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, L, X = data.words, data.links, data.feats
D,_ = W.shape
outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens = queryState.outMeans, queryState.outVarcs, queryState.inMeans, queryState.inVarcs, queryState.inDocCov, queryState.docLens
K, topicMean, topicCov, outDocCov, vocab, A, dtype = modelState.K, modelState.topicMean, modelState.topicCov, modelState.outDocCov, modelState.vocab, modelState.A, modelState.dtype
# Calculate some implicit variables
itopicCov = la.inv(topicCov)
bound = 0
expMeansOut = np.exp(outMeans - outMeans.max(axis=1)[:, np.newaxis])
expMeansIn = np.exp(inMeans - inMeans.max(axis=0)[np.newaxis, :])
lse_at_k = expMeansIn.sum(axis=0)
# Distribution over document topics
bound -= (D*K)/2. * LN_OF_2_PI
bound -= D/2. * safe_log_det(outDocCov * topicCov)
diff = outMeans - topicMean[np.newaxis,:]
bound -= 0.5 * np.sum (diff.dot(itopicCov) * diff * 1./outDocCov)
bound -= (0.5 / outDocCov) * np.sum(outVarcs * np.diag(itopicCov)[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.log(outVarcs).sum()
# Distribution over document in-links
inDocPre = np.reciprocal(inDocCov)
bound -= (D*K)/2. * LN_OF_2_PI
bound -= D/2. * safe_log_det(topicCov)
bound -= K/2 * safe_log(inDocCov).sum()
diff = inMeans - outMeans
bound -= 0.5 * np.sum (diff.dot(itopicCov) * diff * inDocPre[:,np.newaxis])
bound -= 0.5 * np.sum((inVarcs * inDocPre[:,np.newaxis]) * np.diag(itopicCov)[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.log(inVarcs).sum()
# Distribution over topic assignments E[p(Z)] and E[p(Y)]
W_weights = sparseScalarQuotientOfDot(W, expMeansOut, vocab) # D x V [W / TB] is the quotient of the original over the reconstructed doc-term matrix
top_sums = expMeansOut * (W_weights.dot(vocab.T)) # D x K
L_weights = sparseScalarQuotientOfNormedDot(L, expMeansOut, expMeansIn, lse_at_k)
top_sums += expMeansOut * (L_weights.dot(expMeansIn) / lse_at_k[np.newaxis, :])
# E[p(Z,Y)]
linkLens = np.squeeze(np.array(L.sum(axis=1)))
bound += np.sum(outMeans * top_sums)
bound -= np.sum((docLens + linkLens) * np.log(np.sum(expMeansOut, axis=1)))
# H[Z]
bound += ((W_weights.dot(vocab.T)) * expMeansOut * outMeans).sum() \
+ ((W_weights.dot((np.log(vocab) * vocab).T)) * expMeansOut).sum() \
- np.trace(sparseScalarProductOfSafeLnDot(W_weights, expMeansOut, vocab).dot(vocab.T).dot(expMeansOut.T))
# H[Y]
docVocab = (expMeansIn / lse_at_k[np.newaxis,:]).T.copy()
bound += ((L_weights.dot(docVocab.T)) * expMeansOut * outMeans).sum() \
+ ((L_weights.dot((np.log(docVocab) * docVocab).T)) * expMeansOut).sum() \
- np.trace(sparseScalarProductOfSafeLnDot(L_weights, expMeansOut, docVocab).dot(docVocab.T).dot(expMeansOut.T))
# E[p(W)]
vlv = np.log(vocab) * vocab
bound += np.trace(expMeansOut.T.dot(W_weights.dot(vlv.T)))
# E[p(L)
dld = np.log(docVocab) * docVocab
bound += np.trace(expMeansOut.T.dot(L_weights.dot(dld.T)))
return bound
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, L, X = data.words, data.links, data.feats
D,_ = W.shape
means, varcs, docLens = queryState.means, queryState.varcs, queryState.docLens
K, topicMean, topicCov, vocab, A = modelState.K, modelState.topicMean, modelState.topicCov, modelState.vocab, modelState.A
# Calculate some implicit variables
itopicCov = la.inv(topicCov)
bound = 0
expMeansOut = np.exp(means - means.max(axis=1)[:, np.newaxis])
expMeansIn = np.exp(means - means.max(axis=0)[np.newaxis, :])
lse_at_k = expMeansIn.sum(axis=0)
if USE_NIW_PRIOR:
pseudoObsMeans = K + NIW_PSEUDO_OBS_MEAN
pseudoObsVar = K + NIW_PSEUDO_OBS_VAR
# distribution over topic covariance
bound -= 0.5 * K * pseudoObsVar * log(NIW_PSI)
bound -= 0.5 * K * pseudoObsVar * log(2)
bound -= fns.multigammaln(pseudoObsVar / 2., K)
bound -= 0.5 * (pseudoObsVar + K - 1) * safe_log_det(topicCov)
bound += 0.5 * NIW_PSI * np.trace(itopicCov)
# and its entropy
# is a constant which we skip
# distribution over means
bound -= 0.5 * K * log(1./pseudoObsMeans) * safe_log_det(topicCov)
bound -= 0.5 / pseudoObsMeans * (topicMean).T.dot(itopicCov).dot(topicMean)
# and its entropy
bound += 0.5 * safe_log_det(topicCov) # + a constant
# Distribution over document topics
bound -= (D*K)/2. * LN_OF_2_PI
bound -= D/2. * la.det(topicCov)
diff = means - topicMean[np.newaxis,:]
bound -= 0.5 * np.sum (diff.dot(itopicCov) * diff)
bound -= 0.5 * np.sum(varcs * np.diag(itopicCov)[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 and words and the formers
# entropy, and similaarly for out-links. This is somewhat jumbled to
# avoid repeatedly taking the exp and log of the means
W_weights = sparseScalarQuotientOfDot(W, expMeansOut, vocab) # D x V [W / TB] is the quotient of the original over the reconstructed doc-term matrix
w_top_sums = expMeansOut * (W_weights.dot(vocab.T)) # D x K
L_weights = sparseScalarQuotientOfNormedDot(L, expMeansOut, expMeansIn, lse_at_k)
l_top_sums = L_weights.dot(expMeansIn) / lse_at_k[np.newaxis, :] * expMeansOut
bound += np.sum(docLens * np.log(np.sum(expMeansOut, axis=1)))
bound += np.sum(sparseScalarProductOfSafeLnDot(W, expMeansOut, vocab).data)
# means = np.log(expMeans, out=expMeans)
#means = safe_log(expMeansOut, out=means)
bound += np.sum(means * w_top_sums)
bound += np.sum(2 * ssp.diags(docLens,0) * means.dot(A) * means)
bound -= 2. * scaledSelfSoftDot(means, docLens)
bound -= 0.5 * np.sum(docLens[:,np.newaxis] * w_top_sums * (np.diag(A))[np.newaxis,:])
bound -= np.sum(means * w_top_sums)
return bound
