def _doTest (self, W, model, queryState, trainPlan):
D,_ = W.shape
recons = rowwise_softmax(queryState.means).dot(model.vocab)
reconsErr = 1./D * np.sum((np.asarray(W.todense()) - recons) * (np.asarray(W.todense()) - recons))
print ("Initial bound is %f\n\n" % ctm.var_bound(W, model, queryState))
print ("Initial reconstruction error is %f\n\n" % reconsErr)
model, query, (bndItrs, bndVals, likelies) = ctm.train (W, None, model, queryState, trainPlan)
# Plot the bound
fig, ax1 = plt.subplots()
ax1.plot(bndItrs, bndVals, 'b-')
ax1.set_xlabel('Iterations')
ax1.set_ylabel('Bound', color='b')
ax2 = ax1.twinx()
ax2.plot(bndItrs, likelies, 'r-')
ax2.set_ylabel('Likelihood', color='r')
fig.show()
plt.show()
# Plot the inferred vocab
plt.imshow(model.vocab, interpolation="none", cmap = cm.Greys_r)
plt.show()
recons = rowwise_softmax(queryState.means).dot(model.vocab)
reconsErr = 1./D * np.sum((np.asarray(W.todense()) - recons) * (np.asarray(W.todense()) - recons))
print ("Final reconstruction error is %f\n\n" % reconsErr)
def log_likelihood (data, modelState, queryState):
'''
Return the log-likelihood of the given data W according to the model
and the parameters inferred for the entries in W stored in the
queryState object.
'''
probs = rowwise_softmax(queryState.outMeans)
doc_dist = colwise_softmax(queryState.inMeans)
word_likely = np.sum( \
sparseScalarProductOfSafeLnDot(\
data.words, \
probs, \
modelState.vocab \
).data \
)
link_likely = np.sum( \
sparseScalarProductOfSafeLnDot(\
data.links, \
probs, \
doc_dist \
).data \
)
return word_likely + link_likely
def log_likelihood(data, modelState, queryState):
"""
Return the log-likelihood of the given data W according to the model
and the parameters inferred for the entries in W stored in the
queryState object.
"""
return np.sum(sparseScalarProductOfSafeLnDot(data.words, rowwise_softmax(queryState.means), modelState.vocab).data)
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 _sampleFromModel(self, D=200, T=100, K=10, avgWordsPerDoc = 500):
'''
Create a test dataset according to the model
Params:
D - Sample documents (each with associated features)
T - Vocabulary size, the number of "terms". Must be a square number
K - Observed topics
avgWordsPerDoc - average number of words per document generated (Poisson)
Returns:
modelState - a model state object configured for training
tpcs - the matrix of per-document topic distribution
vocab - the matrix of per-topic word distributions
docLens - the vector of document lengths
X - the DxF side information matrix
W - The DxW word matrix
'''
# Generate vocab
beta = 0.1
betaVec = np.ndarray((T,))
betaVec.fill(beta)
vocab = rd.dirichlet(betaVec, size=K)
# Geneate the shared covariance matrix
# ...no real structure in this.
sigT = rd.random((K,K))
sigT = sigT.dot(sigT)
# Generate topic mean
alpha = 1
alphaVec = np.ndarray((K,))
alphaVec.fill(alpha)
topicMean = rd.dirichlet(alphaVec)
# Generate the actual topics.
tpcs = rd.multivariate_normal(topicMean, sigT, size=D)
tpcs = rowwise_softmax(tpcs)
# Generate the corpus
docLens = rd.poisson(avgWordsPerDoc, (D,)).astype(np.float32)
W = tpcs.dot(vocab)
W *= docLens[:, np.newaxis]
W = np.array(W, dtype=np.int32) # truncate word counts to integers
W = ssp.csr_matrix(W)
# Return the initialised model, the true parameter values, and the
# generated observations
return tpcs, vocab, docLens, W
def _doTest (self, W, model, queryState, trainPlan):
D,_ = W.shape
recons = rowwise_softmax(queryState.means).dot(model.vocab)
reconsErr = 1./D * np.sum((np.asarray(W.todense()) - recons) * (np.asarray(W.todense()) - recons))
print ("Initial bound is %f\n\n" % ctm.var_bound(W, model, queryState))
print ("Initial reconstruction error is %f\n\n" % reconsErr)
model, query, (bndItrs, bndVals) = ctm.train (W, None, model, queryState, trainPlan)
# Plot the bound
plt.plot(bndItrs[5:], bndVals[5:])
plt.xlabel("Iterations")
plt.ylabel("Variational Bound")
plt.show()
# Plot the inferred vocab
plt.imshow(model.vocab, interpolation="none", cmap = cm.Greys_r)
plt.show()
recons = rowwise_softmax(queryState.means).dot(model.vocab)
reconsErr = 1./D * np.sum((np.asarray(W.todense()) - recons) * (np.asarray(W.todense()) - recons))
print ("Final reconstruction error is %f\n\n" % reconsErr)
def selfSoftDot(matrix):
'''
Considers the given matrix to be a collection of stacked row-vectors.
