def test_initialise():
I,J,K = 5,3,2
R = numpy.ones((I,J))
M = numpy.ones((I,J))
alphatau, betatau = 3, 1
alpha0, beta0 = 6, 2
priors = { 'alphatau':alphatau, 'betatau':betatau, 'alpha0':alpha0, 'beta0':beta0 }
# First do a random initialisation, ARD - we can then only check whether values are correctly initialised
init_UV = 'random'
BNMF = nmf_icm(R,M,K,True,priors)
BNMF.initialise(init_UV)
assert BNMF.tau >= 0.0
for k in range(K):
assert BNMF.lambdak[k] == alpha0 / beta0
for i,k in itertools.product(range(I),range(K)):
assert BNMF.U[i,k] >= 0.0
for j,k in itertools.product(range(J),range(K)):
assert BNMF.V[j,k] >= 0.0
# Then initialise with expectation values, no ARD
lambdaU, lambdaV = 2., 3.
priors = { 'alphatau':alphatau, 'betatau':betatau, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
init_UV = 'exp'
BNMF = nmf_icm(R,M,K,False,priors)
BNMF.initialise(init_UV)
assert BNMF.tau >= 0.0
for i,k in itertools.product(range(I),range(K)):
assert BNMF.U[i,k] == 1./2.
for j,k in itertools.product(range(J),range(K)):
assert BNMF.V[j,k] == 1./3.
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
}
iterations = 10
burnin, thinning = 4, 2
BNMF = nmf_icm(R, M, K, False, hyperparams)
BNMF.all_U = [numpy.ones((I, K)) for i in range(0, iterations)]
BNMF.all_V = [2 * numpy.ones((J, K)) for i in range(0, iterations)]
BNMF.all_tau = [3. for i in range(0, iterations)]
# expU*expV.T = [[6.]]
log_likelihood = 3. / 2. * (
math.log(3.) - 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', burnin, thinning)
assert AIC == BNMF.quality('AIC', burnin, thinning)
assert BIC == BNMF.quality('BIC', burnin, thinning)
assert MSE == BNMF.quality('MSE', burnin, thinning)
with pytest.raises(AssertionError) as error:
BNMF.quality('FAIL', burnin, thinning)
assert str(error.value) == "Unrecognised metric for model quality: FAIL."
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 = nmf_icm(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_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
alphatau, betatau = 3, 1
alpha0, beta0 = 6, 2
hyperparams = {
'alphatau': alphatau,
'betatau': betatau,
'alpha0': alpha0,
'beta0': beta0
}
init_UV = 'exp'
iterations = 15
BNMF = nmf_icm(R, M, K, True, hyperparams)
BNMF.initialise(init_UV)
BNMF.run(iterations)
assert BNMF.all_U.shape == (iterations, I, K)
assert BNMF.all_V.shape == (iterations, J, K)
assert BNMF.all_lambdak.shape == (iterations, K)
assert BNMF.all_tau.shape == (iterations, )
for k in range(K):
assert BNMF.all_lambdak[0, k] != alpha0 / float(beta0)
for i, k in itertools.product(range(I), range(K)):
assert BNMF.all_U[0, i, k] != 1. / (alpha0 / float(beta0))
for j, k in itertools.product(range(J), xrange(K)):
assert BNMF.all_V[0, j, k] != 1. / (alpha0 / float(beta0))
assert BNMF.all_tau[0] != alphatau / float(betatau)
def test_predict():
burn_in = 2
thinning = 3 # so index 2,5,8 -> m=3,m=6,m=9
(I,J,K) = (5,3,2)
Us = [numpy.ones((I,K)) * 3*m**2 for m in range(1,10+1)] #first is 1's, second is 4's, third is 9's, etc.
Vs = [numpy.ones((J,K)) * 2*m**2 for m in range(1,10+1)]
Us[2][0,0] = 24 #instead of 27 - to ensure we do not get 0 variance in our predictions
taus = [m**2 for m in range(1,10+1)]
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))
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 }
#expected_exp_U = numpy.array([[125.,126.],[126.,126.],[126.,126.],[126.,126.],[126.,126.]])
