def test_compute_statistics():
R = numpy.array([[1, 2], [3, 4]], dtype=float)
M = numpy.array([[1, 1], [0, 1]])
I, J, K = 2, 2, 3
lambdaU = 2 * numpy.ones((I, K))
lambdaV = 3 * numpy.ones((J, K))
alphatau, betatau = 3, 1
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_vb(R, M, K, False, hyperparams)
R_pred = numpy.array([[500, 550], [1220, 1342]], dtype=float)
M_pred = numpy.array([[0, 0], [1, 1]])
MSE_pred = (1217**2 + 1338**2) / 2.0
R2_pred = 1. - (1217**2 + 1338**2) / (0.5**2 + 0.5**2) #mean=3.5
Rp_pred = 61. / (math.sqrt(.5) * math.sqrt(7442.)
) #mean=3.5,var=0.5,mean_pred=1281,var_pred=7442,cov=61
assert MSE_pred == BNMF.compute_MSE(M_pred, R, R_pred)
assert R2_pred == BNMF.compute_R2(M_pred, R, R_pred)
assert Rp_pred == BNMF.compute_Rp(M_pred, R, R_pred)
def test_log_likelihood():
R = numpy.array([[1, 2], [3, 4]], dtype=float)
M = numpy.array([[1, 1], [0, 1]])
I, J, K = 2, 2, 3
lambdaU = 2 * numpy.ones((I, K))
lambdaV = 3 * numpy.ones((J, K))
alphatau, betatau = 3, 1
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.exp_U = numpy.ones((I, K))
BNMF.exp_V = 2 * numpy.ones((J, K))
BNMF.exp_logtau = 5.
BNMF.exp_tau = 3.
# expU*expV.T = [[6.]]
log_likelihood = 3. / 2. * (5. - math.log(2 * math.pi)) - 3. / 2. * (
5**2 + 4**2 + 2**2)
AIC = -2 * log_likelihood + 2 * (2 * 3 + 2 * 3 + 1)
BIC = -2 * log_likelihood + (2 * 3 + 2 * 3 + 1) * math.log(3)
MSE = (5**2 + 4**2 + 2**2) / 3.
assert log_likelihood == BNMF.quality('loglikelihood')
assert AIC == BNMF.quality('AIC')
assert BIC == BNMF.quality('BIC')
assert MSE == BNMF.quality('MSE')
with pytest.raises(AssertionError) as error:
BNMF.quality('FAIL')
assert str(error.value) == "Unrecognised metric for model quality: FAIL."
def test_update_exp_lambdak():
BNMF = bnmf_vb(R, M, K, True, hyperparams)
BNMF.initialise(init_UV='exp')
for k in range(K):
assert abs(BNMF.exp_lambdak[k] - (alpha0 + I + J) /
(beta0 + (I + J) * beta0 / float(alpha0))) < 0.000000000001
assert BNMF.exp_loglambdak[k] == 1.0129704878718551
def test_update_exp_tau():
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.initialise()
assert abs(BNMF.exp_tau - (3 + 12. / 2.) /
(1 + 35.4113198623 / 2.)) < 0.000000000001
assert abs(BNMF.exp_logtau -
(2.1406414779556 -
math.log(1 + 35.4113198623 / 2.))) < 0.000000000001
def test_update_lambdak():
BNMF = bnmf_vb(R, M, K, True, hyperparams)
BNMF.alphak_s, BNMF.betak_s = numpy.zeros(K), numpy.zeros(K)
BNMF.exp_U, BNMF.exp_V = 1. / lambdaU, 1. / lambdaV # [[1./2.]], [[1./3.]]
for k in range(K):
BNMF.update_lambdak(k)
assert BNMF.alphak_s[k] == alpha0 + I + J
assert BNMF.betak_s[k] == (beta0 + I * 1. / 2. + J * 1. / 3.)
def test_update_tau():
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.exp_U = 1. / lambdaU #[[1./2.]]
BNMF.exp_V = 1. / lambdaV #[[1./3.]]
BNMF.var_U = numpy.ones((I, K)) * 2 #[[2.]]
BNMF.var_V = numpy.ones((J, K)) * 3 #[[3.]]
BNMF.update_tau()
assert BNMF.alpha_s == alphatau + 12. / 2.
assert BNMF.beta_s == betatau + 172.66666666666666 / 2.
def test_exp_square_diff():
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.exp_U = 1. / lambdaU #[[1./2.]]