Returns the sum of the dot products of each row-vector and its
soft-max form.
This words on DENSE matrices only, and it appears in this module simply
for convenience.
Uses fast, memory-efficient operations for matrices of single
and double-precision numbers, uses fast-ish numpy code as a
fallback, but at the cost of creating a copy of of the matrix.
'''
assert not np.isfortran(matrix), "Matrix is not stored in row-major form"
if matrix.dtype == np.float64:
return compiled.selfSoftDot_f8(matrix)
elif matrix.dtype == np.float32:
return compiled.selfSoftDot_f4(matrix)
if WarnIfSlow:
sys.stderr.write("WARNING: Slow code path triggered (selfSoftDot)")
return np.sum(matrix * rowwise_softmax(matrix))
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 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 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 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:
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]
data = DataSet(W, feats=X)
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")
priorSigt_diag = np.ndarray(shape=(K,), dtype=dtype)
priorSigt_diag.fill (0.001)
# 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)
# 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)
# Building Blocks - termporarily replaces means with exp(means)
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
if np.isnan(expMeans).any() or np.isinf(expMeans).any():
print ("Yoinks, Scoob..!")
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
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
S = expMeans * R.dot(vocab.T)
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)
# Update the Means
rhs = X.dot(A.T).dot(isigT) * isigScale
rhs += S
rhs += docLens[:,np.newaxis] * means.dot(Ab)
rhs -= docLens[:,np.newaxis] * rowwise_softmax(means, out=means)
# Long version
# inverses = dict()
# sca_means = means.copy()
# for d in range(D):
# if not n[d] in inverses:
# inverses[n[d]] = la.inv(isigT + n[d] * Ab)
# lhs = inverses[n[d]]
# sca_means[d,:] = lhs.dot(rhs[d,:])
# print("Sca-Means: %f, %f, %f, %f" % (sca_means.min(), sca_means.mean(), sca_means.std(), sca_means.max()))
# Faster version?
for lenIdx in range(len(lens)):
nd = lens[lenIdx]
start, end = inds[lenIdx], inds[lenIdx + 1]
lhs = la.inv(isigT + sigScale * nd * Ab) * sigScale
means[start:end,:] = rhs[start:end,:].dot(lhs) # huh?! Left and right refer to eqn for a single mean: once we're talking a DxK matrix it gets swapped
# 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 cross_val_and_eval_hashtag_prec_at_m(data, mdl, sample_model, train_plan, word_dict, num_folds, fold_run_count=-1, model_dir= None):
'''
Evaluate the precision at M for the top 50 hash-tags. In the held-out set, the hashtags
are deleted. We train on all, both training and held-out, then evaluate the precision
at M for the hashtags
For values of M we use 10, 50, 100, 150, 250, 500
:param data: the DataSet object with the data
:param mdl: the module with the train etc. functin
:param sample_model: a preconfigured model which is cloned at the start of each
cross-validation run
:param train_plan: the training plan (number of iterations etc.)
:param word_dict the word dictionary, used to identify hashtags and print them
out when the run is completed.
:param num_folds: the number of folds to cross validation
:param fold_run_count: for debugging stop early after processing the number
of the folds
:param model_dir: if not none, the models are stored in this directory.