#expected_exp_V = numpy.array([[84.,84.],[84.,84.],[84.,84.]])
#R_pred = numpy.array([[21084.,21084.,21084.],[ 21168.,21168.,21168.],[21168.,21168.,21168.],[21168.,21168.,21168.],[21168.,21168.,21168.]])
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 = nmf_icm(R,M,K,False,hyperparams)
BNMF.all_U = Us
BNMF.all_V = Vs
BNMF.all_tau = taus
performances = BNMF.predict(M_test,burn_in,thinning)
assert performances['MSE'] == MSE
assert performances['R^2'] == R2
assert performances['Rp'] == Rp
def test_approx_expectation():
burn_in = 2
thinning = 3 # so index 2,5,8 -> m=3,m=6,m=9
(I,J,K) = (5,3,2)
Us = [numpy.ones((I,K)) * 3*m**2 for m in range(1,10+1)] #first is 1's, second is 4's, third is 9's, etc.
Vs = [numpy.ones((J,K)) * 2*m**2 for m in range(1,10+1)]
taus = [m**2 for m in range(1,10+1)]
expected_exp_tau = (9.+36.+81.)/3.
expected_exp_U = numpy.array([[9.+36.+81.,9.+36.+81.],[9.+36.+81.,9.+36.+81.],[9.+36.+81.,9.+36.+81.],[9.+36.+81.,9.+36.+81.],[9.+36.+81.,9.+36.+81.]])
expected_exp_V = numpy.array([[(9.+36.+81.)*(2./3.),(9.+36.+81.)*(2./3.)],[(9.+36.+81.)*(2./3.),(9.+36.+81.)*(2./3.)],[(9.+36.+81.)*(2./3.),(9.+36.+81.)*(2./3.)]])
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 }
BNMF = nmf_icm(R,M,K,False,hyperparams)
BNMF.all_U = Us
BNMF.all_V = Vs
BNMF.all_tau = taus
(exp_U, exp_V, exp_tau, exp_lambdak) = BNMF.approx_expectation(burn_in,thinning)
assert exp_lambdak is None
assert expected_exp_tau == exp_tau
assert numpy.array_equal(expected_exp_U,exp_U)
assert numpy.array_equal(expected_exp_V,exp_V)
def test_tauV():
BNMF = nmf_icm(R, M, K, False, hyperparams)
BNMF.initialise(init)
BNMF.tau = 3.
#U^2 = [[1/4,1/4],[1/4,1/4],[1/4,1/4],[1/4,1/4],[1/4,1/4]], sum_i U^2 = [1,1,1] (index=j)
tauV = 3. * numpy.array([[1., 1.], [1., 1.], [1., 1.]])
for j, k in itertools.product(range(J), range(K)):
assert BNMF.tauV(k)[j] == tauV[j, k]
def test_tauU():
BNMF = nmf_icm(R,M,K,False,hyperparams)
BNMF.initialise(init)
BNMF.tau = 3.
#V^2 = [[1/9,1/9],[1/9,1/9],[1/9,1/9]], sum_j V^2 = [2/9,1/3,2/9,2/9,1/3] (index=i)
tauU = 3.*numpy.array([[2./9.,2./9.],[1./3.,1./3.],[2./9.,2./9.],[2./9.,2./9.],[1./3.,1./3.]])
for i,k in itertools.product(range(I),range(K)):
assert BNMF.tauU(k)[i] == tauU[i,k]
def test_muV():
BNMF = nmf_icm(R,M,K,False,hyperparams)
BNMF.initialise(init)
BNMF.tau = 3.
#U*V^T - Uik*Vjk = [[1/6,..]], so Rij - Ui * Vj + Uik * Vjk = 5/6
tauV = 3.*numpy.array([[1.,1.],[1.,1.],[1.,1.]])
muV = 1./tauV * ( 3. * numpy.array([[4.*(5./6.)*(1./2.),4.*(5./6.)*(1./2.)],[4.*(5./6.)*(1./2.),4.*(5./6.)*(1./2.)],[4.*(5./6.)*(1./2.),4.*(5./6.)*(1./2.)]]) - lambdaV )
for j,k in itertools.product(range(0,J),range(K)):
assert BNMF.muV(tauV[:,k],k)[j] == muV[j,k]
def test_muU():
BNMF = nmf_icm(R,M,K,False,hyperparams)
BNMF.initialise(init)
BNMF.tau = 3.