BNMF.exp_V = 1. / lambdaV #[[1./3.]]
BNMF.var_U = numpy.ones((I, K)) * 2 #[[2.]]
BNMF.var_V = numpy.ones((J, K)) * 3 #[[3.]]
# expU * expV.T = [[1./3.]]. (varU+expU^2)=2.25, (varV+expV^2)=3.+1./9.
exp_square_diff = 172.66666666666666 #12.*(4./9.) + 12.*(2*(2.25*(3.+1./9.)-0.25/9.))
assert BNMF.exp_square_diff() == exp_square_diff
def test_update_exp_V():
for k in range(0, K):
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.initialise()
BNMF.tau_V = 4 * numpy.ones((J, K)) # muV = [[1./3.]], tauV = [[4.]]
BNMF.update_exp_V(
k
) #-mu*sqrt(tau) = -2./3., lambda(..) = 0.319448 / (1-0.2525) = 0.4273551839464883, gamma =
for j in range(0, J):
assert abs(BNMF.exp_V[j, k] -
(1. / 3. + 1. / 2. * 0.4273551839464883)) < 0.00001
assert abs(BNMF.var_V[j, k] - 1. / 4. *
(1. - 0.4675359092102624)) < 0.00001
def test_update_exp_U():
for k in range(0, K):
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.initialise()
BNMF.tau_U = 4 * numpy.ones((I, K)) # muU = [[0.5]], tauU = [[4.]]
BNMF.update_exp_U(
k
) #-mu*sqrt(tau) = -0.5*2 = -1. lambda(1) = 0.241971 / (1-0.1587) = 0.2876155949126352. gamma = 0.37033832534958433
for i in range(0, I):
assert abs(BNMF.exp_U[i, k] -
(0.5 + 1. / 2. * 0.2876155949126352)) < 0.00001
assert abs(BNMF.var_U[i, k] - 1. / 4. *
(1. - 0.37033832534958433)) < 0.00001
def test_update_V():
for k in range(0, K):
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.mu_V = numpy.zeros((J, K))
BNMF.tau_V = numpy.zeros((J, K))
BNMF.exp_U = 1. / lambdaU #[[1./2.]]
BNMF.exp_V = 1. / lambdaV #[[1./3.]]
BNMF.var_U = numpy.ones((I, K)) * 2 #[[2.]]
BNMF.var_V = numpy.ones((J, K)) * 3 #[[3.]]
BNMF.exp_tau = 3.
BNMF.update_V(k)
for j in range(0, J):
assert BNMF.tau_V[j, k] == 3. * (M[:, j] * (
BNMF.exp_U[:, k] * BNMF.exp_U[:, k] + BNMF.var_U[:, k])).sum()
assert BNMF.mu_V[j,k] == (1./(3. * (M[:,j] * ( BNMF.exp_U[:,k]*BNMF.exp_U[:,k] + BNMF.var_U[:,k] )).sum())) * \
( -3. + BNMF.exp_tau * (M[:,j]*( (BNMF.R[:,j] - numpy.dot(BNMF.exp_U,BNMF.exp_V[j]) + BNMF.exp_U[:,k]*BNMF.exp_V[j,k])*BNMF.exp_U[:,k] )).sum() )
def test_run():
I, J, K = 10, 5, 2
R = numpy.ones((I, J))
M = numpy.ones((I, J))
M[0, 0], M[2, 2], M[3, 1] = 0, 0, 0
R[0, 1], R[0, 2] = 2., 3.
alphatau, betatau = 3, 1
alpha0, beta0 = 6, 2
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'alpha0': alpha0,
'beta0': beta0
}
iterations = 15
BNMF = bnmf_vb(R, M, K, True, hyperparams)
BNMF.initialise()
BNMF.run(iterations)
for k in range(K):
assert BNMF.alphak_s[k] != alpha0
assert BNMF.betak_s[k] != beta0
assert BNMF.exp_lambdak[k] != alpha0 / float(beta0)
for i, k in itertools.product(range(I), range(K)):
assert BNMF.mu_U[i, k] != 1. / (alpha0 / float(beta0))
assert BNMF.tau_U[i, k] != 1.
assert BNMF.exp_U[i, k] != numpy.inf and not math.isnan(BNMF.exp_U[i,
k])
assert BNMF.tau_U[i, k] != numpy.inf and not math.isnan(BNMF.tau_U[i,
k])
for j, k in itertools.product(range(J), range(K)):
assert BNMF.mu_V[j, k] != 1. / (alpha0 / float(beta0))
assert BNMF.tau_V[j, k] != 1.
