def query(data, modelState, queryState, queryPlan):
'''
Given a _trained_ model, attempts to predict the topics for each of
the inputs.
Params:
data - the dataset of words, features and links of which only words are used in this model
modelState - the _trained_ model
queryState - the query state generated for the query dataset
queryPlan - used in this case as we need to tighten up the approx
Returns:
The model state and query state, in that order. The model state is
unchanged, the query is.
'''
iterations, epsilon, logFrequency, diagonalPriorCov, debug = queryPlan.iterations, queryPlan.epsilon, queryPlan.logFrequency, queryPlan.fastButInaccurate, queryPlan.debug
means, expMeans, varcs, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.docLens
K, topicMean, sigT, vocab, vocabPrior, A, dtype = modelState.K, modelState.topicMean, modelState.sigT, modelState.vocab, modelState.vocabPrior, modelState.A, modelState.dtype
debugFn = _debug_with_bound if debug else _debug_with_nothing
W = data.words
D = W.shape[0]
# Necessary temp variables (notably the count of topic to word assignments
# per topic per doc)
isigT = la.inv(sigT)
# Update the Variances
varcs = 1./((n * (K-1.)/K)[:,np.newaxis] + isigT.flat[::K+1])
debugFn (0, varcs, "varcs", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, n)
lastPerp = 1E+300 if dtype is np.float64 else 1E+30
R = W.copy()
for itr in range(iterations):
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
V = expMeans * R.dot(vocab.T)
# Update the Means
rhs = V.copy()
rhs += n[:,np.newaxis] * means.dot(A) + isigT.dot(topicMean)
rhs -= n[:,np.newaxis] * rowwise_softmax(means, out=means)
if diagonalPriorCov:
means = varcs * rhs
else:
for d in range(D):
means[d,:] = la.inv(isigT + n[d] * A).dot(rhs[d,:])
debugFn (itr, means, "means", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, n)
like = log_likelihood(data, modelState, QueryState(means, expMeans, varcs, n))
perp = perplexity_from_like(like, data.word_count)
if itr > 20 and lastPerp - perp < 1:
break
lastPerp = perp
return modelState, queryState
def query(data, modelState, queryState, queryPlan):
'''
Given a _trained_ model, attempts to predict the topics for each of
the inputs.
Params:
data - the dataset of words, features and links of which only words are used in this model
modelState - the _trained_ model
queryState - the query state generated for the query dataset
queryPlan - used in this case as we need to tighten up the approx
Returns:
The model state and query state, in that order. The model state is
unchanged, the query is.
'''
iterations, epsilon, logFrequency, diagonalPriorCov, debug = queryPlan.iterations, queryPlan.epsilon, queryPlan.logFrequency, queryPlan.fastButInaccurate, queryPlan.debug
means, varcs, n = queryState.means, queryState.varcs, queryState.docLens
K, topicMean, topicCov, vocab, A, dtype = modelState.K, modelState.topicMean, modelState.topicCov, modelState.vocab, modelState.A, modelState.dtype
debugFn = _debug_with_bound if debug else _debug_with_nothing
W = data.words
D = W.shape[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)
# Necessary temp variables (notably the count of topic to word assignments
# per topic per doc)
itopicCov = la.inv(topicCov)
# Update the Variances
varcs = 1./((n * (K-1.)/K)[:,np.newaxis] + itopicCov.flat[::K+1])
debugFn (0, varcs, "varcs", W, K, topicMean, topicCov, vocab, dtype, means, varcs, A, n)
R = W.copy()
for itr in range(iterations):
R = sparseScalarQuotientOfDot(W, expMeansOut, vocab, out=R)
V = expMeansOut * R.dot(vocab.T)
# Update the Means
rhs = V.copy()
rhs += n[:, np.newaxis] * means.dot(A) + itopicCov.dot(topicMean)
rhs -= n[:, np.newaxis] * rowwise_softmax(means, out=means)
if diagonalPriorCov:
means = varcs * rhs
else:
for d in range(D):
means[d, :] = la.inv(itopicCov + n[d] * A).dot(rhs[d, :])
debugFn (itr, means, "means", W, K, topicMean, topicCov, vocab, dtype, means, varcs, A, n)
return modelState, queryState
def testscaleProductOfQuotient(self):
rd.seed(0xC0FFEE)
D = 100
T = 200
K = 16
W_d = np.floor(rd.random((D,T)) * 1.4)
W_s = ssp.csr_matrix(W_d)
topics = rd.random((D,K))
vocab = rd.random((K,T))
expected = W_d / topics.dot(vocab)
received = sparseScalarQuotientOfDot(W_s, topics, vocab)
diff = np.asarray(expected - received.todense())
trNorm = np.sum(diff * diff)
print (str(trNorm))
print (str(diff))
def train (data, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
W - the DxT document-term matrix
X - The DxF document-feature matrix, which is IGNORED in this case
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want itr)
A new query object with the update query parameters
'''
W, L, LT, X = data.words, data.links, ssp.csr_matrix(data.links.T), data.feats
D,_ = W.shape
out_links = np.squeeze(np.asarray(data.links.sum(axis=1)))
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, diagonalPriorCov, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
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
emit_counts = docLens + out_links
# Book-keeping for logs
boundIters, boundValues, likelyValues = [], [], []
if debug:
debugFn = _debug_with_bound
initLikely = log_likelihood(data, modelState, queryState)
initPerp = perplexity_from_like(initLikely, data.word_count)
print ("Initial perplexity is: %.2f" % initPerp)
else:
debugFn = _debug_with_nothing
# Initialize some working variables
W_weight = W.copy()
L_weight = L.copy()
LT_weight = LT.copy()
inDocCov, inDocPre = np.ones((D,)), np.ones((D,))
# Interestingly, outDocCov trades off good perplexity fits
# with good ranking fits. > 10 gives better perplexity and
# worse ranking. At 10 both are good. Below 10 both get
# worse. Below 0.5, convergence stalls after the first iter.
outDocCov, outDocPre = 10, 1./10
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the mean and covariance of the prior over out-topics
topicMean = outMeans.mean(axis=0)
debugFn (itr, topicMean, "topicMean", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
outDiff = outMeans - topicMean[np.newaxis, :]
inDiff = inMeans - outMeans
for _ in range(5): # It typically takes three iterations for the three dependant covariances -
# outDocCov, inDocCov and topicCov - to become consistent w.r.t each other
topicCov = (outDocPre * outDiff).T.dot(outDiff)
topicCov += (inDocPre[:,np.newaxis] * inDiff).T.dot(inDiff)
topicCov += np.diag(outVarcs.sum(axis=0))
topicCov += np.diag(inVarcs.sum(axis=0))
topicCov += IWISH_S_SCALE * np.eye(K)
topicCov /= (2 * D + IWISH_DENOM)
itopicCov = la.inv(topicCov)
debugFn (itr, topicMean, "topicCov", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
diffSig = inDiff.dot(itopicCov)
diffSig *= inDiff
inDocCov = diffSig.sum(axis=1)
inDocCov += (outVarcs * np.diagonal(itopicCov)[np.newaxis, :]).sum(axis=1)
inDocCov += (inVarcs * np.diagonal(itopicCov)[np.newaxis, :]).sum(axis=1)
inDocCov += IGAMMA_B
inDocCov /= (IGAMMA_A - 1 + K)
inDocPre = np.reciprocal(inDocCov)
debugFn (itr, inDocCov, "inDocCov", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
diffSig = outDiff.dot(itopicCov)
diffSig *= outDiff
# outDocCov = (IGAMMA_B + diffSig.sum() + (np.diagonal(itopicCov) * outVarcs).sum()) / (IGAMMA_A - 1 + (D * K))
# outDocPre = 1./outDocCov
debugFn (itr, outDocCov, "outDocCov", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
