def var_bound(data, modelState, queryState):
'''
Determines the variational bounds. Values are mutated in place, but are
reset afterwards to their initial values. So it's safe to call in a serial
manner.
'''
# Unpack the the structs, for ease of access and efficiency
W = data.words
D,_ = W.shape
means, expMeans, varcs, lxi, s, docLens = queryState.means, queryState.expMeans, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
K, topicMean, sigT, vocab = modelState.K, modelState.topicMean, modelState.sigT, modelState.vocab
# Calculate some implicit variables
xi = _deriveXi(means, varcs, s)
isigT = la.inv(sigT)
bound = 0
# Distribution over document topics
bound -= (D*K)/2. * LN_OF_2_PI
bound -= D/2. * la.det(sigT)
diff = means - topicMean[np.newaxis,:]
bound -= 0.5 * np.sum (diff.dot(isigT) * diff)
bound -= 0.5 * np.sum (varcs * np.diag(isigT)[np.newaxis,:]) # = -0.5 * sum_d tr(V_d \Sigma^{-1}) when V_d is diagonal only.
# And its entropy
bound += 0.5 * D * K * LN_OF_2_PI_E + 0.5 * np.sum(np.log(varcs))
# Distribution over word-topic assignments
# This also takes into account all the variables that
# constitute the bound on log(sum_j exp(mean_j)) and
# also incorporates the implicit entropy of Z_dvk
bound -= np.sum((means*means + varcs) * docLens[:,np.newaxis] * lxi)
bound += np.sum(means * 2 * docLens[:,np.newaxis] * s[:,np.newaxis] * lxi)
bound += np.sum(means * -0.5 * docLens[:,np.newaxis])
# The last term of line 1 gets cancelled out by part of the first term in line 2
# so neither are included here
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
bound -= -np.sum(sparseScalarProductOfSafeLnDot(W, expMeans, vocab).data)
bound -= np.sum(docLens[:,np.newaxis] * lxi * ((s*s)[:,np.newaxis] - (xi * xi)))
bound += np.sum(0.5 * docLens[:,np.newaxis] * (s[:,np.newaxis] + xi))
# bound -= np.sum(docLens[:,np.newaxis] * safe_log_one_plus_exp_of(xi))
bound -= scaledSumOfLnOnePlusExp(docLens, xi)
bound -= np.dot(s, docLens)
return bound
def var_bound(data, modelState, queryState, XTX = None):
'''
Determines the variational bounds. Values are mutated in place, but are
reset afterwards to their initial values. So it's safe to call in a serial
manner.
'''
# Unpack the the structs, for ease of access and efficiency
W, X = data.words, data.feats
D, _ = W.shape
means, varcs, lxi, s, docLens = queryState.means, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, dtype = modelState.F, modelState.P, modelState.K, modelState.A, modelState.R_A, modelState.fv, modelState.Y, modelState.R_Y, modelState.lfv, modelState.V, modelState.sigT, modelState.vocab, modelState.dtype
# Calculate some implicit variables
xi = ctm._deriveXi(means, varcs, s)
isigT = la.inv(sigT)
#lnDetSigT = np.log(la.det(sigT))
lnDetSigT = lnDetOfDiagMat(sigT)
verifyProper(lnDetSigT, "lnDetSigT")
if XTX is None:
XTX = X.T.dot(X)
bound = 0
# Distribution over latent space
bound -= (P*K)/2. * LN_OF_2_PI
bound -= P * lnDetSigT
bound -= K * P * log(lfv)
bound -= 0.5 * np.sum(1./lfv * isigT.dot(Y) * Y)
bound -= 0.5 * K * np.trace(R_Y)
# And its entropy
detR_Y = safeDet(R_Y, "R_Y")
bound += 0.5 * LN_OF_2_PI_E + P/2. * lnDetSigT + K/2. * log(detR_Y)
# Distribution over mapping from features to topics
diff = (A - Y.dot(V))
bound -= (F*K)/2. * LN_OF_2_PI
bound -= F * lnDetSigT
bound -= K * P * log(fv)
bound -= 0.5 * np.sum (1./lfv * isigT.dot(diff) * diff)
bound -= 0.5 * K * np.trace(R_A)
# And its entropy
detR_A = safeDet(R_A, "R_A")
bound += 0.5 * LN_OF_2_PI_E + F/2. * lnDetSigT + K/2. * log(detR_A)
# Distribution over document topics
bound -= (D*K)/2. * LN_OF_2_PI
bound -= D/2. * lnDetSigT
diff = means - X.dot(A.T)
bound -= 0.5 * np.sum (diff.dot(isigT) * diff)
bound -= 0.5 * np.sum(varcs * np.diag(isigT)[np.newaxis,:]) # = -0.5 * sum_d tr(V_d \Sigma^{-1}) when V_d is diagonal only.
bound -= 0.5 * K * np.trace(XTX.dot(R_A))
# And its entropy
bound += 0.5 * D * K * LN_OF_2_PI_E + 0.5 * np.sum(np.log(varcs))
# Distribution over word-topic assignments
# This also takes into account all the variables that
# constitute the bound on log(sum_j exp(mean_j)) and
# also incorporates the implicit entropy of Z_dvk
bound -= np.sum((means*means + varcs) * docLens[:,np.newaxis] * lxi)
bound += np.sum(means * 2 * docLens[:,np.newaxis] * s[:,np.newaxis] * lxi)
bound += np.sum(means * -0.5 * docLens[:,np.newaxis])
# The last term of line 1 gets cancelled out by part of the first term in line 2
# so neither are included here.
row_maxes = means.max(axis=1)
means -= row_maxes[:,np.newaxis]
expMeans = np.exp(means, out=means)
bound -= -np.sum(sparseScalarProductOfSafeLnDot(W, expMeans, vocab).data)
bound -= np.sum(docLens[:,np.newaxis] * lxi * ((s*s)[:,np.newaxis] - (xi * xi)))
bound += np.sum(0.5 * docLens[:,np.newaxis] * (s[:,np.newaxis] + xi))
# bound -= np.sum(docLens[:,np.newaxis] * safe_log_one_plus_exp_of(xi))
bound -= scaledSumOfLnOnePlusExp(docLens, xi)
bound -= np.dot(s, docLens)
means = np.log(expMeans, out=expMeans)
means += row_maxes[:,np.newaxis]
return bound
