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)))
base = normalizerows_ip(rd.random((D,K*2)).astype(dtype))
means = base[:,:K]
expMeans = base[:,K:]
varcs = np.ones((D,K), dtype=dtype)
return QueryState(means, expMeans, varcs, docLens)
def newVbModelState(K, Q, F, P, T, featVar = 0.01, topicVar = 0.01, latFeatVar = 1, latTopicVar = 1):
'''
Creates a new model state object for a topic model based on side-information. This state
contains all parameters that o§nce trained can be kept fixed for querying.
The parameters are
K - the number of topics
Q - the number of latent topics, Q << K
F - the number of features
P - the number of latent features in the projected space, P << F
T - the number of terms in the vocabulary
topicVar - a scalar providing the isotropic covariance of the topic-space
featVar - a scalar providing the isotropic covariance of the feature-space
latFeatVar - a scalar providing the isotropic covariance of the latent feature-space
latTopicVar - a scalar providing the isotropic covariance of the latent topic-space
The returned object will contain K, Q, F, P and T and also
A - the mean of the KxF matrix mapping F features to K topics.
varA - a vector containing the variance over the F features of the distribution over A
Y - the latent space which is mixed by U and V into the observed space
omY - the row variance of the distribution over Y
sigY - the column variance of the distribution over Y
U - the KxQ transformation from the K dimensional observed topic space to the
Q-dimensional topic space
V - the FxP transformation from the F-dimensinal observed features space to the
latent P-dimensional feature-space
vocab - The K x V matrix of vocabulary distributions.
tau - the row variance of A is tau^2 I_K
sigma - the variance in the estimation of the topic memberships. lambda ~ N(A'x, sigma^2I)
'''
Y = rd.random((Q,P)).astype(DTYPE)
omY = latFeatVar * np.identity(P, DTYPE)
sigY = latTopicVar * np.identity(Q, DTYPE)
sigT = ssp.eye(K, dtype=DTYPE)
U = rd.random((K,Q)).astype(DTYPE)
V = rd.random((F,P)).astype(DTYPE)
A = U.dot(Y).dot(V.T)
varA = featVar * np.identity(F, DTYPE)
varRatio = (featVar * topicVar) / (latFeatVar * latTopicVar)
if varRatio > 1:
raise ValueError ("Model will not converge as (featVar * topicVar) / (latFeatVar * latTopicVar)) = " + str(varRatio) + " when it needs to be no more than one.")
# Vocab is K word distributions so normalize
vocab = normalizerows_ip (rd.random((K, T)).astype(DTYPE)) + sys.float_info.epsilon
return VbSideTopicModelState(K, Q, F, P, T, A, varA, Y, omY, sigY, sigT, U, V, vocab, topicVar, featVar, latTopicVar, latFeatVar)
def newVbModelState(K, F, T, P):
'''
Creates a new model state object for a topic model based on side-information. This state
contains all parameters that once trained can be kept fixed for querying.
The parameters are
K - the number of topics
F - the number of features
P - the number of features in the projected space, P << F
T - the number of terms in the vocabulary
The returned object will contain K, F, V and P and also
A - the mean of the F x K matrix mapping F features to K topics
varA - the column variance of the distribution over A
tau - the row variance of A is tau^2 I_K
V - the mean of the P x K matrix mapping P projected features to K topics
varV - the column variance of the distribution over V (the row variance is again
tau^2 I_K
U - the F x P projection matrix, such that A = UV
sigma - the variance in the estimation of the topic memberships lambda ~ N(A'x, sigma^2I)
vocab - The K x V matrix of vocabulary distributions.
'''
V = rd.random((P, K))
varV = np.identity(P, np.float64)
U = rd.random((F, P))
A = U.dot(V)
varA = np.identity(F, np.float64)
tau = 0.1
sigma = 0.1
# Vocab is K word distributions so normalize
vocab = normalizerows_ip (rd.random((K, T)))
return VbSideTopicModelState(K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab)
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(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.