:return: the list of model files stored
'''
MS = [10, 50, 100, 150, 200, 250, 1000, 1500, 3000, 5000, 10000]
Precision, Recall = "precision", "recall"
model_files = []
if fold_run_count < 1:
fold_run_count = num_folds
if num_folds <= 1:
raise ValueError ("Number of folds must be greater than 1")
hashtag_indices = popular_hashtag_indices (data, word_dict, 50)
folds_finished = 0 # count of folds that finished successfully
fold = 0
while fold < num_folds and folds_finished < fold_run_count:
try:
train_range, query_range = data.cross_valid_split_indices(fold, num_folds)
segment_with_htags = data.words[train_range, :]
held_out_segment_with_htags = data.words[query_range, :]
held_out_segment_without_htags = data.words[query_range, :]
held_out_segment_without_htags[:, hashtag_indices] = 0
train_words = ssp.vstack((segment_with_htags, held_out_segment_without_htags))
train_data = data.copy_with_changes(words=train_words)
# Train the model
print ("Duplicating model template... ", end="")
model = mdl.newModelFromExisting(sample_model)
train_tops = mdl.newQueryState(train_data, model)
print ("Starting training")
model, train_tops, (train_itrs, train_vbs, train_likes) \
= mdl.train(train_data, model, train_tops, train_plan)
# Predict hashtags
dist = rowwise_softmax(train_tops.means)
# For each hash-tag, for each value of M, evaluate the precision
results = {Recall : dict(), Precision : dict()}
for hi in hashtag_indices:
h_probs = dist[query_range,:].dot(model.vocab[:,hi])
h_count = held_out_segment_with_htags[:, hi].sum()
results[Recall][word_dict[hi]] = { -1 : h_count }
results[Precision][word_dict[hi]] = { -1 : h_count }
for m in MS:
top_m = h_probs.argsort()[-m:][::-1]
true_pos = held_out_segment_with_htags[top_m, hi].sum()
rec_denom = min(m, h_count)
results[Precision][word_dict[hi]][m] = true_pos / m
results[Recall][word_dict[hi]][m] = true_pos / rec_denom
print ("%10s\t%20s\t%6s\t" % ("Metric", "Hashtag", "Count") + "\t".join("%5d" % m for m in MS))
for htag, prec_results in results[Precision].items():
print ("%10s\t%20s\t%6d\t%s" % ("Precision", htag, prec_results[-1], "\t".join(("%0.3f" % prec_results[m] for m in MS))))
for htag, prec_results in results[Recall].items():
print ("%10s\t%20s\t%6d\t%s" % ("Recall", htag, prec_results[-1], "\t".join(("%0.3f" % prec_results[m] for m in MS))))
# Save the model
model_files = save_if_necessary(model_files, model_dir, model, data, fold, train_itrs, train_vbs, train_likes, train_tops, None, mdl)
except Exception as e:
traceback.print_exc()
print("Abandoning fold %d due to the error : %s" % (fold, str(e)))
finally:
fold += 1
return model_files
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 _sampleFromModel(self, D=200, T=100, K=10, F=12, P=8, avgWordsPerDoc = 500):
'''
Create a test dataset according to the model
Params:
T - Vocabulary size, the number of "terms". Must be a square number
K - Observed topics
P - Latent features
F - Observed features
D - Sample documents (each with associated features)
avgWordsPerDoc - average number of words per document generated (Poisson)
Returns:
modelState - a model state object configured for training
tpcs - the matrix of per-document topic distribution
vocab - the matrix of per-topic word distributions
docLens - the vector of document lengths
X - the DxF side information matrix
W - The DxW word matrix
'''
# Generate vocab
beta = 0.1
betaVec = np.ndarray((T,))
betaVec.fill(beta)
vocab = np.zeros((K,T))
for k in range(K):
vocab[k,:] = rd.dirichlet(betaVec)
# Geneate the shared covariance matrix
sigT = rd.random((K,K))
sigT = sigT.dot(sigT)
sigT.flat[::K+1] += rd.random((K,)) * 4
# Just link two topics
sigT[K//2, K//3] = 3
sigT[K//3, K//2] = 3
sigT[4 * K//5, K//5] = 4
sigT[K//5, 4 * K//5] = 4
# Generate Y, then V, then A
lfv = 0.1 # latent feature variance (for Y)
fv = 0.1 # feature variance (for A)
Y = matrix_normal(np.zeros((K,P)), lfv * np.eye(P), sigT)
V = matrix_normal(np.zeros((P,F)), fv * np.eye(F), lfv * np.eye(P))
A = matrix_normal(Y.dot(V), fv * np.eye(F), sigT)
# Generate the input features. Assume the features are multinomial and sparse
# (not quite a perfect match for the twitter example: twitter is binary, this
# may not be)
featuresDist = [1. / F] * F
maxNonZeroFeatures = 3
X = np.zeros((D,F), dtype=np.float32)
for d in range(D):
X[d,:] = rd.multinomial(maxNonZeroFeatures, featuresDist)
X = ssp.csr_matrix(X)
# Use the features and the matrix A to generate the topics and documents
tpcs = rowwise_softmax (X.dot(A.T))
docLens = rd.poisson(avgWordsPerDoc, (D,)).astype(np.float32)
W = tpcs.dot(vocab)
W *= docLens[:, np.newaxis]
W = np.array(W, dtype=np.int32) # truncate word counts to integers
W = ssp.csr_matrix(W)
# Return the initialised model, the true parameter values, and the
# generated observations
return tpcs, vocab, docLens, X, W
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))