#U*V^T - Uik*Vjk = [[1/6,..]], so Rij - Ui * Vj + Uik * Vjk = 5/6
tauU = 3.*numpy.array([[2./9.,2./9.],[1./3.,1./3.],[2./9.,2./9.],[2./9.,2./9.],[1./3.,1./3.]])
muU = 1./tauU * ( 3. * numpy.array([[2.*(5./6.)*(1./3.),10./18.],[15./18.,15./18.],[10./18.,10./18.],[10./18.,10./18.],[15./18.,15./18.]]) - lambdaU )
for i,k in itertools.product(range(I),xrange(K)):
assert abs(BNMF.muU(tauU[:,k],k)[i] - muU[i,k]) < 0.000000000000001
def test_betak_s():
BNMF = nmf_icm(R, M, K, True, hyperparams)
BNMF.initialise(init)
betak_s = beta0 + I / 3. + J / 3.
for k in range(K):
assert abs(BNMF.betak_s(k) - betak_s) < 0.000000000000001
def test_alphak_s():
BNMF = nmf_icm(R, M, K, True, hyperparams)
BNMF.initialise(init)
alphak_s = alpha0 + I + J
for k in range(K):
assert BNMF.alphak_s(k) == alphak_s
def test_alpha_s():
BNMF = nmf_icm(R, M, K, False, hyperparams)
BNMF.initialise(init)
alpha_s = alphatau + 6.
assert BNMF.alpha_s() == alpha_s
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:
nmf_icm(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:
nmf_icm(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:
nmf_icm(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:
nmf_icm(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:
nmf_icm(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:
nmf_icm(R4, M1, K, ARD, hyperparams)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
nmf_icm(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 = nmf_icm(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 = nmf_icm(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)))
all_R.append(R)
''' We now run the algorithm on each of the M's for each noise ratio. '''
all_performances = {metric:[] for metric in metrics}
average_performances = {metric:[] for metric in metrics} # averaged over repeats
for (noise,R,Ms,Ms_test) in zip(noise_ratios,all_R,all_Ms,all_Ms_test):
print "Trying noise ratio %s." % noise
# Run the algorithm <repeats> times and store all the performances
for metric in metrics:
all_performances[metric].append([])
for (repeat,M,M_test) in zip(range(0,repeats),Ms,Ms_test):
print "Repeat %s of noise ratio %s." % (repeat+1, noise)
BNMF = nmf_icm(R,M,K,ARD,hyperparams)
BNMF.initialise(init_UV)
BNMF.run(iterations)
# Measure the performances
performances = BNMF.predict(M_test,burn_in,thinning)
for metric in metrics:
# Add this metric's performance to the list of <repeat> performances for this noise ratio
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. '''
M=M) for K in values_K
]
''' 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 K, (Ms_train, Ms_test) in zip(values_K, all_Ms_training_and_test):
print "Trying K=%s." % K
# Run the algorithm <repeats> times and store all the performances
for metric in metrics:
all_performances[metric].append([])
for fold, (M_train, M_test) in enumerate(zip(Ms_train, Ms_test)):
print "Fold %s of K=%s." % (fold + 1, K)
BNMF = nmf_icm(R, M_train, K, ARD, hyperparams)
BNMF.initialise(init_UV)
BNMF.run(iterations)
# Measure the performances
performances = BNMF.predict(M_test, burn_in, thinning)
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]) / no_folds)
''' Print and store the performances. '''
print "values_K = %s \nall_performances = %s \naverage_performances = %s" % \
def test_beta_s():
BNMF = nmf_icm(R, M, K, False, hyperparams)
BNMF.initialise(init)
beta_s = betatau + .5 * (12 * (2. / 3.)**2) #U*V.T = [[1/6+1/6,..]]
assert abs(BNMF.beta_s() - beta_s) < 0.000000000000001