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, _, 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
queryPlan = newInferencePlan(1, epsilon, logFrequency = 0, plot=False)
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)
print ("Training %d topic model with %d x %d word-matrix W, %d x %d feature matrix X, and latent feature and topics spaces of size %d and %d respectively" % (K, D, T, D, F, P, Q))
# No need to recompute this every time
XTX = X.T.dot(X)
# Identity matrices that occur
I_P = ssp.eye(P, dtype=DTYPE)
I_Q = ssp.eye(Q, dtype=DTYPE)
I_QP = ssp.eye(Q*P,Q*P, dtype=DTYPE)
# 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
overSsq = 1. / sigmaSq
overAsq = 1. / alphaSq
overKsq = 1. / kappaSq
overTsq = 1. / tauSq
varRatio = (alphaSq * sigmaSq) / (tauSq * kappaSq)
# 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)
print ("Inverting gram matrix")
aI_XTX = (overAsq * ssp.eye(F, dtype=DTYPE) + XTX).todense()
omA = la.inv (aI_XTX)
scaledWordCounts = W.copy()
# Set up a method to check at every update if we're going in the right
# direction
verify_and_log = _quickPrintElbo if DEBUG else _doNothing
print ("Launching inference")
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(overTsq * overKsq * I_Q + overAsq * overSsq * UTU)
verify_and_log ("E-Step: q(Y) [sigY]", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, expLmda, nu, lxi, s, docLen)
omY = la.inv(overTsq * overKsq * I_P + overAsq * overSsq * VTV)
verify_and_log ("E-Step: q(Y) [omY]", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, expLmda, nu, lxi, s, docLen)
try:
invUTU = la.inv(UTU)
Y = la.solve_sylvester (varRatio * invUTU, VTV, invUTU.dot(U.T).dot(A).dot(V))
except np.linalg.linalg.LinAlgError as e: # U'U seems to rapidly become singular (before 5 iters)
if fastButInaccurate:
invUTU = la.pinvh(UTU) # Obviously unstable, inference stalls much earlier than the correct form
Y = la.solve_sylvester (varRatio * invUTU, VTV, invUTU.dot(U.T).dot(A).dot(V))
else:
Y = np.reshape (la.solve(varRatio * I_QP + np.kron(VTV, UTU), vec(U.T.dot(A).dot(V))), (Q,P), 'F')
verify_and_log ("E-Step: q(Y) [Mean]", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, 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
#
lmda = np.log(expLmda, out=expLmda)
A = omA.dot(X.T.dot(lmda) + overAsq * V.dot(Y.T).dot(U.T)).T
# A = la.solve(aI_XTX, X.T.dot(lmda) + overAsq * V.dot(Y.T).dot(U.T)).T
np.exp(expLmda, out=expLmda)
verify_and_log ("E-Step: q(A)", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, 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, sigmaSq, alphaSq, kappaSq, tauSq), \
# X, W, \
# queryPlan, \
# VbSideTopicQueryState(expLmda, nu, lxi, s, docLen), \
# scaledWordCounts=scaledWordCounts, \
# XAT = XAT)
# =============================================================
# 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
# =============================================================
# vocab
#
sparseScalarQuotientOfDot(W, expLmda, vocab, out=scaledWordCounts)
factor = (scaledWordCounts.T.dot(expLmda)).T # Gets materialized as a dense matrix...
vocab *= factor
normalizerows_ip(vocab)
# A hack to work around the fact that we've got no prior, and thus no
# pseudo counts, so some values will collapse to zero
# vocab[vocab < sys.float_info.min] = sys.float_info.min
verify_and_log ("M-Step: vocab", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, expLmda, nu, lxi, s, docLen)
# U
#
U = A.dot(V).dot(Y.T).dot (la.inv(Y.dot(V.T).dot(V).dot(Y.T) + np.trace(omY.dot(V.T).dot(V)) * sigY))
verify_and_log ("M-Step: U", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, expLmda, nu, lxi, s, docLen)
# V
#
V = A.T.dot(U).dot(Y).dot (la.inv(Y.T.dot(U.T).dot(U).dot(Y) + np.trace(sigY.dot(U.T).dot(U)) * omY))
