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))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
# First do a random initialisation - we can then only check whether values are correctly initialised
init = 'random'
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
BNMF.initialise(init)
assert BNMF.tau >= 0.0
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMF.U[i,k] >= 0.0
for j,k in itertools.product(xrange(0,J),xrange(0,K)):
assert BNMF.V[j,k] >= 0.0
# Then initialise with expectation values
init = 'exp'
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
BNMF.initialise(init)
assert BNMF.tau >= 0.0
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMF.U[i,k] == 1./2.
for j,k in itertools.product(xrange(0,J),xrange(0,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))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
iterations = 10
burnin, thinning = 4, 2
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
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)
BIC = -2 * log_likelihood + (2 * 3 + 2 * 3) * 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_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
lambdaU = 2*numpy.ones((I,K))
lambdaV = 3*numpy.ones((J,K))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
init = 'exp' #U=1/2,V=1/3
U_prior = numpy.ones((I,K))/2.
V_prior = numpy.ones((J,K))/3.
iterations = 15
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
BNMF.initialise(init)
(Us,Vs,taus) = BNMF.run(iterations)
assert BNMF.all_U.shape == (iterations,I,K)
assert BNMF.all_V.shape == (iterations,J,K)
assert BNMF.all_tau.shape == (iterations,)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert Us[0,i,k] != U_prior[i,k]
for j,k in itertools.product(xrange(0,J),xrange(0,K)):
assert Vs[0,j,k] != V_prior[j,k]
assert taus[1] != alpha/float(beta)
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))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
iterations = 10
burnin, thinning = 4, 2
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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)
BIC = -2*log_likelihood + (2*3+2*3)*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_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))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
BNMF.all_U = Us
BNMF.all_V = Vs
BNMF.all_tau = taus
(exp_U, exp_V, exp_tau) = BNMF.approx_expectation(burn_in,thinning)
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_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
lambdaU = 2 * numpy.ones((I, K))
lambdaV = 3 * numpy.ones((J, K))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
init = 'exp' #U=1/2,V=1/3
U_prior = numpy.ones((I, K)) / 2.
V_prior = numpy.ones((J, K)) / 3.
iterations = 15
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.initialise(init)
(Us, Vs, taus) = BNMF.run(iterations)
assert BNMF.all_U.shape == (iterations, I, K)
assert BNMF.all_V.shape == (iterations, J, K)
assert BNMF.all_tau.shape == (iterations, )
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert Us[0, i, k] != U_prior[i, k]
for j, k in itertools.product(xrange(0, J), xrange(0, K)):
assert Vs[0, j, k] != V_prior[j, k]
assert taus[1] != alpha / float(beta)
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))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
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_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))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, '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 = bnmf_gibbs_optimised(R,M,K,priors)
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_tauV():
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
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(xrange(0, J), xrange(0, K)):
assert BNMF.tauV(k)[j] == tauV[j, k]
def test_tauV():
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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(xrange(0,J),xrange(0,K)):
assert BNMF.tauV(k)[j] == tauV[j,k]
def test_tauU():
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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(xrange(0,I),xrange(0,K)):
assert BNMF.tauU(k)[i] == tauU[i,k]
def test_muV():
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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(xrange(0,J),xrange(0,K)):
assert BNMF.muV(tauV[:,k],k)[j] == muV[j,k]
def test_muU():
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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(xrange(0,I),xrange(0,K)):
assert abs(BNMF.muU(tauU[:,k],k)[i] - muU[i,k]) < 0.000000000000001
def test_tauU():
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
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(xrange(0, I), xrange(0, K)):
assert BNMF.tauU(k)[i] == tauU[i, k]
def test_muV():
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
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(xrange(0, J), xrange(0, K)):
assert BNMF.muV(tauV[:, k], k)[j] == muV[j, k]
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))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'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 = bnmf_gibbs_optimised(R, M, K, priors)
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_muU():
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
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(xrange(0, I), xrange(0, K)):
assert abs(BNMF.muU(tauU[:, k], k)[i] - muU[i, k]) < 0.000000000000001
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))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
# First do a random initialisation - we can then only check whether values are correctly initialised
init = 'random'
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.initialise(init)
assert BNMF.tau >= 0.0
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMF.U[i, k] >= 0.0
for j, k in itertools.product(xrange(0, J), xrange(0, K)):
assert BNMF.V[j, k] >= 0.0
# Then initialise with expectation values
init = 'exp'
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.initialise(init)
assert BNMF.tau >= 0.0
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMF.U[i, k] == 1. / 2.
for j, k in itertools.product(xrange(0, J), xrange(0, K)):
assert BNMF.V[j, k] == 1. / 3.