# Apply the exp function to get the (unnormalised) softmaxes in both directions.
expMeansCol = np.exp(inMeans - inMeans.max(axis=0)[np.newaxis, :])
lse_at_k = np.sum(expMeansCol, axis=0)
F = 0.5 * inMeans \
- (0.5/ D) * inMeans.sum(axis=0) \
- expMeansCol / lse_at_k[np.newaxis, :]
expMeansRow = np.exp(outMeans - outMeans.max(axis=1)[:, np.newaxis])
W_weight = sparseScalarQuotientOfDot(W, expMeansRow, vocab, out=W_weight)
# Update the vocabularies
vocab *= (W_weight.T.dot(expMeansRow)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += VocabPrior
vocab = normalizerows_ip(vocab)
docVocab = (expMeansCol / lse_at_k[np.newaxis, :]).T.copy() # FIXME Dupes line in definition of F
# Recalculate w_top_sums with the new vocab and log vocab improvement
W_weight = sparseScalarQuotientOfDot(W, expMeansRow, vocab, out=W_weight)
w_top_sums = W_weight.dot(vocab.T) * expMeansRow
debugFn (itr, vocab, "vocab", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
# Now do likewise for the links, do it twice to model in-counts (first) and
# out-counts (Second). The difference is the transpose
LT_weight = sparseScalarQuotientOfDot(LT, expMeansRow, docVocab, out=LT_weight)
l_intop_sums = LT_weight.dot(docVocab.T) * expMeansRow
in_counts = l_intop_sums.sum(axis=0)
L_weight = sparseScalarQuotientOfDot(L, expMeansRow, docVocab, out=L_weight)
l_outtop_sums = L_weight.dot(docVocab.T) * expMeansRow
# Update the posterior variances
outVarcs = np.reciprocal(emit_counts[:, np.newaxis] * (K-1)/(2*K) + (outDocPre + inDocPre[:,np.newaxis]) * np.diagonal(itopicCov)[np.newaxis,:])
debugFn (itr, outVarcs, "outVarcs", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
inVarcs = np.reciprocal(in_counts[np.newaxis,:] * (D-1)/(2*D) + inDocPre[:,np.newaxis] * np.diagonal(itopicCov)[np.newaxis,:])
debugFn (itr, inVarcs, "inVarcs", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
# Update the out-means and in-means
out_rhs = w_top_sums.copy()
out_rhs += l_outtop_sums
out_rhs += itopicCov.dot(topicMean) / outDocCov
out_rhs += inMeans.dot(itopicCov) / inDocCov[:,np.newaxis]
out_rhs += emit_counts[:, np.newaxis] * (outMeans.dot(A) - rowwise_softmax(outMeans))
scaled_n_in = ((D-1.)/(2*D)) * ssp.diags(in_counts, 0)
in_rhs = (inDocPre[:, np.newaxis] * outMeans).dot(itopicCov)
in_rhs += ((-inMeans.sum(axis=0) * in_counts) / (4*D))[np.newaxis,:]
in_rhs += l_intop_sums
in_rhs += in_counts[np.newaxis, :] * F
for d in range(D):
in_rhs[d, :] += in_counts * inMeans[d, :] / (4*D)
inMeans[d, :] = la.inv(inDocPre[d] * itopicCov + scaled_n_in).dot(in_rhs[d, :])
in_rhs[d,:] -= in_counts * inMeans[d, :] / (4*D)
try:
outCov = la.inv((outDocPre + inDocPre[d]) * itopicCov + emit_counts[d] * A)
outMeans[d, :] = outCov.dot(out_rhs[d,:])
except la.LinAlgError as err:
print ("ABORTING: " + str(err))
return \
ModelState(K, topicMean, topicCov, outDocCov, vocab, A, True, dtype, MODEL_NAME), \
QueryState(outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens), \
(np.array(boundIters), np.array(boundValues), np.array(likelyValues))
debugFn (itr, outMeans, "inMeans/outMeans", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
# debugFn (itr, inMeans, "inMeans", data, K, topicMean, topicCov, outDocCov, inDocCov, vocab, dtype, outMeans, outVarcs, inMeans, inVarcs, A, docLens)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, topicMean, topicCov, outDocCov, vocab, A, True, dtype, MODEL_NAME)
queryState = QueryState(outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens)
boundValues.append(var_bound(data, modelState, queryState))
likelyValues.append(log_likelihood(data, modelState, queryState))
boundIters.append(itr)
print (time.strftime('%X') + " : Iteration %d: bound %f \t Perplexity: %.2f" % (itr, boundValues[-1], perplexity_from_like(likelyValues[-1], docLens.sum())))
if len(boundValues) > 1:
if boundValues[-2] > boundValues[-1]:
printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[-2], boundValues[-1]))
# Check to see if the improvement in the bound has fallen below the threshold
if itr > MinItersBeforeEarlyStop and abs(perplexity_from_like(likelyValues[-1], docLens.sum()) - perplexity_from_like(likelyValues[-2], docLens.sum())) < 1.0:
break
# if True or debug or itr % logFrequency == 0:
# print(" Sigma %6.1f \t %9.3g, %9.3g, %9.3g" % (np.log(la.det(topicCov)), topicCov.min(), topicCov.mean(), topicCov.max()), end=" |")
# print(" rho %6.1f \t %9.3g, %9.3g, %9.3g" % (sum(log(inDocCov[d]) for d in range(D)), inDocCov.min(), inDocCov.mean(), inDocCov.max()), end=" |")
# print(" alpha %6.1f \t %9.3g" % (np.log(la.det(np.eye(K,) * outDocCov)), outDocCov), end=" |")
# print(" inMeans %9.3g, %9.3g, %9.3g" % (inMeans.min(), inMeans.mean(), inMeans.max()), end=" |")
# print(" outMeans %9.3g, %9.3g, %9.3g" % (outMeans.min(), outMeans.mean(), outMeans.max()), end=" |")
# print(" inVarcs %6.1f \t %9.3g, %9.3g, %9.3g" % (sum(safe_log_det(np.diag(inVarcs[d])) for d in range(D)) / D, inVarcs.min(), inVarcs.mean(), inVarcs.max()), end=" |")
# print(" outVarcs %6.1f \t %9.3g, %9.3g, %9.3g" % (sum(safe_log_det(np.diag(outVarcs[d])) for d in range(D)) / D, outVarcs.min(), outVarcs.mean(), outVarcs.max()))
return \
ModelState(K, topicMean, topicCov, outDocCov, vocab, A, True, dtype, MODEL_NAME), \
QueryState(outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens), \
(np.array(boundIters), np.array(boundValues), np.array(likelyValues))
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, docLens = queryState.means, queryState.expMeans, queryState.varcs, queryState.docLens
K, topicMean, sigT, vocab, vocabPrior, A = modelState.K, modelState.topicMean, modelState.sigT, modelState.vocab, modelState.vocabPrior, modelState.A
# Calculate some implicit variables
isigT = la.inv(sigT)
bound = 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(sigT)
bound += 0.5 * NIW_PSI * np.trace(isigT)
# and its entropy
# is a constant which we skip
# distribution over means
bound -= 0.5 * K * log(1./pseudoObsMeans) * safe_log_det(sigT)
bound -= 0.5 / pseudoObsMeans * (topicMean).T.dot(isigT).dot(topicMean)
# and its entropy
bound += 0.5 * safe_log_det(sigT) # + a constant
# 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 and words and the formers
# entropy. This is somewhat jumbled to avoid repeatedly taking the
# exp and log of the means
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab) # D x V [W / TB] is the quotient of the original over the reconstructed doc-term matrix
V = expMeans * (R.dot(vocab.T)) # D x K
bound += np.sum(docLens * np.log(np.sum(expMeans, axis=1)))
bound += np.sum(sparseScalarProductOfSafeLnDot(W, expMeans, vocab).data)
bound += np.sum(means * V)
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] * V * (np.diag(A))[np.newaxis,:])
bound -= np.sum(means * V)
return bound
def train (data, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
W - the DxT document-term matrix
X - The DxF document-feature matrix, which is IGNORED in this case
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want itr)
A new query object with the update query parameters
'''
W = data.words
D,_ = W.shape
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, diagonalPriorCov, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
means, expMeans, varcs, docLens = queryState.means, queryState.expMeans, queryState.varcs, queryState.docLens
K, topicMean, sigT, vocab, vocabPrior, A, dtype = modelState.K, modelState.topicMean, modelState.sigT, modelState.vocab, modelState.vocabPrior, modelState.A, modelState.dtype
# Book-keeping for logs
boundIters, boundValues, likelyValues = [], [], []
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Initialize some working variables
isigT = la.inv(sigT)
R = W.copy()
pseudoObsMeans = K + NIW_PSEUDO_OBS_MEAN
pseudoObsVar = K + NIW_PSEUDO_OBS_VAR
priorSigT_diag = np.ndarray(shape=(K,), dtype=dtype)
priorSigT_diag.fill (NIW_PSI)
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the mean and covariance of the prior
topicMean = means.sum(axis = 0) / (D + pseudoObsMeans) \
if USE_NIW_PRIOR \
else means.mean(axis=0)
debugFn (itr, topicMean, "topicMean", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, docLens)
if USE_NIW_PRIOR:
diff = means - topicMean[np.newaxis,:]
sigT = diff.T.dot(diff) \
+ pseudoObsVar * np.outer(topicMean, topicMean)
sigT += np.diag(varcs.mean(axis=0) + priorSigT_diag)
sigT /= (D + pseudoObsVar - K)
else:
sigT = np.cov(means.T) if sigT.dtype == np.float64 else np.cov(means.T).astype(dtype)