verify_and_log ("M-Step: V", iteration, X, W, K, Q, F, P, T, A, omA, Y, omY, sigY, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq, None, 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 ("\nIteration %5d ELBO %15f Log-Likelihood %15f" % (iteration, elbo, likely))
logIter = min (np.ceil(logIter * multiStepSize), iterations - 1)
if elbo < lastVarBoundValue:
sys.stderr.write('ELBO going in the wrong direction\n')
elif abs(elbo - lastVarBoundValue) < epsilon:
break
lastVarBoundValue = elbo
if plot and plotIncremental:
plot_bound(plotFile + "-iter-" + str(iteration), np.array(iters), np.array(elbos), np.array(likes))
else:
print('.', end='')
sys.stdout.flush()
# Right before we end, plot the evoluation 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, sigT, U, V, vocab, sigmaSq, alphaSq, kappaSq, tauSq), \
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, 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. / tv, 1. / fv, 1. / ltv, 1. / lfv # turn variances into precisions
# FIXME Use passed in hypers
print("tp = %f tv=%f" % (tp, tv))
vocabPrior = np.ones(shape=(T, ), dtype=modelState.dtype)
# FIXME undo truncation
F = 363
A = A[:F, :]
X = X[:, :F]
U = U[:F, :]
data = DataSet(words=W, feats=X)
# Book-keeping for logs
boundIters, boundValues, likelyValues = [], [], []
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Initialize some working variables
if covA is None:
precA = (fp * ssp.eye(F) +
X.T.dot(X)).todense() # As the inverse is almost always dense
covA = la.inv(precA,
overwrite_a=True) # it's faster to densify in advance
uniqLens = np.unique(docLens)
debugFn(-1, covA, "covA", W, X, means, docLens, K, A, U, Y, V, covA, tv,
ltv, fv, lfv, vocab, vocabPrior)
H = 0.5 * (np.eye(K) - np.ones((K, K), dtype=dtype) / K)
expMeans = means.copy()
expMeans = np.exp(means - means.max(axis=1)[:, np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=W.copy())
lhs = H.copy()
rhs = expMeans.copy()
Y_rhs = Y.copy()
# Iterate over parameters
for itr in range(iterations):
# Update U, V given A
V = try_solve_sym_pos(Y.T.dot(U.T).dot(U).dot(Y),
A.T.dot(U).dot(Y).T).T
V /= V[0, 0]
U = try_solve_sym_pos(Y.dot(V.T).dot(V).dot(Y.T),
A.dot(V).dot(Y.T).T).T
# Update Y given U, V, A
Y_rhs[:, :] = U.T.dot(A).dot(V)
Sv, Uv = la.eigh(V.T.dot(V), overwrite_a=True)
Su, Uu = la.eigh(U.T.dot(U), overwrite_a=True)
s = np.outer(Sv, Su).flatten()
s += ltv * lfv
np.reciprocal(s, out=s)
M = Uu.T.dot(Y_rhs).dot(Uv)
M *= unvec(s, row_count=M.shape[0])
Y = Uu.dot(M).dot(Uv.T)
debugFn(itr, Y, "Y", W, X, means, docLens, K, A, U, Y, V, covA, tv,
ltv, fv, lfv, vocab, vocabPrior)
A = covA.dot(fp * U.dot(Y).dot(V.T) + X.T.dot(means))
debugFn(itr, A, "A", W, X, means, docLens, K, A, U, Y, V, covA, tv,
ltv, fv, lfv, vocab, vocabPrior)
# And now this is the E-Step, though itr's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# TODO One big sort by size, plus batch it.
# Update the Means
rhs[:, :] = expMeans
rhs *= R.dot(vocab.T)
rhs += X.dot(A) * tp
rhs += docLens[:, np.newaxis] * means.dot(H)
rhs -= docLens[:, np.newaxis] * rowwise_softmax(means, out=means)
for l in uniqLens:
inds = np.where(docLens == l)[0]
lhs[:, :] = l * H
lhs[np.diag_indices_from(lhs)] += tp
lhs[:, :] = la.inv(lhs)
means[inds, :] = rhs[inds, :].dot(
lhs
) # left and right got switched going from vectors to matrices :-/
debugFn(itr, means, "means", W, X, means, docLens, K, A, U, Y, V, covA,
tv, ltv, fv, lfv, vocab, vocabPrior)
# Standard deviation
# DK = means.shape[0] * means.shape[1]
# newTp = np.sum(means)
# newTp = (-newTp * newTp)
# rhs[:,:] = means
# rhs *= means
# newTp = DK * np.sum(rhs) - newTp
# newTp /= DK * (DK - 1)
# newTp = min(max(newTp, 1E-36), 1E+36)
# tp = 1 / newTp
# if itr % logFrequency == 0:
# print ("Iter %3d stdev = %f, prec = %f, np.std^2=%f, np.mean=%f" % (itr, sqrt(newTp), tp, np.std(means.reshape((D*K,))) ** 2, np.mean(means.reshape((D*K,)))))
# Update the vocabulary
expMeans = np.exp(means - means.max(axis=1)[:, np.newaxis],
