def testInferenceFromModelDerivedExample(self):
rd.seed(0xDEADD0C5) # Global init for repeatable test
T = 100 # Vocabulary size, the number of "terms". Must be a square number
K = 6 # Topics: This cannot be changed without changing the code that generates the vocabulary
F = 8 # Features
P = 6 # Size of principle subspace
D = 200 # Sample documents (each with associated features)
avgWordsPerDoc = 500
# Generate vocab
beta = 0.01
betaVec = np.ndarray((T,))
betaVec.fill(beta)
vocab = np.zeros((K,T))
for k in range(K):
vocab[k,:] = rd.dirichlet(betaVec)
# Generate U, then V, then A
vStdev = 5.0
uStdev = 5.0
aStdev = 2.0
tau = 0.1
U = matrix_normal(np.zeros((F,P)), np.eye(P), uStdev * np.eye(F))
V = matrix_normal(np.zeros((P,K)), tau**2 * np.eye(K), vStdev**2 * np.eye(P))
A = matrix_normal (U.dot(V), tau**2 * np.eye(K), aStdev**2 * np.eye(F))
# Generate the input features. Assume the features are multinomial and sparse
# (almost matches the twitter example: twitter is binary, this may not be)
featuresDist = [1. / F] * F
maxNonZeroFeatures = 3
X = np.zeros((D,F))
for d in range(D):
X[d,:] = rd.multinomial(maxNonZeroFeatures, featuresDist)
# Use the features and the matrix A to generate the topics and documents
A = matrix_normal (U.dot(V), tau**2 * np.eye(K), aStdev**2 * np.eye(F))
tpcs = rowwise_softmax (X.dot(A))
docLens = rd.poisson(avgWordsPerDoc, (D,))
W = tpcs.dot(vocab)
W *= docLens[:, np.newaxis]
W = np.array(W, dtype=np.int32) # truncate word counts to integers
#
# Now finally try to train the model
#
modelState = newVbModelState(K, F, T, P)
(trainedState, queryState) = train (modelState, X, W, logInterval=1, iterations=1)
tpcs_inf = rowwise_softmax(queryState.lmda)
W_inf = np.array(tpcs_inf.dot(trainedState.vocab) * queryState.docLen[:,np.newaxis], dtype=np.int32)
priorReconsError = np.sum(np.abs(W - W_inf)**2) / D
(trainedState, queryState) = train (modelState, X, W, logInterval=1, iterations=200)
tpcs_inf = rowwise_softmax(queryState.lmda)
W_inf = np.array(tpcs_inf.dot(trainedState.vocab) * queryState.docLen[:,np.newaxis], dtype=np.int32)
print ("Model Driven: Prior Reconstruction Error: %f" % (priorReconsError,))
print ("Model Driven: Final Reconstruction Error: %f" % (np.sum(np.abs(W - W_inf)**2) / D,))
print("End of Test")
def _testInferenceFromHandcraftedExample(self):
rd.seed(0xC0FFEE) # Global init for repeatable test
T = 100 # Vocabulary size, the number of "terms". Must be a square number
K = 6 # Topics: This cannot be changed without changing the code that generates the vocabulary
F = 8 # Features
D = 200 # Sample documents (each with associated features)
avgWordsPerDoc = 500
# Determine what A, U and V should be by doing PCA on
# a random matrix A, then recomputing it given the decomposition
A = rd.random((F,K)) * 10
(U, S, _) = la.svd (A)
cdf = [sum(S[:f]) for f in range(1,F+1)]
P = len ([i for i in range(F) if cdf[i] > 0.75 * sum(S)])
if P == F: raise ValueError("Can't reduce the dimension")
U = U[:,:P];
V = np.ndarray((P,K))
for col in range(K):
(soln, _, _, _ ) = la.lstsq(U, A[:,col])
V[:,col] = soln
A = U.dot(V)
# The vocabulary. Presented graphically there are two with horizontal bands
# (upper lower); two with vertical bands (left, right); and two with
# horizontal bands (inside, outside)
vocab = makeSixTopicVocab(T)
# Create our (sparse) features X, then our topic proportions ("tpcs")
# then our word counts W
X = np.array([1 if rd.random() < 0.3 else 0 for _ in range(D*F)]).reshape(D,F)
# X = ssp.csr_matrix(X)
lmda = X.dot(A)
print ("lmda.mean() = %f" % (lmda.mean()))
tpcs = rowwise_softmax (lmda)
docLens = rd.poisson(avgWordsPerDoc, (D,))
W = tpcs.dot(vocab)
W *= docLens[:, np.newaxis]
W = np.array(W, dtype=np.int32) # truncate word counts to integers
#
# Now finally try to train the model
#
modelState = newVbModelState(K, F, T, P)
(trainedState, queryState) = train (modelState, X, W, logInterval=1, iterations=200)
tpcs_inf = rowwise_softmax(queryState.lmda)
W_inf = np.array(tpcs_inf.dot(trainedState.vocab) * queryState.docLen[:,np.newaxis], dtype=np.int32)
print("Handcrafted Test-Case")
print("=====================================================================")
print("Average, squared, per-element difference between true and estimated:")
print(" Topic Distribution: %f" % (np.sum((tpcs - tpcs_inf)**2) / len(tpcs),))
print(" Vocab Distribution: %f" % (np.sum((vocab - trainedState.vocab)**2) / len(vocab),))
print("Average absolute difference between true and reconstructed documents")
print(" Documents: %f" % (np.sum(np.abs(W - W_inf)) / np.sum(W),))
print("End of Test")