sigT += np.diag(varcs.mean(axis=0))
if diagonalPriorCov:
diag = np.diag(sigT)
sigT = np.diag(diag)
isigT = np.diag(1./ diag)
else:
isigT = la.inv(sigT)
# FIXME Undo debug
sigT = np.eye(K)
isigT = la.inv(sigT)
debugFn (itr, sigT, "sigT", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, docLens)
# print(" sigT.det = " + str(la.det(sigT)))
# Building Blocks - temporarily replaces means with exp(means)
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
# Update the vocabulary
vocab *= (R.T.dot(expMeans)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += vocabPrior
vocab = normalizerows_ip(vocab)
# Reset the means to their original form, and log effect of vocab update
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
V = expMeans * R.dot(vocab.T)
debugFn (itr, vocab, "vocab", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, docLens)
# And now this is the E-Step, though itr's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# Update the Variances: var_d = (2 N_d * A + isigT)^{-1}
varcs = np.reciprocal(docLens[:,np.newaxis] * (K-1.)/K + np.diagonal(sigT))
debugFn (itr, varcs, "varcs", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, docLens)
# Update the Means
rhs = V.copy()
rhs += docLens[:,np.newaxis] * means.dot(A) + isigT.dot(topicMean)
rhs -= docLens[:,np.newaxis] * rowwise_softmax(means, out=means)
if diagonalPriorCov:
means = varcs * rhs
else:
for d in range(D):
means[d, :] = la.inv(isigT + docLens[d] * A).dot(rhs[d, :])
# means -= (means[:,0])[:,np.newaxis]
debugFn (itr, means, "means", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, A, docLens)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, topicMean, sigT, vocab, vocabPrior, A, dtype, MODEL_NAME)
queryState = QueryState(means, expMeans, varcs, docLens)
boundValues.append(var_bound(data, modelState, queryState))
likelyValues.append(log_likelihood(data, modelState, queryState))
boundIters.append(itr)
print (time.strftime('%X') + " : Iteration %d: bound %f \t Perplexity: %.2f" % (itr, boundValues[-1], perplexity_from_like(likelyValues[-1], docLens.sum())))
if len(boundValues) > 1:
if boundValues[-2] > boundValues[-1]:
if debug: printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[-2], boundValues[-1]))
# Check to see if the improvement in the bound has fallen below the threshold
if itr > 100 and len(likelyValues) > 3 \
and abs(perplexity_from_like(likelyValues[-1], docLens.sum()) - perplexity_from_like(likelyValues[-2], docLens.sum())) < 1.0:
break
return \
ModelState(K, topicMean, sigT, vocab, vocabPrior, A, dtype, MODEL_NAME), \
QueryState(means, expMeans, varcs, docLens), \
(np.array(boundIters), np.array(boundValues), np.array(likelyValues))
def query(data, modelState, queryState, queryPlan):
'''
Given a _trained_ model, attempts to predict the topics for each of
the inputs.
Params:
data - the dataset of words, features and links of which only words and
features are used in this model
modelState - the _trained_ model
queryState - the query state generated for the query dataset
queryPlan - used in this case as we need to tighten up the approx
Returns:
The model state and query state, in that order. The model state is
unchanged, the query is.
'''
W, X = data.words, data.feats
D, _ = W.shape
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, fastButInaccurate, debug = queryPlan.iterations, queryPlan.epsilon, queryPlan.logFrequency, queryPlan.fastButInaccurate, queryPlan.debug
means, expMeans, varcs, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, Ab, 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.vocabPrior, modelState.Ab, modelState.dtype
# Debugging
debugFn = _debug_with_bound if debug else _debug_with_nothing
_debug_with_bound.old_bound = 0
# Necessary values
isigT = la.inv(sigT)
lastPerp = 1E+300 if dtype is np.float64 else 1E+30
for itr in range(iterations):
# Counts of topic assignments
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab)
S = expMeans * R.dot(vocab.T)
# the variance
varcs[:] = 1./((n * (K-1.)/K)[:,np.newaxis] + isigT.flat[::K+1])
debugFn (itr, varcs, "query-varcs", W, X, None, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, n)
# Update the Means
rhs = X.dot(A.T).dot(isigT)
rhs += S
rhs += n[:,np.newaxis] * means.dot(Ab)
rhs -= n[:,np.newaxis] * rowwise_softmax(means, out=means)
# Long version
inverses = dict()
for d in range(D):
if not n[d] in inverses:
inverses[n[d]] = la.inv(isigT + n[d] * Ab)
lhs = inverses[n[d]]
means[d,:] = lhs.dot(rhs[d,:])
debugFn (itr, means, "query-means", W, X, None, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, n)
like = log_likelihood(data, modelState, QueryState(means, expMeans, varcs, n))
perp = perplexity_from_like(like, data.word_count)
if itr > 20 and lastPerp - perp < 1:
break
lastPerp = perp
return modelState, queryState # query vars altered in-place
def train(data, modelState, queryState, trainPlan):
"""
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
W - the DxT document-term matrix
X - The DxF document-feature matrix, which is IGNORED in this case
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want itr)
A new query object with the update query parameters
"""
W, X = data.words, data.feats
D, T = W.shape
F = X.shape[1]
# tmpNumDense = np.array([
# 4 , 8 , 2 , 0 , 0,
# 0 , 6 , 0 , 17, 0,
# 12 , 13 , 1 , 7 , 8,
# 0 , 5 , 0 , 0 , 0,
# 0 , 6 , 0 , 0 , 44,
# 0 , 7 , 2 , 0 , 0], dtype=np.float64).reshape((6,5))
# tmpNum = ssp.csr_matrix(tmpNumDense)
#
# tmpDenomleft = (rd.random((tmpNum.shape[0], 12)) * 5).astype(np.int32).astype(np.float64) / 10
# tmpDenomRight = (rd.random((12, tmpNum.shape[1])) * 5).astype(np.int32).astype(np.float64)
#
# tmpResult = tmpNum.copy()
# tmpResult = sparseScalarQuotientOfDot(tmpNum, tmpDenomleft, tmpDenomRight)
#
# print (str(tmpNum.todense()))
# print (str(tmpDenomleft.dot(tmpDenomRight)))
# print (str(tmpResult.todense()))
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, diagonalPriorCov, debug = (
trainPlan.iterations,
trainPlan.epsilon,
trainPlan.logFrequency,
trainPlan.fastButInaccurate,
trainPlan.debug,
)
means, docLens = queryState.means, queryState.docLens
K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior, dtype = (
modelState.K,
modelState.A,
modelState.U,
modelState.Y,
modelState.V,
modelState.covA,
modelState.tv,
modelState.ltv,
modelState.fv,
modelState.lfv,
modelState.vocab,
modelState.vocabPrior,
modelState.dtype,
)
tp, fp, ltp, lfp = 1.0 / tv, 1.0 / fv, 1.0 / ltv, 1.0 / lfv # turn variances into precisions
# FIXME Use passed in hypers
print("tp = %f tv=%f" % (tp, tv))
vocabPrior = np.ones(shape=(T,), dtype=modelState.dtype)
# FIXME undo truncation
F = 363
A = A[:F, :]
X = X[:, :F]
U = U[:F, :]
data = DataSet(words=W, feats=X)
# Book-keeping for logs
boundIters, boundValues, likelyValues = [], [], []
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Initialize some working variables
if covA is None:
precA = (fp * ssp.eye(F) + X.T.dot(X)).todense() # As the inverse is almost always dense
covA = la.inv(precA, overwrite_a=True) # it's faster to densify in advance
uniqLens = np.unique(docLens)
debugFn(-1, covA, "covA", W, X, means, docLens, K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior)
H = 0.5 * (np.eye(K) - np.ones((K, K), dtype=dtype) / K)
expMeans = means.copy()
expMeans = np.exp(means - means.max(axis=1)[:, np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=W.copy())
lhs = H.copy()
rhs = expMeans.copy()
Y_rhs = Y.copy()
# Iterate over parameters
for itr in range(iterations):
# Update U, V given A
V = try_solve_sym_pos(Y.T.dot(U.T).dot(U).dot(Y), A.T.dot(U).dot(Y).T).T
V /= V[0, 0]
U = try_solve_sym_pos(Y.dot(V.T).dot(V).dot(Y.T), A.dot(V).dot(Y.T).T).T
# Update Y given U, V, A
Y_rhs[:, :] = U.T.dot(A).dot(V)
Sv, Uv = la.eigh(V.T.dot(V), overwrite_a=True)
Su, Uu = la.eigh(U.T.dot(U), overwrite_a=True)
s = np.outer(Sv, Su).flatten()
s += ltv * lfv
np.reciprocal(s, out=s)
M = Uu.T.dot(Y_rhs).dot(Uv)
M *= unvec(s, row_count=M.shape[0])
Y = Uu.dot(M).dot(Uv.T)
debugFn(itr, Y, "Y", W, X, means, docLens, K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior)
A = covA.dot(fp * U.dot(Y).dot(V.T) + X.T.dot(means))
debugFn(itr, A, "A", W, X, means, docLens, K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior)
# And now this is the E-Step, though itr's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# TODO One big sort by size, plus batch it.