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))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.all_U = Us
BNMF.all_V = Vs
BNMF.all_tau = taus
(exp_U, exp_V, exp_tau) = BNMF.approx_expectation(burn_in, thinning)
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_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))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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)
check_empty_rows_columns(M,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,M_test) in zip(range(0,repeats),Ms,Ms_test):
print "Repeat %s of fraction %s." % (repeat+1, fraction)
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
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])/repeats)
def test_beta_s():
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.initialise(init)
beta_s = beta + .5 * (12 * (2. / 3.)**2) #U*V.T = [[1/6+1/6,..]]
assert abs(BNMF.beta_s() - beta_s) < 0.000000000000001
def test_alpha_s():
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.initialise(init)
alpha_s = alpha + 6.
assert BNMF.alpha_s() == alpha_s
import numpy, matplotlib.pyplot as plt
##########
standardised = False #standardised Sanger or unstandardised
iterations = 1000
burnin = 800
thinning = 5
init_UV = 'random'
I, J, K = 622,138,10
alpha, beta = 1., 1.
lambdaU = numpy.ones((I,K))/10.
lambdaV = numpy.ones((J,K))/10.
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
# Load in data
(_,X_min,M,_,_,_,_) = load_gdsc(standardised=standardised)
# Run the Gibbs sampler
BNMF = bnmf_gibbs_optimised(X_min,M,K,priors)
BNMF.initialise(init_UV)
BNMF.run(iterations)
# Plot the tau expectation values to check convergence
plt.plot(BNMF.all_tau)
# Print the performances across iterations (MSE)
print "all_performances = %s" % BNMF.all_performances['MSE']
def test_alpha_s():
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
BNMF.initialise(init)
alpha_s = alpha + 6.
assert BNMF.alpha_s() == alpha_s
def test_beta_s():
BNMF = bnmf_gibbs_optimised(R,M,K,priors)
BNMF.initialise(init)
beta_s = beta + .5*(12*(2./3.)**2) #U*V.T = [[1/6+1/6,..]]
assert abs(BNMF.beta_s() - beta_s) < 0.000000000000001
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))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R1,M,K,priors)
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_gibbs_optimised(R2,M,K,priors)
assert str(error.value) == "Input matrix R is not a two-dimensional array, but instead 3-dimensional."
R3 = numpy.ones((3,2))
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R3,M,K,priors)
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))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4,M,K,priors)
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))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4,M,K,priors)
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
lambdaU = numpy.ones((2,1))
lambdaV = numpy.ones((3,1))
M1 = [[1,1,1],[0,0,0]]
M2 = [[1,1,0],[1,0,0]]
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4,M1,K,priors)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4,M2,K,priors)
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))
lambdaU = numpy.ones((I,K))
lambdaV = numpy.ones((J,K))
M = numpy.ones((I,J))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
BNMF = bnmf_gibbs_optimised(R5,M,K,priors)
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.alpha == alpha
assert BNMF.beta == beta
assert numpy.array_equal(BNMF.lambdaU,lambdaU)
assert numpy.array_equal(BNMF.lambdaV,lambdaV)
# 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))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaU':lambdaU, 'lambdaV':lambdaV }
BNMF = bnmf_gibbs_optimised(R5,M,K,priors)
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.alpha == alpha
assert BNMF.beta == beta
assert numpy.array_equal(BNMF.lambdaU,lambdaU*numpy.ones((I,K)))
assert numpy.array_equal(BNMF.lambdaV,lambdaV*numpy.ones((J,K)))
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))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R1, M, K, priors)
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_gibbs_optimised(R2, M, K, priors)
assert str(
error.value
) == "Input matrix R is not a two-dimensional array, but instead 3-dimensional."
