def lda_recalculate_beta(text, beta, phi):
"""
update topics: βk,wnew ∝ ΣdΣn 1(wd,n = w) φkd,n
Accepts beta matrix (KxW) and
phi, a D-length list of (N x K) matrices.
"""
(K,W) = beta.shape
D = len(phi)
beta[:,:] = np.zeros(beta.shape)
if isinstance(text[0], np.ndarray):
for d in xrange(D):
ensure(phi[d].shape[1] == K)
for n,word in enumerate(text[d]):
beta[:,word] += phi[d][n,:]
#words, indexes = text[d], np.array(range(len(text[d])))
#beta[:,words] += phi[d][indexes,:].T
else:
for d in xrange(D):
ensure(phi[d].shape[1] == K)
for n,word,count in iterwords(text[d]):
beta[:,word] += phi[d][n,:]
graphlib.row_normalize(beta)
return beta
def test_row_normalize():
t = np.ones((3,4))
out = graphlib.row_normalize(t)
answer = np.ones(t.shape) * 0.25
assert same(out, answer)
a = np.array([[ 0.75 , 0. , 0.25 ],
[ 0.16666667, 0.66666667, 0.16666667]])
graphlib.row_normalize(a)
assert a.shape == (2, 3)
def test_slda_update_phi():
gamma = np.array([3,4,5])
text = [(0,1), (1,1)]
beta = np.array([
[0.75, 0.25],
[0.40, 0.60],
[0.10, 0.90],
])
y_d = -0.5
eta = np.array([-2.5, 1.6, 0.1])
sigma_squared = 0.8
phi = np.array([
[0.65, 0.25, 0.10],
[0.09, 0.78, 0.13],
])
"""
update phid:
φd,n ∝ exp{ E[log θ|γ] +
E[log p(wn|β1:K)] +
(y / Nσ2) η —
[2(ηTφd,-n)η + (η∘η)] / (2N2σ2) }
Note that E[log p(wn|β1:K)] = log βTwn
"""
eta_dot_eta = np.array([6.25, 2.56, 0.01])
term1 = np.array([-1.51987734, -1.18654401154, -0.93654401154401])
term2 = np.log(np.array([0.75, 0.40, 0.10]))
term3 = np.array([0.78125, -0.5, -0.03125])
term4 = -0.15625 * ((2 * (np.dot(eta, phi[1])) * eta) + eta_dot_eta)
first_row = np.exp(term1 + term2 + term3 + term4)
first_row /= np.sum(first_row) # normalize it, then set
# note that this happens in sequential order, so must use first row, not old phi[0]
term2 = np.log(np.array([0.25, 0.60, 0.90]))
term4 = -0.15625 * ((2 * (np.dot(eta, first_row)) * eta) + eta_dot_eta)
second_row = np.exp(term1 + term2 + term3 + term4)
answer = np.array([first_row, second_row])
graphlib.row_normalize(answer)
out = phi.copy()
lm.slda_update_phi(text, out, gamma, beta, y_d, eta, sigma_squared)
assert same(out, answer)
# test the fast updates; which will be slightly different
fast_answer = answer.copy()
fast_answer[1,:] = np.array([0.03422278, 0.26873478, 0.69704244])
out = phi.copy()
docarray = lm.doc_to_array([(0,1), (1,1)])
lm.slda_update_phi(docarray, out, gamma, beta, y_d, eta, sigma_squared)
assert same(out, fast_answer)
def test_calculate_EZZT():
big_phi = lm.calculate_big_phi(phi1[0], phi2[0])
out = lm.calculate_EZZT(big_phi)
e = 8.0 / 9.0
t = 2.0 / 9.0
h = 3.0 / 2.0
answer = (1.0 / 25) * np.array([
[e, t, t, 1, 1],
[t, e, t, 1, 1],
[t, t, e, 1, 1],
[1, 1, 1, 3, h],
[1, 1, 1, h, 3],
])
assert same(out, answer)
out = lm.calculate_EZZT_from_small_phis(phi1[0], phi2[0])
assert same(out, answer)
# try it on logs
out = lm.calculate_EZZT_from_small_log_phis(log_phi1, log_phi2)
assert same(out, np.log(answer))
# now try a harder random matrix
r1 = answer.copy()
r1[0,0] = 5
r1[1,1] = 9
r1 = graphlib.row_normalize(r1)
r2 = r1.copy()
r1[1,1] = 2
r1[1,0] = 1
r1 = graphlib.row_normalize(r1)
big_phi = lm.calculate_big_phi(r1, r2)
answer = lm.calculate_EZZT(big_phi)
out = lm.calculate_EZZT_from_small_phis(r1, r2)
assert same(out, answer)
# test out same anwer on logs
out = lm.calculate_EZZT_from_small_log_phis(np.log(r1), np.log(r2))
assert same(out, np.log(answer))
b[4,1] = 8
out = lm.calculate_big_phi(a, b)
answer = np.array([
[1, 1, 5, 0, 0, 0, 0,],
[1, 1, 1, 0, 0, 0, 0,],
[0, 0, 0, 1, 1, 1, 1,],
[0, 0, 0, 1, 1, 1, 1,],
[0, 0, 0, 1, 1, 1, 1,],
[0, 0, 0, 1, 1, 1, 1,],
[0, 0, 0, 1, 8, 1, 1,],
[0, 0, 0, 1, 1, 1, 1,],
])
assert same(out, answer)
phi1 = [graphlib.row_normalize(np.ones((2,3))), ]
phi2 = [graphlib.row_normalize(np.ones((3,2))), ]
log_phi1, log_phi2 = np.log(phi1[0]), np.log(phi2[0])
def test_calculate_EZ():
big_phi = lm.calculate_big_phi(phi1[0], phi2[0])
out = lm.calculate_EZ(big_phi)
answer = (1.0 / 25) * np.array([30.0/9, 30.0/9, 30.0/9, 7.5, 7.5])
assert same(out, answer)
out = lm.calculate_EZ_from_small_phis(phi1[0], phi2[0])
assert same(out, answer)
# now test log phis
big_log_phi = lm.calculate_big_log_phi(log_phi1, log_phi2)
out = lm.calculate_EZ_from_big_log_phi(big_log_phi)