out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
vocab *= (
R.T.dot(expMeans)
).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += vocabPrior
vocab = normalizerows_ip(vocab)
debugFn(itr, vocab, "vocab", W, X, means, docLens, K, A, U, Y, V, covA,
tv, ltv, fv, lfv, vocab, vocabPrior)
# print ("Iter %3d Vocab.min = %f" % (itr, vocab.min()))
# Update the vocab prior
# vocabPrior = estimate_dirichlet_param (vocab, vocabPrior)
# print ("Iter %3d VocabPrior.(min, max) = (%f, %f) VocabPrior.mean=%f" % (itr, vocabPrior.min(), vocabPrior.max(), vocabPrior.mean()))
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(K, A, U, Y, V, covA, tv, ltv, fv, lfv,
vocab, vocabPrior, dtype, modelState.name)
queryState = QueryState(means, docLens)
boundValues.append(var_bound(data, modelState, queryState))
likelyValues.append(log_likelihood(data, modelState, queryState))
boundIters.append(itr)
print(
time.strftime('%X') +
" : Iteration %d: bound %f \t Perplexity: %.2f" %
(itr, boundValues[-1],
perplexity_from_like(likelyValues[-1], docLens.sum())))
if len(boundValues) > 1:
if boundValues[-2] > boundValues[-1]:
if debug:
printStderr("ERROR: bound degradation: %f > %f" %
(boundValues[-2], boundValues[-1]))
# Check to see if the improvement in the bound has fallen below the threshold
if itr > 100 and len(likelyValues) > 3 \
and abs(perplexity_from_like(likelyValues[-1], docLens.sum()) - perplexity_from_like(likelyValues[-2], docLens.sum())) < 1.0:
break
return \
ModelState(K, A, U, Y, V, covA, tv, ltv, fv, lfv, vocab, vocabPrior, dtype, modelState.name), \
QueryState(means, expMeans, docLens), \
(np.array(boundIters), np.array(boundValues), np.array(likelyValues))
def train (data, modelState, queryState, trainPlan):
'''
Infers the topic distributions in general, and specifically for
each individual datapoint.
Params:
data - the dataset of words, features and links of which only words and
features are used in this model
modelState - the actual CTM model
queryState - the query results - essentially all the "local" variables
matched to the given observations
trainPlan - how to execute the training process (e.g. iterations,
log-interval etc.)
Return:
A new model object with the updated model (note parameters are
updated in place, so make a defensive copy if you want it)
A new query object with the update query parameters
'''
W, X = data.words, data.feats
assert W.dtype == modelState.dtype
assert X.dtype == modelState.dtype
D,_ = W.shape
# Unpack the the structs, for ease of access and efficiency
iterations, epsilon, logFrequency, fastButInaccurate, debug = trainPlan.iterations, trainPlan.epsilon, trainPlan.logFrequency, trainPlan.fastButInaccurate, trainPlan.debug
means, expMeans, varcs, lxi, s, n = queryState.means, queryState.expMeans, queryState.varcs, queryState.lxi, queryState.s, queryState.docLens
F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype = modelState.F, modelState.P, modelState.K, modelState.A, modelState.R_A, modelState.fv, modelState.Y, modelState.R_Y, modelState.lfv, modelState.V, modelState.sigT, modelState.vocab, modelState.vocabPrior, modelState.dtype
# Book-keeping for logs
boundIters = np.zeros(shape=(iterations // logFrequency,))
boundValues = np.zeros(shape=(iterations // logFrequency,))
likeValues = np.zeros(shape=(iterations // logFrequency,))
bvIdx = 0
_debug_with_bound.old_bound = 0
debugFn = _debug_with_bound if debug else _debug_with_nothing
# Initialize some working variables
isigT = la.inv(sigT)
R = W.copy()
sigT_regularizer = 0.001
aI_P = 1./lfv * ssp.eye(P, dtype=dtype)
tI_F = 1./fv * ssp.eye(F, dtype=dtype)
print("Creating posterior covariance of A, this will take some time...")