assert BNMF.exp_V[j, k] != numpy.inf and not math.isnan(BNMF.exp_V[j,
k])
assert BNMF.tau_V[j, k] != numpy.inf and not math.isnan(BNMF.tau_V[j,
k])
assert BNMF.alpha_s != alphatau
assert BNMF.beta_s != betatau
assert BNMF.exp_tau != numpy.inf and not math.isnan(BNMF.exp_tau)
assert BNMF.exp_logtau != numpy.inf and not math.isnan(BNMF.exp_logtau)
def test_predict():
(I, J, K) = (5, 3, 2)
R = numpy.array(
[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]],
dtype=float)
M = numpy.ones((I, J))
K = 3
lambdaU = 2 * numpy.ones((I, K))
lambdaV = 3 * numpy.ones((J, K))
alphatau, betatau = 3, 1
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
expU = numpy.array([[125., 126.], [126., 126.], [126., 126.], [126., 126.],
[126., 126.]])
expV = numpy.array([[84., 84.], [84., 84.], [84., 84.]])
M_test = numpy.array([[0, 0, 1], [0, 1, 0], [0, 0, 0], [1, 1, 0],
[0, 0,
0]]) #R->3,5,10,11, P_pred->21084,21168,21168,21168
MSE = (444408561. + 447872569. + 447660964. + 447618649) / 4.
R2 = 1. - (444408561. + 447872569. + 447660964. + 447618649) / (
4.25**2 + 2.25**2 + 2.75**2 + 3.75**2) #mean=7.25
Rp = 357. / (
math.sqrt(44.75) * math.sqrt(5292.)
) #mean=7.25,var=44.75, mean_pred=21147,var_pred=5292, corr=(-4.25*-63 + -2.25*21 + 2.75*21 + 3.75*21)
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.exp_U = expU
BNMF.exp_V = expV
performances = BNMF.predict(M_test)
assert performances['MSE'] == MSE
assert performances['R^2'] == R2
assert performances['Rp'] == Rp
def test_initialise():
I, J, K = 5, 3, 2
R = numpy.ones((I, J))
M = numpy.ones((I, J))
lambdaU = 2 * numpy.ones((I, K))
lambdaV = 3 * numpy.ones((J, K))
alphatau, betatau = 3, 1
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
# Initialisation with expectation
init = 'exp'
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.initialise(init)
assert BNMF.alpha_s == alphatau + 15. / 2.
assert BNMF.beta_s == betatau + BNMF.exp_square_diff() / 2.
for i, k in itertools.product(range(I), range(K)):
assert BNMF.tau_U[i, k] == 1.
assert BNMF.mu_U[i, k] == 1. / lambdaU[i, k]
for j, k in itertools.product(range(J), range(K)):
assert BNMF.tau_V[j, k] == 1.
assert BNMF.mu_V[j, k] == 1. / lambdaV[j, k]
assert BNMF.exp_tau == (alphatau +
15. / 2.) / (betatau + BNMF.exp_square_diff() / 2.)
for i, k in itertools.product(range(I), range(K)):
assert abs(BNMF.exp_U[i, k] - (0.5 + 0.352065 / (1 - 0.3085))) < 0.0001
for j, k in itertools.product(range(J), range(K)):
assert abs(BNMF.exp_V[j, k] - (1. / 3. + 0.377383 /
(1 - 0.3694))) < 0.0001
# With ARD
init_UV = 'exp'
alphatau, betatau = 3, 1
alpha0, beta0 = 6, 2
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'alpha0': alpha0,
'beta0': beta0
}
BNMF = bnmf_vb(R, M, K, True, hyperparams)
BNMF.initialise(init_UV)
for k in range(K):
assert BNMF.exp_lambdak[k] == alpha0 / float(beta0)
assert BNMF.exp_loglambdak[k] == 1.0129704878718551
for i, k in itertools.product(range(I), range(K)):
assert BNMF.tau_U[i, k] == 1.
assert BNMF.mu_U[i, k] == 1. / (alpha0 / float(beta0))
for j, k in itertools.product(range(J), range(K)):
assert BNMF.tau_V[j, k] == 1.