# Update the Means
rhs[:, :] = expMeans
rhs *= R.dot(vocab.T)
rhs += X.dot(A) * tp
rhs += docLens[:, np.newaxis] * means.dot(H)
rhs -= docLens[:, np.newaxis] * rowwise_softmax(means, out=means)
for l in uniqLens:
inds = np.where(docLens == l)[0]
lhs[:, :] = l * H
lhs[np.diag_indices_from(lhs)] += tp
lhs[:, :] = la.inv(lhs)
means[inds, :] = rhs[inds, :].dot(lhs) # left and right got switched going from vectors to matrices :-/
debugFn(itr, means, "means", W, X, means, docLens, K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior)
# Standard deviation
# DK = means.shape[0] * means.shape[1]
# newTp = np.sum(means)
# newTp = (-newTp * newTp)
# rhs[:,:] = means
# rhs *= means
# newTp = DK * np.sum(rhs) - newTp
# newTp /= DK * (DK - 1)
# newTp = min(max(newTp, 1E-36), 1E+36)
# tp = 1 / newTp
# if itr % logFrequency == 0:
# print ("Iter %3d stdev = %f, prec = %f, np.std^2=%f, np.mean=%f" % (itr, sqrt(newTp), tp, np.std(means.reshape((D*K,))) ** 2, np.mean(means.reshape((D*K,)))))
# Update the vocabulary
expMeans = np.exp(means - means.max(axis=1)[:, np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
vocab *= (R.T.dot(expMeans)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += vocabPrior
vocab = normalizerows_ip(vocab)
debugFn(itr, vocab, "vocab", W, X, means, docLens, K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior)
# print ("Iter %3d Vocab.min = %f" % (itr, vocab.min()))
# Update the vocab prior
# vocabPrior = estimate_dirichlet_param (vocab, vocabPrior)
# print ("Iter %3d VocabPrior.(min, max) = (%f, %f) VocabPrior.mean=%f" % (itr, vocabPrior.min(), vocabPrior.max(), vocabPrior.mean()))
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior, dtype, modelState.name)
queryState = QueryState(means, docLens)
boundValues.append(var_bound(data, modelState, queryState))
likelyValues.append(log_likelihood(data, modelState, queryState))
boundIters.append(itr)
print(
time.strftime("%X")
+ " : Iteration %d: bound %f \t Perplexity: %.2f"
% (itr, boundValues[-1], perplexity_from_like(likelyValues[-1], docLens.sum()))
)
if len(boundValues) > 1:
if boundValues[-2] > boundValues[-1]:
if debug:
printStderr("ERROR: bound degradation: %f > %f" % (boundValues[-2], boundValues[-1]))
# Check to see if the improvement in the bound has fallen below the threshold
if (
itr > 100
and len(likelyValues) > 3
and abs(
perplexity_from_like(likelyValues[-1], docLens.sum())
- perplexity_from_like(likelyValues[-2], docLens.sum())
)
< 1.0
):
break
return (
ModelState(K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior, dtype, modelState.name),
QueryState(means, expMeans, docLens),
(np.array(boundIters), np.array(boundValues), np.array(likelyValues)),
)
def train (data, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
data - the dataset of words, features and links of which only words and
features are used in this model
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want it)
A new query object with the update query parameters
'''
W, X = data.words, data.feats
assert W.dtype == modelState.dtype
assert X.dtype == modelState.dtype
D,_ = W.shape
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, fastButInaccurate, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
means, expMeans, varcs, lxi, s, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, 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.vocabPrior, modelState.dtype
# Book-keeping for logs
boundIters = np.zeros(shape=(iterations // logFrequency,))
boundValues = np.zeros(shape=(iterations // logFrequency,))
likeValues = np.zeros(shape=(iterations // logFrequency,))
bvIdx = 0
_debug_with_bound.old_bound = 0
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Initialize some working variables
isigT = la.inv(sigT)
R = W.copy()
sigT_regularizer = 0.001
aI_P = 1./lfv * ssp.eye(P, dtype=dtype)
tI_F = 1./fv * ssp.eye(F, dtype=dtype)
print("Creating posterior covariance of A, this will take some time...")
XTX = X.T.dot(X)
R_A = XTX
if ssp.issparse(R_A):
R_A = R_A.todense() # dense inverse typically as fast or faster than sparse inverse
R_A.flat[::F+1] += 1./fv # and the result is usually dense in any case
R_A = la.inv(R_A)
print("Covariance matrix calculated, launching inference")
s.fill(0)
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the covariance of the prior
diff_a_yv = (A-Y.dot(V))
diff_m_xa = (means-X.dot(A.T))
sigT = 1./lfv * (Y.dot(Y.T))
sigT += 1./fv * diff_a_yv.dot(diff_a_yv.T)
sigT += diff_m_xa.T.dot(diff_m_xa)
sigT.flat[::K+1] += varcs.sum(axis=0)
sigT /= (P+F+D)
sigT.flat[::K+1] += sigT_regularizer
# Diagonalize it
sigT = np.diag(sigT.flat[::K+1])
# and invert it.
isigT = np.diag(np.reciprocal(sigT.flat[::K+1]))
debugFn (itr, sigT, "sigT", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Building Blocks - temporarily replaces means with exp(means)
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
S = expMeans * R.dot(vocab.T)
# Update the vocabulary
vocab *= (R.T.dot(expMeans)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += vocabPrior
vocab = normalizerows_ip(vocab)
# Reset the means to their original form, and log effect of vocab update
debugFn (itr, vocab, "vocab", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Finally update the parameter V
V = la.inv(R_Y + Y.T.dot(isigT).dot(Y)).dot(Y.T.dot(isigT).dot(A))
debugFn (itr, V, "V", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# And now this is the E-Step, though it's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# Update the distribution on the latent space
R_Y_base = aI_P + 1/fv * V.dot(V.T)
R_Y = la.inv(R_Y_base)
debugFn (itr, R_Y, "R_Y", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
Y = 1./fv * A.dot(V.T).dot(R_Y)
debugFn (itr, Y, "Y", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the mapping from the features to topics
A = (1./fv * (Y).dot(V) + (X.T.dot(means)).T).dot(R_A)
debugFn (itr, A, "A", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Means
vMat = (s[:,np.newaxis] * lxi - 0.5) * n[:,np.newaxis] + S
rhsMat = vMat + X.dot(A.T).dot(isigT) # TODO Verify this
lhsMat = np.reciprocal(np.diag(isigT)[np.newaxis,:] + n[:,np.newaxis] * lxi) # inverse of D diagonal matrices...
means = lhsMat * rhsMat # as LHS is a diagonal matrix for all d, it's equivalent
# do doing a hadamard product for all d
debugFn (itr, means, "means", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Variances
varcs = 1./(n[:,np.newaxis] * lxi + isigT.flat[::K+1])
debugFn (itr, varcs, "varcs", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the approximation parameters
lxi = 2 * ctm.negJakkolaOfDerivedXi(means, varcs, s)
debugFn (itr, lxi, "lxi", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# s can sometimes grow unboundedly
# Follow Bouchard's suggested approach of fixing it at zero
#
# s = (np.sum(lxi * means, axis=1) + 0.25 * K - 0.5) / np.sum(lxi, axis=1)
# debugFn (itr, s, "s", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, MODEL_NAME)
queryState = QueryState(means, expMeans, varcs, lxi, s, n)
boundValues[bvIdx] = var_bound(data, modelState, queryState, XTX)
likeValues[bvIdx] = log_likelihood(data, modelState, queryState)
boundIters[bvIdx] = itr
perp = perplexity_from_like(likeValues[bvIdx], n.sum())
print (time.strftime('%X') + " : Iteration %d: Perplexity %4.2f bound %f" % (itr, perp, boundValues[bvIdx]))
if bvIdx > 0 and boundValues[bvIdx - 1] > boundValues[bvIdx]:
printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[bvIdx - 1], boundValues[bvIdx]))
# print ("Means: min=%f, avg=%f, max=%f\n\n" % (means.min(), means.mean(), means.max()))
# Check to see if the improvment in the likelihood has fallen below the threshold
if bvIdx > 1 and boundIters[bvIdx] > 50:
lastPerp = perplexity_from_like(likeValues[bvIdx - 1], n.sum())
if lastPerp - perp < 1:
boundIters, boundValues, likelyValues = clamp (boundIters, boundValues, likeValues, bvIdx)
return modelState, queryState, (boundIters, boundValues, likeValues)
bvIdx += 1
return \
ModelState(F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, MODEL_NAME), \
QueryState(means, expMeans, varcs, lxi, s, n), \
(boundIters, boundValues, likeValues)
def query(dataset, modelState, queryState, queryPlan):
'''
Given a _trained_ model, attempts to predict the topics for each of
the inputs.