R3 = numpy.ones((3, 2))
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R3, M, K, priors)
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))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4, M, K, priors)
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))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4, M, K, priors)
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
lambdaU = numpy.ones((2, 1))
lambdaV = numpy.ones((3, 1))
M1 = [[1, 1, 1], [0, 0, 0]]
M2 = [[1, 1, 0], [1, 0, 0]]
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4, M1, K, priors)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmf_gibbs_optimised(R4, M2, K, priors)
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))
lambdaU = numpy.ones((I, K))
lambdaV = numpy.ones((J, K))
M = numpy.ones((I, J))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_gibbs_optimised(R5, M, K, priors)
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.alpha == alpha
assert BNMF.beta == beta
assert numpy.array_equal(BNMF.lambdaU, lambdaU)
assert numpy.array_equal(BNMF.lambdaV, lambdaV)
# 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))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaU': lambdaU,
'lambdaV': lambdaV
}
BNMF = bnmf_gibbs_optimised(R5, M, K, priors)
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.alpha == alpha
assert BNMF.beta == beta
assert numpy.array_equal(BNMF.lambdaU, lambdaU * numpy.ones((I, K)))
assert numpy.array_equal(BNMF.lambdaV, lambdaV * numpy.ones((J, K)))
init_UV = 'random'
I, J, K = 100, 80, 10
alpha, beta = 1., 1.
lambdaU = numpy.ones((I, K)) / 10
lambdaV = numpy.ones((J, K)) / 10
priors = {'alpha': alpha, 'beta': beta, 'lambdaU': lambdaU, 'lambdaV': lambdaV}
# Load in data
R = numpy.loadtxt(input_folder + "R.txt")
M = numpy.ones((I, J))
M_test = calc_inverse_M(numpy.loadtxt(input_folder + "M.txt"))
# Run the Gibbs sampler
BNMF = bnmf_gibbs_optimised(R, M, K, priors)
BNMF.initialise(init_UV)
BNMF.run(iterations)
taus = BNMF.all_tau
Us = BNMF.all_U
Vs = BNMF.all_V
# Plot tau against iterations to see that it converges
f, axarr = plt.subplots(3, sharex=True)
x = range(1, len(taus) + 1)
axarr[0].set_title('Convergence of values')
axarr[0].plot(x, taus)
axarr[0].set_ylabel("tau")
axarr[1].plot(x, Us[:, 0, 0])
axarr[1].set_ylabel("U[0,0]")
burnin = 800
thinning = 5
init_UV = 'random'
I, J, K = 622, 139, 10
alpha, beta = 1., 1.
lambdaU = numpy.ones((I, K)) / 10.
lambdaV = numpy.ones((J, K)) / 10.
priors = {'alpha': alpha, 'beta': beta, 'lambdaU': lambdaU, 'lambdaV': lambdaV}
# Load in data
(_, X_min, M, _, _, _, _) = load_Sanger(standardised=standardised)
# Run the Gibbs sampler
BNMF = bnmf_gibbs_optimised(X_min, M, K, priors)
BNMF.initialise(init_UV)
BNMF.run(iterations)
# Also measure the performances on the training data
performances = BNMF.predict(M, burnin, thinning)
print performances
# Plot the tau expectation values to check convergence
plt.plot(BNMF.all_tau)
# Print the performances across iterations (MSE)
print "all_performances = %s" % BNMF.all_performances['MSE']
'''