assert BNMF.mu_V[j, k] == 1. / (alpha0 / float(beta0))
def test_elbo():
I, J, K = 5, 3, 2
R = numpy.ones((I, J))
M = numpy.ones((I, J))
M[0, 0], M[2, 2], M[3, 1] = 0, 0, 0 # size Omega = 12
lambdaU = 2 * numpy.ones((I, K))
lambdaV = 3 * numpy.ones((J, K))
alphatau, betatau = 3, 1
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
exp_U = 5 * numpy.ones((I, K))
exp_V = 6 * numpy.ones((J, K))
var_U = 11 * numpy.ones((I, K))
var_V = 12 * numpy.ones((J, K))
exp_tau = 8.
exp_logtau = 9.
mu_U = 14 * numpy.ones((I, K))
mu_V = 15 * numpy.ones((J, K))
tau_U = numpy.ones((I, K)) / 100.
tau_V = numpy.ones((J, K)) / 101.
alpha_s = 20.
beta_s = 21.
# expU * expV = [[60]]
# (R - expU*expV)^2 = 12*59^2 = 41772
# Var[U*V] = 12*K*((11+5^2)*(12+6^2)-5^2*6^2) = 12*2*828 = 19872
# -muU*sqrt(tauU) = -14*math.sqrt(100) = -1.4
# -muV*sqrt(tauV) = -15*math.sqrt(101) = -1.4925557853149838
# cdf(-1.4) = 0.080756659233771066
# cdf(-1.4925557853149838) = 0.067776752211548219
ELBO = 12./2.*(exp_logtau - math.log(2*math.pi)) - 8./2.*(41772+19872) \
+ 5*2*(math.log(2.) - 2.*5.) + 3*2*(math.log(3.) - 3.*6.) \
+ 3.*numpy.log(1.) - numpy.log(math.gamma(3.)) + 2.*9. - 1.*8. \
- 20.*numpy.log(21.) + numpy.log(math.gamma(20.)) - 19.*9. + 21.*8. \
- 0.5*5*2*math.log(1./100.) + 0.5*5*2*math.log(2*math.pi) + 5*2*math.log(1.-0.080756659233771066) \
+ 0.5*5*2*1./100.*(11.+81.) \
- 0.5*3*2*math.log(1./101.) + 0.5*3*2*math.log(2*math.pi) + 3*2*math.log(1.-0.067776752211548219) \
+ 0.5*3*2*1./101.*(12.+81.)
BNMF = bnmf_vb(R, M, K, False, hyperparams)
BNMF.exp_U = exp_U
BNMF.exp_V = exp_V
BNMF.var_U = var_U
BNMF.var_V = var_V
BNMF.exp_tau = exp_tau
BNMF.exp_logtau = exp_logtau
BNMF.mu_U = mu_U
BNMF.mu_V = mu_V
BNMF.tau_U = tau_U
BNMF.tau_V = tau_V
BNMF.alpha_s = alpha_s
BNMF.beta_s = beta_s
assert BNMF.elbo() == ELBO
for matrix in Ms:
check_empty_rows_columns(matrix, fraction)
''' We now run the Gibbs sampler on each of the M's for each fraction. '''
all_performances = {metric: [] for metric in metrics}
average_performances = {metric: []
for metric in metrics} # averaged over repeats
for (fraction, Ms, Ms_test) in zip(fractions_unknown, all_Ms, all_Ms_test):
print "Trying fraction %s." % fraction
# Run the algorithm <repeats> times and store all the performances
for metric in metrics:
all_performances[metric].append([])
for (repeat, M_train, M_test) in zip(range(0, repeats), Ms, Ms_test):
print "Repeat %s of fraction %s." % (repeat + 1, fraction)
BNMF = bnmf_vb(R, M_train, K, ARD, hyperparams)
BNMF.initialise(init_UV)
BNMF.run(iterations)
# Measure the performances
performances = BNMF.predict(M_test)
for metric in metrics:
# Add this metric's performance to the list of <repeat> performances for this fraction
all_performances[metric][-1].append(performances[metric])
# Compute the average across attempts
for metric in metrics:
average_performances[metric].append(
sum(all_performances[metric][-1]) / repeats)
''' Print and store the performances. '''
print "repeats=%s \nfractions_unknown = %s \nall_performances = %s \naverage_performances = %s" % \
'alpha0': alpha0,
'beta0': beta0,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
''' Load in data. '''
R, M = load_ccle_ec50()
''' Run the algorithm, :repeats times, and average the timestamps. '''
times_repeats = []
performances_repeats = []
for i in range(0, repeats):
# Set all the seeds
numpy.random.seed(0), random.seed(0), scipy.random.seed(0)
# Run the classifier
BNMF = bnmf_vb(R, M, K, ARD, hyperparams)
BNMF.initialise(init_UV)
BNMF.run(iterations)
# Extract the performances and timestamps across all iterations
times_repeats.append(BNMF.all_times)
performances_repeats.append(BNMF.all_performances)
''' Check whether seed worked: all performances should be the same. '''
METRICS = ['MSE', 'R^2', 'Rp']
def excluse_nan(performances):
return {
metric: [v for v in performances[metric] if not numpy.isnan(v)]
for metric in METRICS
}
def test_init():
# Test getting an exception when R and M are different sizes, and when R is not a 2D array.
R1 = numpy.ones(3)
M = numpy.ones((2, 3))
I, J, K = 5, 3, 1
lambdaU = numpy.ones((I, K))
lambdaV = numpy.ones((J, K))
alphatau, betatau = 3, 1
alpha0, beta0 = 6, 2
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'alpha0': alpha0,
'beta0': beta0
}
ARD = True
# Test R is 2-dim
with pytest.raises(AssertionError) as error:
bnmf_vb(R1, M, K, ARD, hyperparams)
assert str(
error.value
) == "Input matrix R is not a two-dimensional array, but instead 1-dimensional."
R2 = numpy.ones((4, 3, 2))
with pytest.raises(AssertionError) as error:
bnmf_vb(R2, M, K, ARD, hyperparams)
assert str(
error.value
) == "Input matrix R is not a two-dimensional array, but instead 3-dimensional."
# Test R is the same shape as M
R3 = numpy.ones((3, 2))
with pytest.raises(AssertionError) as error:
bnmf_vb(R3, M, K, ARD, hyperparams)
assert str(
error.value
) == "Input matrix R is not of the same size as the indicator matrix M: (3, 2) and (2, 3) respectively."
# Similarly for lambdaU, lambdaV
R4 = numpy.ones((2, 3))
lambdaU = numpy.ones((2 + 1, 1))
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
with pytest.raises(AssertionError) as error:
bnmf_vb(R4, M, K, False, hyperparams)
assert str(
error.value
) == "Prior matrix lambdaU has the wrong shape: (3, 1) instead of (2, 1)."
lambdaU = numpy.ones((2, 1))
lambdaV = numpy.ones((3 + 1, 1))
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
with pytest.raises(AssertionError) as error:
bnmf_vb(R4, M, K, False, hyperparams)
assert str(
error.value
) == "Prior matrix lambdaV has the wrong shape: (4, 1) instead of (3, 1)."
# Test getting an exception if a row or column is entirely unknown
M1 = [[1, 1, 1], [0, 0, 0]]
M2 = [[1, 1, 0], [1, 0, 0]]
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'alpha0': alpha0,
'beta0': beta0
}
with pytest.raises(AssertionError) as error:
bnmf_vb(R4, M1, K, ARD, hyperparams)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmf_vb(R4, M2, K, ARD, hyperparams)
assert str(error.value) == "Fully unobserved column in R, column 2."
# Finally, a successful case
I, J, K = 3, 2, 2
R5 = 2 * numpy.ones((I, J))
M = numpy.ones((I, J))
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'alpha0': alpha0,
'beta0': beta0
}
BNMF = bnmf_vb(R5, M, K, ARD, hyperparams)
assert numpy.array_equal(BNMF.R, R5)
assert numpy.array_equal(BNMF.M, M)
assert BNMF.I == I
assert BNMF.J == J
assert BNMF.K == K
assert BNMF.size_Omega == I * J
assert BNMF.alphatau == alphatau
assert BNMF.betatau == betatau
assert BNMF.alpha0 == alpha0
assert BNMF.beta0 == beta0
# And when lambdaU and lambdaV are integers
I, J, K = 3, 2, 2
R5 = 2 * numpy.ones((I, J))
lambdaU = 3.
lambdaV = 4.
M = numpy.ones((I, J))
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_vb(R5, M, K, False, hyperparams)
assert numpy.array_equal(BNMF.R, R5)
assert numpy.array_equal(BNMF.M, M)
assert BNMF.I == I
assert BNMF.J == J
assert BNMF.K == K
assert BNMF.size_Omega == I * J
assert BNMF.alphatau == alphatau
assert BNMF.betatau == betatau
assert numpy.array_equal(BNMF.lambdaU, lambdaU * numpy.ones((I, K)))
assert numpy.array_equal(BNMF.lambdaV, lambdaV * numpy.ones((J, K)))