Params:
data - the dataset of words, features and links of which only words are used in this model
modelState - the _trained_ model
queryState - the query state generated for the query dataset
queryPlan - used in this case as we need to tighten up the approx
Returns:
The model state and query state, in that order. The model state is
unchanged, the query is.
'''
W = dataset.words
D = W.shape[0]
iterations, epsilon, logFrequency, fastButInaccurate, debug = queryPlan.iterations, queryPlan.epsilon, queryPlan.logFrequency, queryPlan.fastButInaccurate, queryPlan.debug
means, expMeans, varcs, lxi, s, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
K, topicMean, sigT, vocab, vocabPrior, dtype = modelState.K, modelState.topicMean, modelState.sigT, modelState.vocab, modelState.vocabPrior, modelState.dtype
# Necessary temp variables (notably the count of topic to word assignments
# per topic per doc)
isigT = la.inv(sigT)
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab)
S = expMeans * R.dot(vocab.T)
# Enable logging or not. If enabled, we need the inner product of the feat matrix
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Iterate over parameters
lastPerp = 1E+300 if dtype is np.float64 else 1E+30
for itr in range(iterations):
# Update the Means
vMat = (s[:,np.newaxis] * lxi - 0.5) * n[:,np.newaxis] + S
rhsMat = vMat + isigT.dot(topicMean)
for d in range(D):
try:
means[d,:] = la.inv(isigT + ssp.diags(n[d] * lxi[d,:], 0)).dot(rhsMat[d,:])
except ValueError as e:
print(str(e))
print ("Ah")
debugFn (itr, means, "means", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Variances
varcs = 1./(n[:,np.newaxis] * lxi + isigT.flat[::K+1])
debugFn (itr, varcs, "varcs", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the approximation parameters
lxi = 2 * negJakkolaOfDerivedXi(means, varcs, s)
debugFn (itr, lxi, "lxi", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# s can sometimes grow unboundedly
# Follow Bouchard's suggested approach of fixing it at zero
#
s = (np.sum(lxi * means, axis=1) + 0.25 * K - 0.5) / np.sum(lxi, axis=1)
debugFn (itr, s, "s", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
like = log_likelihood(dataset, modelState, QueryState(means, expMeans, varcs, lxi, s, n))
perp = perplexity_from_like(like, dataset.word_count)
if itr > 20 and lastPerp - perp < 1:
break
lastPerp = perp
return modelState, QueryState (means, expMeans, varcs, lxi, s, n)
def train (dataset, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
data - the dataset of words, features and links of which only words are used in this model
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want it)
A new query object with the update query parameters
'''
W = dataset.words
D,_ = W.shape
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, diagonalPriorCov, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
means, expMeans, varcs, lxi, s, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
K, topicMean, sigT, vocab, vocabPrior, dtype = modelState.K, modelState.topicMean, modelState.sigT, modelState.vocab, modelState.vocabPrior, modelState.dtype
# Book-keeping for logs
boundIters = np.zeros(shape=(iterations // logFrequency,))
boundValues = np.zeros(shape=(iterations // logFrequency,))
likelyValues = np.zeros(shape=(iterations // logFrequency,))
bvIdx = 0
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Initialize some working variables
isigT = la.inv(sigT)
R = W.copy()
s.fill(0)
priorSigt_diag = np.ndarray(shape=(K,), dtype=dtype)
priorSigt_diag.fill (0.1)
kappa = K + 2
expMeans = means.copy()
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the mean and covariance of the prior
# topicMean = means.mean(axis = 0)
topicMean = means.sum(axis=0) / (D + kappa) \
if USE_NIW_PRIOR \
else means.mean(axis=0)
debugFn (itr, topicMean, "topicMean", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# diff = means - topicMean
# sigT = diff.T.dot(diff) / D
sigT, _ = oas(means, assume_centered=False)
if dtype is not np.float64:
sigT = sigT.astype(dtype)
sigT += np.diag(varcs.mean(axis=0))
if USE_NIW_PRIOR:
sigT.flat[::K+1] += priorSigt_diag
sigT += (kappa * D)/(kappa + D) * np.outer(topicMean, topicMean)
# Building blocks...
# 1/4 Create the precision matrix from the covariance
if True or diagonalPriorCov:
diag = np.diag(sigT)
sigT = np.diag(diag)
isigT = np.diag(1. / diag)
else:
isigT = la.inv(sigT)
debugFn (itr, sigT, "sigT", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# print (" Det sigT = " + str(la.det(sigT)))
# 2/4 temporarily replace means with exp(means)
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
# S = expMeans * R.dot(vocab.T)
# 3/4 Update the vocabulary
vocab *= (R.T.dot(expMeans)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += vocabPrior
vocab = normalizerows_ip(vocab)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
S = expMeans * R.dot(vocab.T)
# 4/4 Reset the means to their original form, and log effect of vocab update
#means = np.log(expMeans, out=expMeans)
debugFn (itr, vocab, "vocab", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# And now this is the E-Step, though it's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# Update the Variances
varcs = np.reciprocal(n[:,np.newaxis] * lxi + isigT.flat[::K+1])
debugFn (itr, varcs, "varcs", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Means
vMat = (s[:,np.newaxis] * lxi - 0.5) * n[:,np.newaxis] + S
rhsMat = vMat + isigT.dot(topicMean)
# for d in range(D):
# means[d,:] = la.inv(isigT + ssp.diags(n[d] * lxi[d,:], 0)).dot(rhsMat[d,:])
means = varcs * rhsMat
means -= (means[:,0])[:,np.newaxis]
debugFn (itr, means, "means", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the approximation parameters
lxi = 2 * negJakkolaOfDerivedXi(means, varcs, s)
debugFn (itr, lxi, "lxi", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# s can sometimes grow unboundedly
# If so Bouchard's suggested approach of fixing it at zero
#
#s = (np.sum(lxi * means, axis=1) + 0.25 * K - 0.5) / np.sum(lxi, axis=1)
debugFn (itr, s, "s", W, K, topicMean, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, topicMean, sigT, vocab, vocabPrior, dtype, MODEL_NAME)
queryState = QueryState(means, expMeans, varcs, lxi, s, n)
boundValues[bvIdx] = var_bound(dataset, modelState, queryState)
likelyValues[bvIdx] = log_likelihood(dataset, modelState, queryState)
boundIters[bvIdx] = itr
perp = perplexity_from_like(likelyValues[bvIdx], n.sum())
print (time.strftime('%X') + " : Iteration %5d: Perplexity %4.2f Bound %10.2f " % (itr, perp, boundValues[bvIdx]))
if bvIdx > 0 and boundValues[bvIdx - 1] > boundValues[bvIdx]:
printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[bvIdx - 1], boundValues[bvIdx]))
# print ("Means: min=%f, avg=%f, max=%f\n\n" % (means.min(), means.mean(), means.max()))
# Check to see if the improvment in the likelihood has fallen below the threshold
if bvIdx > 1 and boundIters[bvIdx] >= 30:
lastPerp = perplexity_from_like(likelyValues[bvIdx - 1], n.sum())
if lastPerp - perp < 1:
boundIters, boundValues, likelyValues = clamp (boundIters, boundValues, likelyValues, bvIdx)
return modelState, queryState, (boundIters, boundValues, likelyValues)
bvIdx += 1
return \
ModelState(K, topicMean, sigT, vocab, vocabPrior, dtype, MODEL_NAME), \
QueryState(means, expMeans, varcs, lxi, s, n), \
(boundIters, boundValues, likelyValues)
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, expMeans, varcs, docLens = queryState.means, queryState.expMeans, queryState.varcs, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, Ab, 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.Ab, modelState.dtype
# Calculate some implicit variables
isigT = la.inv(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, and their entropy
# and distribution over words. This is re-arranged as we need
# means for some parts, and exp(means) for other parts
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab) # D x V [W / TB] is the quotient of the original over the reconstructed doc-term matrix
S = expMeans * (R.dot(vocab.T)) # D x K
bound += np.sum(docLens * np.log(np.sum(expMeans, axis=1)))
bound += np.sum(sparseScalarProductOfSafeLnDot(W, expMeans, vocab).data)
bound += np.sum(means * S)
bound += np.sum(2 * ssp.diags(docLens,0) * means.dot(Ab) * means)
bound -= 2. * scaledSelfSoftDot(means, docLens)
bound -= 0.5 * np.sum(docLens[:,np.newaxis] * S * (np.diag(Ab))[np.newaxis,:])
bound -= np.sum(means * S)
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
def query(data, modelState, queryState, queryPlan):
'''
Given a _trained_ model, attempts to predict the topics for each of
the inputs. The assumption is that there are no out-links associated
with the documents, and that no documents in the training set link
to any of these documents in the query set.
