def test_doc_to_array():
text = [(0,1), (1,1)]
out = lm.doc_to_array(text)
answer = np.array([0, 1])
assert same(out, answer)
doc1 = [(1,3), (2,2), (0,1)]
out = lm.doc_to_array(doc1)
answer = np.array([1, 1, 1, 2, 2, 0])
assert same(out, answer)
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_initialize_beta():
out = lm.initialize_beta(3, 4)
assert out.shape == (3,4)
sumrows = np.sum(out, axis=1)
assert same(sumrows, np.ones(out.shape[0]))
# test the log version
out = lm.initialize_log_beta(3, 4)
assert out.shape == (3,4)
sumrows = lm.logsumexp(out, axis=1)
assert same(np.exp(sumrows), np.ones(out.shape[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)
assert same(out, np.log(answer))
out = lm.calculate_EZ_from_small_log_phis(log_phi1, log_phi2)
assert same(out, np.log(answer))
def test_lda_update_gamma():
K = 3
phi = np.array([
[0.75, 0.25, 0],
[ 0.5, 0, 0.5],
[ 0.3, 0.3, 0.4],
])
alpha = np.array([0.3, 2.3, 0.8])
gamma = np.zeros((K,))
out = gamma.copy()
lm.lda_update_gamma(alpha, phi, out)
answer = alpha + np.array([1.55, 0.55, 0.9])
assert not same(out, gamma)
assert same (out, answer)
out = np.log(gamma.copy())
lm.lda_update_log_gamma(np.log(alpha), np.log(phi), out)
assert not same(np.exp(out), gamma)
assert same (np.exp(out), 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))
def test_lda_recalculate_beta():
K = 2
W = 3
doc0 = [(0,3), (1,1)]
doc1 = [(1,3), (2,2), (0,1)]
text = [doc0,doc1]
text = [doc0,doc1]
beta = np.empty((K,W), dtype=float)
out = beta.copy()
phi0 = np.zeros((sum([d[1] for d in doc0]), K))
# two to topic one (word 0)
# two to topic two (word 1)
phi0[0][0] = 1
phi0[1][0] = 1
phi0[2][1] = 1
phi0[3][1] = 1
phi1 = np.zeros((sum([d[1] for d in doc1]), K))
phi1[0][1] = 1
phi1[1][1] = 1
phi1[2][1] = 1
phi1[3][0] = 1
phi1[4][1] = 1
phi1[5][0] = 1
phi = [phi0, phi1]
answer = np.array([[0.75, 0.0, 0.25],
[1.0/6, 2.0/3, 1.0/6]])
assert out.shape == (2,3)
lm.lda_recalculate_beta(text, out, phi)
assert out.shape == (2,3)
assert not same(beta, out)
assert same(out, answer)
# now test on docarray
out = beta.copy()
assert out.shape == (2,3)
lm.lda_recalculate_beta([lm.doc_to_array(t) for t in text], out, phi)
assert out.shape == (2,3)
assert not same(beta, out)
assert same(out, answer)
# test log space
log_out = np.log(out)
log_phi = [np.log(p) for p in phi]
assert log_out.shape == (2,3)
lm.lda_recalculate_log_beta(text, log_out, log_phi)
assert log_out.shape == (2,3)
assert not same(beta, np.exp(log_out))
assert same(np.exp(log_out), answer)
def test_calculate_big_phi():
a = np.ones((2,3))
b = np.ones((6,4))
a[0, 2] = 5
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)