XTX = X.T.dot(X)
R_A = XTX
if ssp.issparse(R_A):
R_A = R_A.todense() # dense inverse typically as fast or faster than sparse inverse
R_A.flat[::F+1] += 1./fv # and the result is usually dense in any case
R_A = la.inv(R_A)
print("Covariance matrix calculated, launching inference")
s.fill(0)
# Iterate over parameters
for itr in range(iterations):
# We start with the M-Step, so the parameters are consistent with our
# initialisation of the RVs when we do the E-Step
# Update the covariance of the prior
diff_a_yv = (A-Y.dot(V))
diff_m_xa = (means-X.dot(A.T))
sigT = 1./lfv * (Y.dot(Y.T))
sigT += 1./fv * diff_a_yv.dot(diff_a_yv.T)
sigT += diff_m_xa.T.dot(diff_m_xa)
sigT.flat[::K+1] += varcs.sum(axis=0)
sigT /= (P+F+D)
sigT.flat[::K+1] += sigT_regularizer
# Diagonalize it
sigT = np.diag(sigT.flat[::K+1])
# and invert it.
isigT = np.diag(np.reciprocal(sigT.flat[::K+1]))
debugFn (itr, sigT, "sigT", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Building Blocks - temporarily replaces means with exp(means)
expMeans = np.exp(means - means.max(axis=1)[:,np.newaxis], out=expMeans)
R = sparseScalarQuotientOfDot(W, expMeans, vocab, out=R)
S = expMeans * R.dot(vocab.T)
# Update the vocabulary
vocab *= (R.T.dot(expMeans)).T # Awkward order to maintain sparsity (R is sparse, expMeans is dense)
vocab += vocabPrior
vocab = normalizerows_ip(vocab)
# Reset the means to their original form, and log effect of vocab update
debugFn (itr, vocab, "vocab", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Finally update the parameter V
V = la.inv(R_Y + Y.T.dot(isigT).dot(Y)).dot(Y.T.dot(isigT).dot(A))
debugFn (itr, V, "V", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# And now this is the E-Step, though it's followed by updates for the
# parameters also that handle the log-sum-exp approximation.
# Update the distribution on the latent space
R_Y_base = aI_P + 1/fv * V.dot(V.T)
R_Y = la.inv(R_Y_base)
debugFn (itr, R_Y, "R_Y", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
Y = 1./fv * A.dot(V.T).dot(R_Y)
debugFn (itr, Y, "Y", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the mapping from the features to topics
A = (1./fv * (Y).dot(V) + (X.T.dot(means)).T).dot(R_A)
debugFn (itr, A, "A", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Means
vMat = (s[:,np.newaxis] * lxi - 0.5) * n[:,np.newaxis] + S
rhsMat = vMat + X.dot(A.T).dot(isigT) # TODO Verify this
lhsMat = np.reciprocal(np.diag(isigT)[np.newaxis,:] + n[:,np.newaxis] * lxi) # inverse of D diagonal matrices...
means = lhsMat * rhsMat # as LHS is a diagonal matrix for all d, it's equivalent
# do doing a hadamard product for all d
debugFn (itr, means, "means", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the Variances
varcs = 1./(n[:,np.newaxis] * lxi + isigT.flat[::K+1])
debugFn (itr, varcs, "varcs", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# Update the approximation parameters
lxi = 2 * ctm.negJakkolaOfDerivedXi(means, varcs, s)
debugFn (itr, lxi, "lxi", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
# s can sometimes grow unboundedly
# Follow Bouchard's suggested approach of fixing it at zero
#
# s = (np.sum(lxi * means, axis=1) + 0.25 * K - 0.5) / np.sum(lxi, axis=1)
# debugFn (itr, s, "s", W, X, XTX, F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, means, varcs, lxi, s, n)
if logFrequency > 0 and itr % logFrequency == 0:
modelState = ModelState(F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, MODEL_NAME)
queryState = QueryState(means, expMeans, varcs, lxi, s, n)
boundValues[bvIdx] = var_bound(data, modelState, queryState, XTX)
likeValues[bvIdx] = log_likelihood(data, modelState, queryState)
boundIters[bvIdx] = itr
perp = perplexity_from_like(likeValues[bvIdx], n.sum())
print (time.strftime('%X') + " : Iteration %d: Perplexity %4.2f bound %f" % (itr, perp, boundValues[bvIdx]))
if bvIdx > 0 and boundValues[bvIdx - 1] > boundValues[bvIdx]:
printStderr ("ERROR: bound degradation: %f > %f" % (boundValues[bvIdx - 1], boundValues[bvIdx]))
# print ("Means: min=%f, avg=%f, max=%f\n\n" % (means.min(), means.mean(), means.max()))
# Check to see if the improvment in the likelihood has fallen below the threshold
if bvIdx > 1 and boundIters[bvIdx] > 50:
lastPerp = perplexity_from_like(likeValues[bvIdx - 1], n.sum())
if lastPerp - perp < 1:
boundIters, boundValues, likelyValues = clamp (boundIters, boundValues, likeValues, bvIdx)
return modelState, queryState, (boundIters, boundValues, likeValues)
bvIdx += 1
return \
ModelState(F, P, K, A, R_A, fv, Y, R_Y, lfv, V, sigT, vocab, vocabPrior, dtype, MODEL_NAME), \
QueryState(means, expMeans, varcs, lxi, s, n), \
(boundIters, boundValues, likeValues)
def train(modelState, X, W, iterations=10000, epsilon=0.001, logInterval = 0):
'''
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.
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, F, T, P, A, varA, V, varV, U, sigma, tau, vocab) = (modelState.K, modelState.F, modelState.T, modelState.P, modelState.A, modelState.varA, modelState.V, modelState.varV, modelState.U, modelState.sigma, modelState.tau, modelState.vocab)
# Get ready to plot the evolution of the likelihood
if logInterval > 0:
elbos = np.zeros((iterations / logInterval,))
iters = np.zeros((iterations / logInterval,))
# We'll need the total word count per doc, and total count of docs
docLen = W.sum(axis=1)
D = len(docLen)
# No need to recompute this every time
XTX = X.T.dot(X)
# Assign initial values to the query parameters
lmda = rd.random((D, K))
nu = np.ones((D,K), np.float64)
s = np.zeros((D,))
lxi = negJakkola (np.ones((D, K), np.float64))
XA = X.dot(A)
for iteration in range(iterations):
# Save repeated computation
tsq = tau * tau;
tsqIP = tsq * np.eye(P)
trTsqIK = K * tsq # trace of the matrix tau * tau * np.eye(K)
halfSig2 = 1./(sigma*sigma)
tau2sig2 = (tau * tau) / (sigma * sigma)
# =============================================================
# E-Step
# Model dists are q(Theta|A;Lambda;nu) q(A|V) q(V)
# Where lambda is the posterior mean of theta.
# =============================================================
#
# V, varV
varV = la.inv (tsqIP + U.T.dot(U))
V = varV.dot(U.T).dot(A)
_quickPrintElbo ("E-Step: q(V)", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# A, varA
# TODO, since only tau2sig2 changes at each step, would it be possible just to
# amend the old inverse?
# TODO Use sparse inverse
varA = la.inv (tau2sig2 * XTX + np.eye(F))
A = varA.dot (U.dot(V) + X.T.dot(lmda))
XA = X.dot(A)
_quickPrintElbo ("E-Step: q(A|V)", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# lmda_dk
lnVocab = safe_log (vocab)
Z = rowwise_softmax (lmda[:,:,np.newaxis] + lnVocab[np.newaxis,:,:]) # Z is DxKxT
rho = 2 * s[:,np.newaxis] * lxi - 0.5 \
+ np.einsum('dt,dkt->dk', W, Z) / docLen[:,np.newaxis]
rhs = docLen[:,np.newaxis] * rho + halfSig2 * X.dot(A)
lmda = rhs / (docLen[:,np.newaxis] * 2 * lxi + halfSig2)
_quickPrintElbo ("E-Step: q(Theta|A;lamda)", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# nu_dk
# TODO Double check this again...
nu = 1./ np.sqrt(2. * docLen[:, np.newaxis] * lxi + halfSig2)
_quickPrintElbo ("E-Step: q(Theta|A;nu)", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
# =============================================================
# M-Step
# Parameters for the softmax bound: lxi and s
# The projection used for A: U
# The vocabulary : vocab
# The variances: tau, sigma
# =============================================================
#
# s_d
# s = (K/4. + (lxi * lmda).sum(axis = 1)) / lxi.sum(axis=1)
# _quickPrintElbo ("M-Step: max s", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# xi_dk
lxi = negJakkolaOfDerivedXi(lmda, nu, s)
_quickPrintElbo ("M-Step: max xi", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# vocab