The word and link vocabularies are kept fixed. Due to the assumption
of no in-links, we don't learn the prior in-document covariance, nor
the posterior distribution over in-links. Also, we don't modify
Params:
data - the dataset of words, features and links of which only words are used in this model
modelState - the _trained_ model
queryState - the query state generated for the query dataset
queryPlan - used in this case as we need to tighten up the approx
Returns:
The model state and query state, in that order. The model state is
unchanged, the query is.
'''
W, L, LT, X = data.words, data.links, ssp.csr_matrix(data.links.T), data.feats
D,_ = W.shape
out_links = np.squeeze(np.asarray(data.links.sum(axis=1)))
# Book-keeping for logs
boundIters, boundValues, likelyValues = [], [], []
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, diagonalPriorCov, debug = queryPlan.iterations, queryPlan.epsilon, queryPlan.logFrequency, queryPlan.fastButInaccurate, queryPlan.debug
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
emit_counts = docLens + out_links
# Initialize some working variables
W_weight = W.copy()
outDocPre = 1./outDocCov
inDocPre = np.reciprocal(inDocCov)
itopicCov = la.inv(topicCov)
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
expMeansRow = np.exp(outMeans - outMeans.max(axis=1)[:, np.newaxis])
W_weight = sparseScalarQuotientOfDot(W, expMeansRow, vocab, out=W_weight)
w_top_sums = W_weight.dot(vocab.T) * expMeansRow
# Update the posterior variances
outVarcs = np.reciprocal(emit_counts[:, np.newaxis] * (K-1)/(2*K) + (outDocPre + inDocPre[:,np.newaxis]) * np.diagonal(itopicCov)[np.newaxis,:])
# Update the out-means and in-means
out_rhs = w_top_sums.copy()
# No link outputs to model.
out_rhs += itopicCov.dot(topicMean) / outDocCov
out_rhs += emit_counts[:, np.newaxis] * (outMeans.dot(A) - rowwise_softmax(outMeans))
for d in range(D):
outCov = la.inv(outDocPre * itopicCov + emit_counts[d] * A)
outMeans[d, :] = outCov.dot(out_rhs[d,:])
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, topicMean, topicCov, outDocCov, vocab, A, True, dtype, MODEL_NAME)
queryState = QueryState(outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens)
boundValues.append(0)
likelyValues.append(log_likelihood(data, modelState, queryState))
boundIters.append(itr)
print (time.strftime('%X') + " : Iteration %d: bound %f \t Perplexity: %.2f" % (itr, boundValues[-1], perplexity_from_like(likelyValues[-1], docLens.sum())))
if len(boundValues) > 1:
# Check to see if the improvement in the bound has fallen below the threshold
if itr > MinItersBeforeEarlyStop and abs(perplexity_from_like(likelyValues[-1], docLens.sum()) - perplexity_from_like(likelyValues[-2], docLens.sum())) < 1.0:
break
return \
ModelState(K, topicMean, topicCov, outDocCov, vocab, A, True, dtype, MODEL_NAME), \
QueryState(outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens)
def query(data, modelState, queryState, queryPlan):
'''
Given a _trained_ model, attempts to predict the topics for each of
the inputs.
Params:
data - the dataset of words, features and links of which only words and
features are used in this model
modelState - the _trained_ model
queryState - the query state generated for the query dataset
queryPlan - used in this case as we need to tighten up the approx
Returns:
The model state and query state, in that order. The model state is
unchanged, the query is.
'''
iterations, epsilon, logFrequency, fastButInaccurate, debug = queryPlan.iterations, queryPlan.epsilon, queryPlan.logFrequency, queryPlan.fastButInaccurate, queryPlan.debug
means, expMeans, varcs, lxi, s, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, 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.vocabPrior, modelState.dtype
# Necessary temp variables (notably the count of topic to word assignments
# per topic per doc)
isigT = la.inv(sigT)
W,X = data.words, data.feats
# Enable logging or not. If enabled, we need the inner product of the feat matrix
if debug:
XTX = X.T.dot(X)
debugFn = _debug_with_bound
_debug_with_bound.old_bound=0
else:
XTX = None
debugFn = _debug_with_nothing
# Iterate over parameters
lastPerp = 1E+300 if dtype is np.float64 else 1E+30
for itr in range(iterations):
# Estimate Z_dvk
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab)
S = expMeans * R.dot(vocab.T)
# Update the Means
vMat = (2 * s[:,np.newaxis] * lxi - 0.5) * n[:,np.newaxis] + S
rhsMat = vMat + X.dot(A.T).dot(isigT) # TODO Verify this
lhsMat = np.reciprocal(np.diag(isigT)[np.newaxis,:] + n[:,np.newaxis] * 2 * lxi) # inverse of D diagonal matrices...
means = lhsMat * rhsMat # as LHS is a diagonal matrix for all d, it's equivalent
# to doing a hadamard product for all d
debugFn (itr, means, "query-means", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Variances
varcs = 1./(2 * n[:,np.newaxis] * lxi + isigT.flat[::K+1])
debugFn (itr, varcs, "query-varcs", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the approximation parameters
lxi = ctm.negJakkolaOfDerivedXi(means, varcs, s)
debugFn (itr, lxi, "query-lxi", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# s can sometimes grow unboundedly
# Follow Bouchard's suggested approach of fixing it at zero
#
# s = (np.sum(lxi * means, axis=1) + 0.25 * K - 0.5) / np.sum(lxi, axis=1)
# debugFn (itr, s, "s", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
like = log_likelihood(data, modelState, QueryState(means, expMeans, varcs, lxi, s, n))
perp = perplexity_from_like(like, data.word_count)
if itr > 20 and lastPerp - perp < 1:
break
lastPerp = perp
return modelState, QueryState (means, expMeans, varcs, lxi, s, n)
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 train (data, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
data - the dataset of words, features and links of which only words and
features are used in this model
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want itr)
A new query object with the update query parameters
'''
W, X = data.words, data.feats
D, _ = W.shape
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, fastButInaccurate, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
means, expMeans, varcs, docLens = queryState.means, queryState.expMeans, queryState.varcs, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, Ab, 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.vocabPrior, modelState.Ab, modelState.dtype
# Book-keeping for logs
boundIters = np.zeros(shape=(iterations // logFrequency,))
boundValues = np.zeros(shape=(iterations // logFrequency,))
boundLikes = np.zeros(shape=(iterations // logFrequency,))
bvIdx = 0
debugFn = _debug_with_bound if debug else _debug_with_nothing
_debug_with_bound.old_bound = 0
# For efficient inference, we need a separate covariance for every unique
# document length. For products to execute quickly, the doc-term matrix
# therefore needs to be ordered in ascending terms of document length
originalDocLens = docLens
sortIdx = np.argsort(docLens, kind=STABLE_SORT_ALG) # sort needs to be stable in order to be reversible
W = W[sortIdx,:] # deep sorted copy
X = X[sortIdx,:]
means, varcs = means[sortIdx,:], varcs[sortIdx,:]
docLens = originalDocLens[sortIdx]
lens, inds = np.unique(docLens, return_index=True)
inds = np.append(inds, [W.shape[0]])
# Initialize some working variables
R = W.copy()
aI_P = 1./lfv * ssp.eye(P, dtype=dtype)
print("Creating posterior covariance of A, this will take some time...")
XTX = X.T.dot(X)
R_A = XTX
R_A = R_A.todense() # dense inverse typically as fast or faster than sparse inverse
R_A.flat[::F+1] += 1./fv # and the result is usually dense in any case
R_A = la.inv(R_A)
print("Covariance matrix calculated, launching inference")
diff_m_xa = (means-X.dot(A.T))
means_cov_with_x_a = diff_m_xa.T.dot(diff_m_xa)
expMeans = np.zeros((BatchSize, K), dtype=dtype)
R = np.zeros((BatchSize, K), dtype=dtype)
S = np.zeros((BatchSize, K), dtype=dtype)
vocabScale = np.ones(vocab.shape, dtype=dtype)
# Iterate over parameters
batchIter = 0
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the covariance of the prior
diff_a_yv = (A-Y.dot(V))
sigT = 1./lfv * (Y.dot(Y.T))
sigT += 1./fv * diff_a_yv.dot(diff_a_yv.T)
sigT += means_cov_with_x_a
sigT.flat[::K+1] += varcs.sum(axis=0)
# As small numbers lead to instable inverse estimates, we use the
# fact that for a scalar a, (a .* X)^-1 = 1/a * X^-1 and use these
# scales whenever we use the inverse of the unscaled covariance
sigScale = 1. / (P+D+F)
isigScale = 1. / sigScale
isigT = la.inv(sigT)
debugFn (itr, sigT, "sigT", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
# Update the vocabulary
# vocab *= vocabScale
# vocab += vocabPrior
# vocab = normalizerows_ip(vocab)
# debugFn (itr, vocab, "vocab", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
# Finally update the parameter V
V = la.inv(sigScale * R_Y + Y.T.dot(isigT).dot(Y)).dot(Y.T.dot(isigT).dot(A))
debugFn (itr, V, "V", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
#
# And now this is the E-Step
#
# Update the distribution on the latent space
R_Y_base = aI_P + 1/fv * V.dot(V.T)
R_Y = la.inv(R_Y_base)
debugFn (itr, R_Y, "R_Y", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
Y = 1./fv * A.dot(V.T).dot(R_Y)
debugFn (itr, Y, "Y", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
# Update the mapping from the features to topics
A = (1./fv * Y.dot(V) + (X.T.dot(means)).T).dot(R_A)
debugFn (itr, A, "A", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
# Update the Variances
varcs = 1./((docLens * (K-1.)/K)[:,np.newaxis] + isigScale * isigT.flat[::K+1])
debugFn (itr, varcs, "varcs", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
# Faster version?
vocabScale[:,:] = 0
means_cov_with_x_a[:,:] = 0
for lenIdx in range(len(lens)):
nd = lens[lenIdx]
start, end = inds[lenIdx], inds[lenIdx + 1]
lhs = la.inv(isigT + sigScale * nd * Ab) * sigScale
for d in range(start, end, BatchSize):
end_d = min(d + BatchSize, end)
span = end_d - d
expMeans[:span,:] = np.exp(means[d:end_d,:] - means[d:end_d,:].max(axis=1)[:span,np.newaxis], out=expMeans[:span,:])
R = sparseScalarQuotientOfDot(W[d:end_d,:], expMeans[d:end_d,:], vocab)
S[:span,:] = expMeans[:span, :] * R.dot(vocab.T)
# Convert expMeans to a softmax(means)
expMeans[:span,:] /= expMeans[:span,:].sum(axis=1)[:span,np.newaxis]
mu = X[d:end_d,:].dot(A.T)
rhs = mu.dot(isigT) * isigScale
rhs += S[:span,:]
rhs += docLens[d:end_d,np.newaxis] * means[d:end_d,:].dot(Ab)
rhs -= docLens[d:end_d,np.newaxis] * expMeans[:span,:] # here expMeans is actually softmax(means)
means[d:end_d,:] = rhs.dot(lhs) # huh?! Left and right refer to eqn for a single mean: once we're talking a DxK matrix it gets swapped
expMeans[:span,:] = np.exp(means[d:end_d,:] - means[d:end_d,:].max(axis=1)[:span,np.newaxis], out=expMeans[:span,:])
R = sparseScalarQuotientOfDot(W[d:end_d,:], expMeans[:span,:], vocab, out=R)
stepSize = (Tau + batchIter) ** -Kappa
batchIter += 1
# Do a gradient update of the vocab
vocabScale = (R.T.dot(expMeans[:span,:])).T
vocabScale *= vocab
normalizerows_ip(vocabScale)
# vocabScale += vocabPrior
vocabScale *= stepSize
vocab *= (1 - stepSize)
vocab += vocabScale
diff = (means[d:end_d,:] - mu)
means_cov_with_x_a += diff.T.dot(diff)
# print("Vec-Means: %f, %f, %f, %f" % (means.min(), means.mean(), means.std(), means.max()))
debugFn (itr, means, "means", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, Ab, docLens)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT * sigScale, vocab, vocabPrior, Ab, dtype, MODEL_NAME)
queryState = QueryState(means, expMeans, varcs, docLens)
boundValues[bvIdx] = var_bound(DataSet(W, feats=X), modelState, queryState, XTX)
boundLikes[bvIdx] = log_likelihood(DataSet(W, feats=X), modelState, queryState)
boundIters[bvIdx] = itr
perp = perplexity_from_like(boundLikes[bvIdx], docLens.sum())
print (time.strftime('%X') + " : Iteration %d: Perplexity %4.0f bound %f" % (itr, perp, boundValues[bvIdx]))
if bvIdx > 0 and boundValues[bvIdx - 1] > boundValues[bvIdx]:
printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[bvIdx - 1], boundValues[bvIdx]))
# print ("Means: min=%f, avg=%f, max=%f\n\n" % (means.min(), means.mean(), means.max()))
# Check to see if the improvement in the likelihood has fallen below the threshold
if bvIdx > 1 and boundIters[bvIdx] > 20:
lastPerp = perplexity_from_like(boundLikes[bvIdx - 1], docLens.sum())
if lastPerp - perp < 1:
boundIters, boundValues, likelyValues = clamp (boundIters, boundValues, boundLikes, bvIdx)
break
bvIdx += 1
revert_sort = np.argsort(sortIdx, kind=STABLE_SORT_ALG)
means = means[revert_sort,:]
varcs = varcs[revert_sort,:]
docLens = docLens[revert_sort]
return \
ModelState(F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT * sigScale, vocab, vocabPrior, Ab, dtype, MODEL_NAME), \
QueryState(means, expMeans, varcs, docLens), \
(boundIters, boundValues, boundLikes)
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 repeatedly.
"""
# Unpack the the structs, for ease of access and efficiency
W, X = data.words, data.feats
D, T, F = W.shape[0], W.shape[1], X.shape[1]
means, docLens = queryState.means, queryState.docLens
K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior, dtype = (
modelState.K,
modelState.A,
modelState.U,
modelState.Y,
modelState.V,
modelState.covA,
modelState.tv,
modelState.ltv,
modelState.fv,
modelState.lfv,
modelState.vocab,
modelState.vocabPrior,
modelState.dtype,
)
H = 0.5 * (np.eye(K) - np.ones((K, K), dtype=dtype) / K)
Log2Pi = log(2 * pi)
bound = 0
# U and V are parameters with no distribution
#
# Y has a normal distribution, it's covariance is unfortunately an expensive computation
#
P, Q = U.shape[1], V.shape[1]
covY = np.eye(P * Q) * (lfv * ltv)
covY += np.kron(V.T.dot(V), U.T.dot(U))
covY = la.inv(covY, overwrite_a=True)
# The expected likelihood of Y
bound -= 0.5 * P * Q * Log2Pi
bound -= 0.5 * P * Q * log(ltv * lfv)
bound -= 0.5 / (lfv * ltv) * np.sum(Y * Y) # 5x faster than np.trace(Y.dot(Y.T))
bound -= 0.5 * np.trace(covY) * (lfv * ltv)
# the traces of the posterior+prior covariance products cancel out across likelihoods
# The entropy of Y
bound += 0.5 * P * Q * (Log2Pi + 1) + 0.5 * safe_log_det(covY)
#
# A has a normal distribution/
#
F, K = A.shape[0], A.shape[1]
diff = A - U.dot(Y).dot(V.T)
diff *= diff
# The expected likelihood of A
bound -= 0.5 * K * F * Log2Pi
bound -= 0.5 * K * F * log(tv * fv)
bound -= 0.5 / (fv * tv) * np.sum(diff)
# The entropy of A
bound += 0.5 * F * K * (Log2Pi + 1) + 0.5 * K * safe_log_det(covA)
#
# Theta, the matrix of means, has a normal distribution. Its row-covarince is diagonal
# (i.e. it's several independent multi-var normal distros). The posterior is made
# up of D K-dimensional normals with diagonal covariances
#
# We iterate through the topics in batches, to control memory use
batchSize = min(BatchSize, D)
batchCount = ceil(D / batchSize)
feats = np.ndarray(shape=(batchSize, F), dtype=dtype)
tops = np.ndarray(shape=(batchSize, K), dtype=dtype)
trace = 0
for b in range(0, batchCount):
start = b * batchSize
end = min(start + batchSize, D)
batchSize = min(batchSize, end - start)
feats[:batchSize, :] = X[start:end, :].toarray()
np.dot(feats[:batchSize, :], A, out=tops[:batchSize, :])
tops[:batchSize, :] -= means[start:end, :]