all_performances = [70.259413341682688, 4.8971290647901098, 3.3366462476811503, 3.0455206033882209, 2.7447108749105587, 2.578435577932114, 2.4833813872813524, 2.415888300731782, 2.3536778144262742, 2.3088912946697913, 2.2786420788211239, 2.2509724374956193, 2.22667741922423, 2.2031884180283976, 2.1847566352846948, 2.1648189088246772, 2.1460938492581767, 2.1278516243120729, 2.1062953182339323, 2.0926693199948403, 2.0848241907939036, 2.0685862785831257, 2.0570830259861981, 2.0462940795476516, 2.0363409068498219, 2.029886686971718, 2.0176899697641772, 2.0106525727433837, 2.0020713949604159, 2.002281406734058, 1.9915030498718691, 1.9858194977875878, 1.9784353255998126, 1.9714051757376778, 1.9670522298960877, 1.968008185696684, 1.958200794994801, 1.9512012470672166, 1.9477052707167406, 1.9441854808214387, 1.9381855724814856, 1.9364174709592417, 1.9356997589656086, 1.9352627387119066, 1.9348522789686642, 1.9268881475296915, 1.9226271597884173, 1.9227851205336726, 1.9238989731434151, 1.9200171025517994, 1.9188880484063568, 1.9197134237406113, 1.916425415282702, 1.9153621414295772, 1.9146371137589364, 1.9117992681911631, 1.9168120579196799, 1.9127152168907351, 1.9136381248527585, 1.9124659290909347, 1.9066105730057274, 1.9037046201625576, 1.9028382053907444, 1.9021808021820057, 1.9004858423544877, 1.8992801612891583, 1.9026757750113414, 1.8989792109356545, 1.9002989177295584, 1.8992655262831213, 1.8934610682212321, 1.8979909500121086, 1.8945815858012922, 1.8907158205439492, 1.8917927364302576, 1.8865372627921817, 1.8912813674331883, 1.8898267699326203, 1.8893514208248487, 1.8882906674495989, 1.8889217948546417, 1.8910702063291298, 1.8862765947755964, 1.8877016402682192, 1.8828696751101761, 1.8831999040158809, 1.8889025568532367, 1.8888870564800815, 1.8836578818889995, 1.8869617280625401, 1.8860400812198455, 1.8863000130495331, 1.8851087719269559, 1.8845040611080666, 1.8827057480448237, 1.8832954206478851, 1.87928254801469, 1.878876141623214, 1.8829304461976393, 1.8811097684308042, 1.8814313662987925, 1.8795462994449332, 1.8810082200277263, 1.8773722023867854, 1.8764619038465475, 1.8728679469329701, 1.8770515486775219, 1.8782980320737679, 1.8826121584711468, 1.8757288208822585, 1.8788258706355208, 1.8772802429060622, 1.8788864164135914, 1.8734299681695261, 1.8700347675886981, 1.870333214887979, 1.8723530679008547, 1.8709157139185337, 1.8740720223330249, 1.8712399129163875, 1.8709338966727382, 1.8718862112612891, 1.8659499249172649, 1.8659120681815102, 1.8672445444726185, 1.8714215601165245, 1.8728733348608553, 1.8687953661295253, 1.8652660451550196, 1.8683144529757103, 1.8654813288418781, 1.8629133657731987, 1.8615308199301024, 1.8633835652892472, 1.8635299360830686, 1.8622117225019912, 1.8600044049985365, 1.8613448830605202, 1.8596049965966128, 1.8630259368735869, 1.8626525242951686, 1.8630774878788063, 1.8601220734028741, 1.8600599783429403, 1.857457934904525, 1.8601271403367068, 1.8568535971646063, 1.8612346254514536, 1.8611408140481331, 1.8614386100282956, 1.8606892342850505, 1.8599826470711498, 1.8553177075213387, 1.8529554429655664, 1.8567829829776814, 1.8571288841122873, 1.8569144996257509, 1.8548402647829396, 1.8531725091430296, 1.8493709639763063, 1.8547317468555411, 1.8536901989635526, 1.8527616039027608, 1.8509969217011817, 1.8516130649294436, 1.8508041898180099, 1.8559929427103923, 1.8499277325619743, 1.8517657229166384, 1.8518300974399386, 1.8481858431631508, 1.8474364251979238, 1.8463942884787827, 1.844509210684329, 1.8496115746219548, 1.8505740385190306, 1.85030649486764, 1.8552041644809307, 1.8542898912085684, 1.8529955711377819, 1.8487825126859405, 1.8540838202162937, 1.8504676234789401, 1.849470388801967, 1.8483163335076953, 1.8517654585449175, 1.8510913579940835, 1.8469128107788015, 1.8473778093911559, 1.847004385971597, 1.8458021102144542, 1.8509265306309526, 1.8503474650542513, 1.8516603607739082, 1.8474027900532639, 1.8468857200220394, 1.8448214813999044, 1.8450267968203624, 1.8491166487307811, 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