|
||||||
|
_psi1_exponent1 = np.log(gamma[:,None,:]) -0.5 * (_psi1_dist_sq + np.log(_psi1_denom[:, None,:])) # NxMxQ
|
||||||
|
_psi1_exponent2 = np.log(1.-gamma[:,None,:]) -0.5 * (np.square(Z[None,:,:])/lengthscale2) # NxMxQ
|
||||||
|
_psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)
|
||||||
|
_psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ
|
||||||
|
_psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM
|
||||||
|
_psi1_exp_dist_sq = np.exp(-0.5*_psi1_dist_sq) # NxMxQ
|
||||||
|
_psi1_exp_Z = np.exp(-0.5*np.square(Z[None,:,:])/lengthscale2) # 1xMxQ
|
||||||
|
_psi1_q = variance * np.exp(_psi1_exp_sum[:,:,None] - _psi1_exponent) # NxMxQ
|
||||||
|
_psi1 = variance * np.exp(_psi1_exp_sum) # NxM
|
||||||
|
_dL_dvariance = np.einsum('nm,nm->',dL_dpsi1, _psi1)/variance # 1
|
||||||
|
_dL_dgamma = np.einsum('nm,nmq,nmq->nq',dL_dpsi1, _psi1_q, (_psi1_exp_dist_sq/_psi1_denom_sqrt[:,None,:]-_psi1_exp_Z)) # NxQ
|
||||||
|
_dL_dmu = np.einsum('nm, nmq, nmq, nmq, nq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_dist,_psi1_common) # NxQ
|
||||||
|
_dL_dS = np.einsum('nm,nmq,nmq,nq,nmq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_common,(_psi1_dist_sq-1.))/2. # NxQ
|
||||||
|
_dL_dZ = np.einsum('nm,nmq,nmq->mq',dL_dpsi1,_psi1_q, (- _psi1_common[:,None,:] * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z))
|
||||||
|
_dL_dlengthscale = lengthscale* np.einsum('nm,nmq,nmq->q',dL_dpsi1,_psi1_q,(_psi1_common[:,None,:]*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + (1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z))
|
||||||
|
|
||||||
|
return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
|
||||||
|
|
||||||
|
def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S, gamma):
|
||||||
|
"""
|
||||||
|
Z - MxQ
|
||||||
|
mu - NxQ
|
||||||
|
S - NxQ
|
||||||
|
gamma - NxQ
|
||||||
|
dL_dpsi2 - MxM
|
||||||
|
"""
|
||||||
|
# here are the "statistics" for psi2
|
||||||
|
# Produced the derivatives w.r.t. psi2:
|
||||||
|
# _dL_dvariance 1
|
||||||
|
# _dL_dlengthscale Q
|
||||||
|
# _dL_dZ MxQ
|
||||||
|
# _dL_dgamma NxQ
|
||||||
|
# _dL_dmu NxQ
|
||||||
|
# _dL_dS NxQ
|
||||||
|
|
||||||
|
lengthscale2 = np.square(lengthscale)
|
||||||
|
|
||||||
|
_psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
|
||||||
|
_psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
|
||||||
|
_psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q
|
||||||
|
_psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ
|
||||||
|
|
||||||
|
# psi2
|
||||||
|
_psi2_denom = 2.*S / lengthscale2 + 1. # NxQ
|
||||||
|
_psi2_denom_sqrt = np.sqrt(_psi2_denom)
|
||||||
|
_psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q
|
||||||
|
_psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom[:,None,None,:])
|
||||||
|
_psi2_common = gamma/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # NxQ
|
||||||
|
_psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom[:,None,None,:])+np.log(gamma[:,None,None,:]) #N,M,M,Q
|
||||||
|
_psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ
|
||||||
|
_psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)
|
||||||
|
_psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))
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_psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM
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_psi2_q = variance*variance * np.exp(_psi2_exp_sum[:,:,:,None]-_psi2_exponent) # NxMxMxQ
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_psi2_exp_dist_sq = np.exp(-_psi2_Zdist_sq -_psi2_mudist_sq) # NxMxMxQ
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_psi2_exp_Z = np.exp(-0.5*_psi2_Z_sq_sum) # MxMxQ
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_psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM
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_dL_dvariance = np.einsum('mo,mo->',dL_dpsi2,_psi2)*2./variance
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_dL_dgamma = np.einsum('mo,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,(_psi2_exp_dist_sq/_psi2_denom_sqrt[:,None,None,:] - _psi2_exp_Z))
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_dL_dmu = -2.*np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,_psi2_common,_psi2_mudist,_psi2_exp_dist_sq)
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_dL_dS = np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q, _psi2_common, (2.*_psi2_mudist_sq-1.), _psi2_exp_dist_sq)
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_dL_dZ = 2.*np.einsum('mo,nmoq,nmoq->mq',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(-_psi2_Zdist*_psi2_denom[:,None,None,:]+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z))
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_dL_dlengthscale = 2.*lengthscale* np.einsum('mo,nmoq,nmoq->q',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom[:,None,None,:]+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z))
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return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma
|
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|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue