def newQueryState(data, modelState, withLdaTopics=None):
'''
Creates a new CTM Query state object. This contains all
parameters and random variables tied to individual
datapoints.
Param:
data - the dataset of words, features and links of which only words are used in this model
modelState - the model state object
withLdaQuery - if not null, this is used to instantiate the
initial topics. IT IS ALSO USED TO MUTATE THE MODEL
REturn:
A CtmQueryState object
'''
if INIT_WITH_CTM:
return _newQueryStateFromCtm(data, modelState)
elif withLdaTopics is not None:
return _newQueryStateFromLda(data, modelState, withLdaTopics)
K, vocab, dtype = modelState.K, modelState.vocab, modelState.dtype
D,T = data.words.shape
assert T == vocab.shape[1], "The number of terms in the document-term matrix (" + str(T) + ") differs from that in the model-states vocabulary parameter " + str(vocab.shape[1])
docLens = np.squeeze(np.asarray(data.words.sum(axis=1)))
outMeans = normalizerows_ip(rd.random((D,K)).astype(dtype))
outVarcs = np.ones((D,K), dtype=dtype)
inMeans = normalizerows_ip(outMeans + 0.1 * rd.random((D,K)).astype(dtype))
inVarcs = np.ones((D,K), dtype=dtype)
inDocCov = np.ones((D,), dtype=dtype)
return QueryState(outMeans, outVarcs, inMeans, inVarcs, inDocCov, docLens)
def newQueryState(data, modelState):
"""
Creates a new CTM Query state object. This contains all
parameters and random variables tied to individual
datapoints.
Param:
data - the dataset of words, features and links of which only words are used in this model
modelState - the model state object
REturn:
A CtmQueryState object
"""
K, vocab, dtype = modelState.K, modelState.vocab, modelState.dtype
D, T = data.words.shape
assert T == vocab.shape[1], (
"The number of terms in the document-term matrix ("
+ str(T)
+ ") differs from that in the model-states vocabulary parameter "
+ str(vocab.shape[1])
)
docLens = np.squeeze(np.asarray(data.words.sum(axis=1)))
means = normalizerows_ip(rd.random((D, K)).astype(dtype))
return QueryState(means, docLens)
def newQueryState(data, modelState):
'''
Creates a new CTM Query state object. This contains all
parameters and random variables tied to individual
datapoints.
Param:
data - the dataset of words, features and links of which only words are used in this model
modelState - the model state object
REturn:
A CtmQueryState object
'''
K, vocab, dtype = modelState.K, modelState.vocab, modelState.dtype
W = data.words
D,T = W.shape
assert T == vocab.shape[1], "The number of terms in the document-term matrix (" + str(T) + ") differs from that in the model-states vocabulary parameter " + str(vocab.shape[1])
docLens = np.squeeze(np.asarray(W.sum(axis=1)))
base = normalizerows_ip(rd.random((D,K*2)).astype(dtype))
means = base[:,:K]
expMeans = base[:,K:]
varcs = np.ones((D,K), dtype=dtype)
s = np.ndarray(shape=(D,), dtype=dtype)
s.fill(0)
lxi = negJakkolaOfDerivedXi(means, varcs, s)
return QueryState(means, expMeans, varcs, lxi, s, docLens)
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:
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 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 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 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 _testOnModelHandcraftedData(self):
#
# Create the vocab
#
T = 3 * 3
K = 5
# Horizontal bars
vocab1 = ssp.coo_matrix(([1, 1, 1], ([0, 0, 0], [0, 1, 2])), shape=(3,3)).todense()
#vocab2 = ssp.coo_matrix(([1, 1, 1], ([1, 1, 1], [0, 1, 2])), shape=(3,3)).todense()
vocab3 = ssp.coo_matrix(([1, 1, 1], ([2, 2, 2], [0, 1, 2])), shape=(3,3)).todense()
# Vertical bars
vocab4 = ssp.coo_matrix(([1, 1, 1], ([0, 1, 2], [0, 0, 0])), shape=(3,3)).todense()
#vocab5 = ssp.coo_matrix(([1, 1, 1], ([0, 1, 2], [1, 1, 1])), shape=(3,3)).todense()
vocab6 = ssp.coo_matrix(([1, 1, 1], ([0, 1, 2], [2, 2, 2])), shape=(3,3)).todense()
# Diagonals
vocab7 = ssp.coo_matrix(([1, 1, 1], ([0, 1, 2], [0, 1, 2])), shape=(3,3)).todense()
#vocab8 = ssp.coo_matrix(([1, 1, 1], ([2, 1, 0], [0, 1, 2])), shape=(3,3)).todense()
# Put together
T = vocab1.shape[0] * vocab1.shape[1]
vocabs = [vocab1, vocab3, vocab4, vocab6, vocab7]
# Create a single matrix with the flattened vocabularies
vocabVectors = []
for vocab in vocabs:
vocabVectors.append (np.squeeze(np.asarray (vocab.reshape((1,T)))))
vocab = normalizerows_ip(np.array(vocabVectors, dtype=DTYPE))
# Plot the vocab
ones = np.ones(vocabs[0].shape)
for k in range(K):
plt.subplot(2, 3, k)
plt.imshow(ones - vocabs[k], interpolation="none", cmap = cm.Greys_r)
plt.show()
#
# Create the corpus
#
rd.seed(0xC0FFEE)
D = 1000
# Make sense (of a sort) of this by assuming that these correspond to
# Kittens Omelettes Puppies Oranges Tomatoes Dutch People Basketball Football
#topicMean = np.array([10, 25, 5, 15, 5, 5, 10, 25])
# topicCovar = np.array(\
# [[ 100, 5, 55, 20, 5, 15, 4, 0], \
# [ 5, 100, 5, 10, 70, 5, 0, 0], \
# [ 55, 5, 100, 5, 5, 10, 0, 5], \
# [ 20, 10, 5, 100, 30, 30, 20, 10], \
# [ 5, 70, 5, 30, 100, 0, 0, 0], \
# [ 15, 5, 10, 30, 0, 100, 10, 40], \
# [ 4, 0, 0, 20, 0, 10, 100, 20], \
# [ 0, 0, 5, 10, 0, 40, 20, 100]], dtype=DTYPE) / 100.0
topicMean = np.array([25, 15, 40, 5, 15])
self.assertEqual(100, topicMean.sum())
topicCovar = np.array(\
[[ 100, 5, 55, 20, 5 ], \
[ 5, 100, 5, 10, 70 ], \
[ 55, 5, 100, 5, 5 ], \
[ 20, 10, 5, 100, 30 ], \
[ 5, 70, 5, 30, 100 ], \
], dtype=DTYPE) / 100.0
meanWordCount = 80
wordCounts = rd.poisson(meanWordCount, size=D)
topicDists = rd.multivariate_normal(topicMean, topicCovar, size=D)
W = topicDists.dot(vocab) * wordCounts[:, np.newaxis]
W = ssp.csr_matrix (W.astype(DTYPE))
#
# Train the model
#
model = ctm.newModelAtRandom(W, K, dtype=DTYPE)
queryState = ctm.newQueryState(W, model)
trainPlan = ctm.newTrainPlan(iterations=65, plot=True, logFrequency=1)
self.assertTrue (0.99 < np.sum(model.topicMean) < 1.01)
return self._doTest (W, model, queryState, trainPlan)
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 train(modelState, X, W, plan):
'''
Creates a new query state object for a topic model based on side-information.
This contains all those estimated parameters that are specific to the actual
date being queried - this must be used in conjunction with a model state.
The parameters are
modelState - the model state with all the model parameters
X - the D x F matrix of side information vectors
W - the D x V matrix of word **count** vectors.
iterations - how long to iterate for
epsilon - currently ignored, in future, allows us to stop early.
logInterval - the interval between iterations where we calculate and display
the log-likelihood bound
plotInterval - the interval between iterations we we display the log-likelihood
bound values calcuated at each log-interval
fastButInaccurate - if true, we may use a psedo-inverse instead of an inverse
when solving for Y when the true inverse is unavailable.
This returns a tuple of new model-state and query-state. The latter object will
contain X and W and also
s - A D-dimensional vector describing the offset in our bound on the true value of ln sum_k e^theta_dk
lxi - A DxK matrix used in the above bound, containing the negative Jakkola function applied to the
quadratic term xi
lambda - the topics we've inferred for the current batch of documents
nu - the variance of topics we've inferred (independent)
'''
# Unpack the model state tuple for ease of use and maybe speed improvements
K, Q, F, P, T, A, varA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq = modelState.K, modelState.Q, modelState.F, modelState.P, modelState.T, modelState.A, modelState.varA, modelState.Y, modelState.omY, modelState.sigY, modelState.sigT, modelState.U, modelState.V, modelState.vocab, modelState.topicVar, modelState.featVar, modelState.lowTopicVar, modelState.lowFeatVar
iterations, epsilon, logCount, plot, plotFile, plotIncremental, fastButInaccurate = plan.iterations, plan.epsilon, plan.logFrequency, plan.plot, plan.plotFile, plan.plotIncremental, plan.fastButInaccurate
mu0 = 0.0001
if W.dtype.kind == 'i': # for the sparseScalorQuotientOfDot() method to work
W = W.astype(DTYPE)
# Get ready to plot the evolution of the likelihood, with multiplicative updates (e.g. 1, 2, 4, 8, 16, 32, ...)
if logCount > 0:
multiStepSize = np.power (iterations, 1. / logCount)
logIter = 1
elbos = []
likes = []
iters = []
else:
logIter = iterations + 1
lastVarBoundValue = -sys.float_info.max
# We'll need the total word count per doc, and total count of docs
docLen = np.squeeze(np.asarray (W.sum(axis=1))) # Force to a one-dimensional array for np.newaxis trick to work
D = len(docLen)
# No need to recompute this every time
if X.dtype != DTYPE:
X = X.astype (DTYPE)
XTX = X.T.dot(X)
# Identity matrices that occur
I_P = ssp.eye(P,P, 0, DTYPE)
I_Q = ssp.eye(Q,Q, 0, DTYPE)
I_QP = ssp.eye(Q*P,Q*P, 0, DTYPE)
I_F = ssp.eye(F,F, 0, DTYPE, "csc") # X is CSR, XTX is consequently CSC, sparse inverse requires CSC
T_QP = sp_vec_trans_matrix(Y.shape)
# Assign initial values to the query parameters
expLmda = np.exp(rd.random((D, K)).astype(DTYPE))
nu = np.ones((D, K), DTYPE)
s = np.zeros((D,), DTYPE)
lxi = negJakkola (np.ones((D,K), DTYPE))
# If we don't bother optimising either tau or sigma we can just do all this here once only
tsq = tauSq
ssq = sigmaSq
overTsq = 1. / tsq
overSsq = 1. / ssq
overTsqSsq = 1./(tsq * ssq)
# TODO the inverse being almost always dense means that it might
# be faster to convert to dense and use the normal solver, despite
# the size constraints.
# varA = 1./K * sla.inv (overTsq * I_F + overSsq * XTX)
tI_sXTX = (overTsq * I_F + overSsq * XTX).todense();
omA = la.inv (tI_sXTX)
scaledWordCounts = W.copy()
for iteration in range(iterations):
# =============================================================
# E-Step
# Model dists are q(Theta|A;Lambda;nu) q(A|Y) q(Y) and q(Z)....
# Where lambda is the posterior mean of theta.
# =============================================================
# Y, sigY, omY
#
# If U'U is invertible, use inverse to convert Y to a Sylvester eqn
# which has a much, much faster solver. Recall update for Y is of the form
# Y + AYB = C where A = U'U, B = V'V and C=U'AV
#
VTV = V.T.dot(V)
UTU = U.T.dot(U)
sigy = la.inv(I_QP + overTsqSsq * np.kron(VTV, UTU))
_quickPrintElbo ("E-Step: q(Y) [sigY]", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma, expLmda, nu, lxi, s, docLen)
Y = mu0 + np.reshape (overTsqSsq * sigy.dot(vec(U.T.dot(A).dot(V))), (Q,P), order='F')
_quickPrintElbo ("E-Step: q(Y) [Mean]", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma, expLmda, nu, lxi, s, docLen)
# A
#
# So it's normally A = (UYV' + L'X) omA with omA = inv(t*I_F + s*XTX)
# so A inv(omA) = UYV' + L'X
# so inv(omA)' A' = VY'U' + X'L
# at which point we can use a built-in solve
#
# A = (overTsq * U.dot(Y).dot(V.T) + X.T.dot(expLmda).T).dot(omA)
lmda = np.log(expLmda, out=expLmda)
A = la.solve(tI_sXTX, X.T.dot(lmda) + V.dot(Y.T).dot(U.T)).T
np.exp(expLmda, out=expLmda)
_quickPrintElbo ("E-Step: q(A)", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma, expLmda, nu, lxi, s, docLen)
# lmda_dk, nu_dk, s_d, and xi_dk
#
XAT = X.dot(A.T)
query (VbSideTopicModelState (K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma), \
X, W, \
VbSideTopicQueryState(expLmda, nu, lxi, s, docLen), \
scaledWordCounts=scaledWordCounts, \
XAT = XAT, \
iterations=10, \
logInterval = 0, plotInterval = 0)
# =============================================================
# M-Step
# Parameters for the softmax bound: lxi and s
# The projection used for A: U and V
# The vocabulary : vocab
# The variances: tau, sigma
# =============================================================
# U
#
try:
U = A.dot(V).dot(Y.T).dot (la.inv( \
Y.dot(V.T).dot(V).dot(Y.T) \
+ (vec_transpose_csr(T_QP, P).T.dot(np.kron(I_QP, VTV)).dot(vec_transpose(T_QP.dot(sigy), P))).T
))
except np.linalg.linalg.LinAlgError as e:
print(str(e))
print ("Ruh-ro")
# order of last line above reversed to handle numpy bug preventing dot product from dense to sparse
_quickPrintElbo ("M-Step: U", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma, expLmda, nu, lxi, s, docLen)
# V
#
# Temporarily this requires that we re-order sigY until I've implemented a fortran order
# vec transpose in Cython
sigY = sigY.T.copy()
V = A.T.dot(U).dot(Y).dot (la.inv ( \
Y.T.dot(U.T).dot(U).dot(Y) \
+ vec_transpose (sigY, Q).T.dot(np.kron(I_QP, UTU).dot(vec_transpose(I_QP, Q))) \
))
_quickPrintElbo ("M-Step: V", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma, expLmda, nu, lxi, s, docLen)
# vocab
#
factor = (scaledWordCounts.T.dot(expLmda)).T # Gets materialized as a dense matrix...
vocab *= factor
normalizerows_ip(vocab)
_quickPrintElbo ("M-Step: \u03A6", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, tau, sigma, expLmda, nu, lxi, s, docLen)
# =============================================================
# Handle logging of variational bound, likelihood, etc.
# =============================================================
if iteration == logIter:
modelState = VbSideTopicModelState (K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq)
queryState = VbSideTopicQueryState(expLmda, nu, lxi, s, docLen)
elbo = varBound (modelState, queryState, X, W, None, XAT, XTX)
likely = log_likelihood(modelState, X, W, queryState) #recons_error(modelState, X, W, queryState)
elbos.append (elbo)
iters.append (iteration)
likes.append (likely)
print ("Iteration %5d ELBO %15f Log-Likelihood %15f" % (iteration, elbo, likely))
logIter = min (np.ceil(logIter * multiStepSize), iterations - 1)
if elbo - lastVarBoundValue < epsilon:
break
else:
lastVarBoundValue = elbo
if plot and plotIncremental:
plot_bound(plotFile + "-iter-" + str(iteration), np.array(iters), np.array(elbos), np.array(likes))
# Right before we end, plot the evolution of the bound and likelihood
# if we've been asked to do so.
if plot:
plot_bound(plotFile, iters, elbos, likes)
return VbSideTopicModelState (K, Q, F, P, T, A, omA, Y, omY, sigY, U, V, vocab, tau, sigma), \
VbSideTopicQueryState (expLmda, nu, lxi, s, docLen)
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))