tops[:batchSize, :] *= tops[:batchSize, :]
trace += np.sum(tops[:batchSize, :])
feats = None
# The expected likelihood of the topic-assignments
bound -= 0.5 * D * K * Log2Pi
bound -= 0.5 * D * K * log(tv)
bound -= 0.5 / tv * trace
bound -= 0.5 * tv * np.sum(covA) # this trace doesn't cancel as we
# don't have a posterior on tv
# The entropy of the topic-assignments
bound += 0.5 * D * K * (Log2Pi + 1) + 0.5 * np.sum(covA)
# Distribution over word-topic assignments and words and the formers
# entropy. This is somewhat jumbled to avoid repeatedly taking the
# exp and log of the means
# Again we batch this for safety
batchSize = min(BatchSize, D)
batchCount = ceil(D / batchSize)
V = np.ndarray(shape=(batchSize, K), dtype=dtype)
for b in range(0, batchCount):
start = b * batchSize
end = min(start + batchSize, D)
batchSize = min(batchSize, end - start)
meansBatch = means[start:end, :]
docLensBatch = docLens[start:end]
np.exp(meansBatch - meansBatch.max(axis=1)[:, np.newaxis], out=tops[:batchSize, :])
expMeansBatch = tops[:batchSize, :]
R = sparseScalarQuotientOfDot(
W, expMeansBatch, vocab, start=start, end=end
) # BatchSize x V: [W / TB] is the quotient of the original over the reconstructed doc-term matrix
V[:batchSize, :] = expMeansBatch * (R[:batchSize, :].dot(vocab.T)) # BatchSize x K
VBatch = V[:batchSize, :]
bound += np.sum(docLensBatch * np.log(np.sum(expMeansBatch, axis=1)))
bound += np.sum(sparseScalarProductOfSafeLnDot(W, expMeansBatch, vocab, start=start, end=end).data)
bound += np.sum(meansBatch * VBatch)
bound += np.sum(2 * ssp.diags(docLensBatch, 0) * meansBatch.dot(H) * meansBatch)
bound -= 2.0 * scaledSelfSoftDot(meansBatch, docLensBatch)
bound -= 0.5 * np.sum(docLensBatch[:, np.newaxis] * VBatch * (np.diag(H))[np.newaxis, :])
bound -= np.sum(meansBatch * VBatch)
return bound
def train (data, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
W - the DxT document-term matrix
X - The DxF document-feature matrix, which is IGNORED in this case
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want itr)
A new query object with the update query parameters
'''
W, L, LT, X = data.words, data.links, ssp.csr_matrix(data.links.T), data.feats
D,_ = W.shape
out_links = np.squeeze(np.asarray(data.links.sum(axis=1)))
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, diagonalPriorCov, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
means, varcs, docLens = queryState.means, queryState.varcs, queryState.docLens
K, topicMean, topicCov, vocab, A, dtype = modelState.K, modelState.topicMean, modelState.topicCov, modelState.vocab, modelState.A, modelState.dtype
emit_counts = docLens + out_links
# Book-keeping for logs
boundIters, boundValues, likelyValues = [], [], []
if debug:
debugFn = _debug_with_bound
initLikely = log_likelihood(data, modelState, queryState)
initPerp = perplexity_from_like(initLikely, data.word_count)
print ("Initial perplexity is: %.2f" % initPerp)
else:
debugFn = _debug_with_nothing
# Initialize some working variables
W_weight = W.copy()
L_weight = L.copy()
LT_weight = LT.copy()
pseudoObsMeans = K + NIW_PSEUDO_OBS_MEAN
pseudoObsVar = K + NIW_PSEUDO_OBS_VAR
priorSigT_diag = np.ndarray(shape=(K,), dtype=dtype)
priorSigT_diag.fill (NIW_PSI)
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the mean and covariance of the prior
topicMean = means.sum(axis = 0) / (D + pseudoObsMeans) \
if USE_NIW_PRIOR \
else means.mean(axis=0)
debugFn (itr, topicMean, "topicMean", data, K, topicMean, topicCov, vocab, dtype, means, varcs, A, docLens)
if USE_NIW_PRIOR:
diff = means - topicMean[np.newaxis,:]
topicCov = diff.T.dot(diff) \
+ pseudoObsVar * np.outer(topicMean, topicMean)
topicCov += np.diag(varcs.mean(axis=0) + priorSigT_diag)
topicCov /= (D + pseudoObsVar - K)
else:
topicCov = np.cov(means.T) if topicCov.dtype == np.float64 else np.cov(means.T).astype(dtype)
topicCov += np.diag(varcs.mean(axis=0))
if diagonalPriorCov:
diag = np.diag(topicCov)
topicCov = np.diag(diag)
itopicCov = np.diag(1./ diag)
else:
itopicCov = la.inv(topicCov)
debugFn (itr, topicCov, "topicCov", data, K, topicMean, topicCov, vocab, dtype, means, varcs, A, docLens)
# print(" topicCov.det = " + str(la.det(topicCov)))
# Building Blocks - temporarily replaces means with exp(means)
expMeansCol = np.exp(means - means.max(axis=0)[np.newaxis, :])
lse_at_k = np.sum(expMeansCol, axis=0)
F = 0.5 * means \
- (1. / (2*D + 2)) * means.sum(axis=0) \
- expMeansCol / lse_at_k[np.newaxis, :]
expMeansRow = np.exp(means - means.max(axis=1)[:, np.newaxis])
W_weight = sparseScalarQuotientOfDot(W, expMeansRow, vocab, out=W_weight)
# Update the vocabularies
vocab *= (W_weight.T.dot(expMeansRow)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += VocabPrior
vocab = normalizerows_ip(vocab)
docVocab = (expMeansCol / lse_at_k[np.newaxis, :]).T # FIXME Dupes line in definitino of F
# Recalculate w_top_sums with the new vocab and log vocab improvement
W_weight = sparseScalarQuotientOfDot(W, expMeansRow, vocab, out=W_weight)
w_top_sums = W_weight.dot(vocab.T) * expMeansRow
debugFn (itr, vocab, "vocab", data, K, topicMean, topicCov, vocab, dtype, means, varcs, A, docLens)
# Now do likewise for the links, do it twice to model in-counts (first) and
# out-counts (Second). The difference is the transpose
LT_weight = sparseScalarQuotientOfDot(LT, expMeansRow, docVocab, out=LT_weight)
l_intop_sums = LT_weight.dot(docVocab.T) * expMeansRow
in_counts = l_intop_sums.sum(axis=0)
L_weight = sparseScalarQuotientOfDot(L, expMeansRow, docVocab, out=L_weight)
l_outtop_sums = L_weight.dot(docVocab.T) * expMeansRow
# Reset the means and use them to calculate the weighted sum of means
meanSum = means.sum(axis=0) * in_counts
# And now this is the E-Step, though itr's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# Update the Variances: var_d = (2 N_d * A + itopicCov)^{-1}
varcs = np.reciprocal(docLens[:, np.newaxis] * (0.5 - 1./K) + np.diagonal(topicCov))
debugFn (itr, varcs, "varcs", data, K, topicMean, topicCov, vocab, dtype, means, varcs, A, docLens)
# Update the Means
rhs = w_top_sums.copy()
rhs += l_intop_sums
rhs += l_outtop_sums
rhs += itopicCov.dot(topicMean)
rhs += emit_counts[:, np.newaxis] * (means.dot(A) - rowwise_softmax(means))
rhs += in_counts[np.newaxis, :] * F
if diagonalPriorCov:
raise ValueError("Not implemented")
else:
for d in range(D):
rhs_ = rhs[d, :] + (1. / (4 * D + 4)) * (meanSum - in_counts * means[d, :])
means[d, :] = la.inv(itopicCov + emit_counts[d] * A + np.diag(D * in_counts / (2 * D + 2))).dot(rhs_)
if np.any(np.isnan(means[d, :])) or np.any (np.isinf(means[d, :])):
pass
if np.any(np.isnan(np.exp(means[d, :] - means[d, :].max()))) or np.any (np.isinf(np.exp(means[d, :] - means[d, :].max()))):
pass
debugFn (itr, means, "means", data, K, topicMean, topicCov, vocab, dtype, means, varcs, A, docLens)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, topicMean, topicCov, vocab, A, dtype, MODEL_NAME)
queryState = QueryState(means, varcs, docLens)
boundValues.append(var_bound(data, modelState, queryState))
likelyValues.append(log_likelihood(data, modelState, queryState))
boundIters.append(itr)
print (time.strftime('%X') + " : Iteration %d: bound %f \t Perplexity: %.2f" % (itr, boundValues[-1], perplexity_from_like(likelyValues[-1], docLens.sum())))
if len(boundValues) > 1:
if boundValues[-2] > boundValues[-1]:
printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[-2], boundValues[-1]))
# Check to see if the improvement in the bound has fallen below the threshold
if False and itr > 100 and abs(perplexity_from_like(likelyValues[-1], docLens.sum()) - perplexity_from_like(likelyValues[-2], docLens.sum())) < 1.0:
break
return \
ModelState(K, topicMean, topicCov, vocab, A, dtype, MODEL_NAME), \
QueryState(means, varcs, docLens), \
(np.array(boundIters), np.array(boundValues), np.array(likelyValues))