#
# TODO, since vocab is in the RHS, is there any way to optimize this?
Z = rowwise_softmax (lmda[:,:,np.newaxis] + lnVocab[np.newaxis,:,:]) # Z is DxKxV
vocab = normalizerows_ip (np.einsum('dt,dkt->kt', W, Z))
_quickPrintElbo ("M-Step: max vocab", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# U
U = A.dot(V.T).dot (la.inv(trTsqIK * varV + V.dot(V.T)))
_quickPrintElbo ("M-Step: max U", iteration, X, W, K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab, lmda, nu, lxi, s, docLen)
#
# sigma
# Equivalent to \frac{1}{DK} \left( \sum_d (\sum_k nu_{dk}) + tr(\Omega_A) x_d^{T} \Sigma_A x_d + (\lambda - A^{T} x_d)^{T}(\lambda - A^{T} x_d) \right)
#
# sigma = 1./(D*K) * (np.sum(nu) + D*K * tsq * np.sum(XTX * varA) + np.sum((lmda - XA)**2))
#
# tau
# Equivalent to \frac{1}{KF} \left( tr(\Sigma_A)tr(\Omega_A) + tr(\Sigma_V U U^{T})tr(\Omega_V) + tr ((M_A - U M_V)^{T} (M_A - U M_V)) \right)
#
varA_U = varA.dot(U)
# tau_term1 = np.trace(varA)*K*tsq
# tau_term2 = sum(varA_U[p,:].dot(U[p,:]) for p in xrange(P)) * K * tsq
# tau_term3 = np.sum((A - U.dot(V)) ** 2)
#
# tau = 1./(K*F) * (tau_term1 + tau_term2 + tau_term3)
if (logInterval > 0) and (iteration % logInterval == 0):
elbo = varBound ( \
VbSideTopicModelState (K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab), \
VbSideTopicQueryState(lmda, nu, lxi, s, docLen),
X, W, Z, lnVocab, varA_U, XA, XTX)
elbos[iteration / logInterval] = elbo
iters[iteration / logInterval] = iteration
print ("Iteration %5d ELBO %f" % (iteration, elbo))
if logInterval > 0:
plot_bound(iters, elbos)
return (VbSideTopicModelState (K, F, T, P, A, varA, V, varV, U, sigma, tau, vocab), \
VbSideTopicQueryState (lmda, nu, lxi, s, docLen))
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, logFrequency=1)
self.assertTrue(0.99 < np.sum(model.topicMean) < 1.01)
return self._doTest(W, model, queryState, trainPlan)
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, boundValues, boundLikes = [], [], []
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
leastSquares = lambda feats, targets: la.lstsq(
feats, targets, lapack_driver="gelsy")[0].T
if ssp.issparse(
R_A): # dense inverse typically as fast or faster than sparse
R_A = to_dense_array(
R_A) # inverse and the result is usually dense in any case
leastSquares = lambda feats, targets: np.array(
[ssp.linalg.lsqr(feats, targets[:, k])[0] for k in range(K)])
R_A.flat[::F + 1] += 1. / fv
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):
A = leastSquares(X, means)
diff_a_yv = (A - Y.dot(V))
for _ in range(10): #(50 if itr == 0 else 1):
# Update the covariance of the prior
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)
# 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)
# 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)
# 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)
expMeans = np.exp(means - means.max(axis=1)[:, np.newaxis],
out=expMeans)
# for _ in range(150):
# # 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)
#
# # 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)
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.append(
var_bound(DataSet(W, feats=X), modelState, queryState, XTX))
boundLikes.append(
log_likelihood(DataSet(W, feats=X), modelState, queryState))
boundIters.append(itr)
perp = perplexity_from_like(boundLikes[-1], docLens.sum())
print(
time.strftime('%X') +
" : Iteration %d: Perplexity %4.0f bound %f" %
(itr, perp, boundValues[-1]))
if len(boundIters) >= 2 and boundValues[-2] > boundValues[-1]:
printStderr("ERROR: bound degradation: %f > %f" %
(boundValues[-2], boundValues[-1]))
# 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 len(boundIters) > 2 and boundIters[-1] > 20:
lastPerp = perplexity_from_like(boundLikes[-2], docLens.sum())
if lastPerp - perp < 1:
break
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 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(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))