def test_initialise():
I,J,K,L = 5,3,2,4
R = numpy.ones((I,J))
M = numpy.ones((I,J))
lambdaF = 2*numpy.ones((I,K))
lambdaS = 3*numpy.ones((K,L))
lambdaG = 4*numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
# First do a random initialisation - we can then only check whether values are correctly initialised
init_S = 'random'
init_FG = 'random'
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
assert BNMTF.tau >= 0.0
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMTF.F[i,k] >= 0.0
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.S[k,l] >= 0.0
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.G[j,l] >= 0.0
# Initialisation of S using random draws from prior
init_S, init_FG = 'random', 'exp'
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMTF.F[i,k] == 1./lambdaF[i,k]
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.S[k,l] != 1./lambdaS[k,l] # test whether we overwrote the expectation
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.G[j,l] == 1./lambdaG[j,l]
# Initialisation of F and G using random draws from prior
init_S, init_FG = 'exp', 'random'
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMTF.F[i,k] != 1./lambdaF[i,k] # test whether we overwrote the expectation
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.S[k,l] == 1./lambdaS[k,l]
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.G[j,l] != 1./lambdaG[j,l] # test whether we overwrote the expectation
# Initialisation of F and G using Kmeans
init_S, init_FG = 'exp', 'kmeans'
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMTF.F[i,k] == 0.2 or BNMTF.F[i,k] == 1.2
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.G[j,l] == 0.2 or BNMTF.G[j,l] == 1.2
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.S[k,l] == 1./lambdaS[k,l]
def test_beta_s():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
beta_s = beta + .5 * (12 * (
11. / 15.)**2) #F*S = [[1/6+1/6=1/3,..]], F*S*G^T = [[1/15*4=4/15,..]]
assert abs(BNMTF.beta_s() - beta_s) < 0.00000000000001
def test_log_likelihood():
R = numpy.array([[1,2],[3,4]],dtype=float)
M = numpy.array([[1,1],[0,1]])
I, J, K, L = 2, 2, 3, 4
lambdaF = 2*numpy.ones((I,K))
lambdaS = 3*numpy.ones((K,L))
lambdaG = 4*numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
iterations = 10
burnin, thinning = 4, 2
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.all_F = [numpy.ones((I,K)) for i in range(0,iterations)]
BNMTF.all_S = [2*numpy.ones((K,L)) for i in range(0,iterations)]
BNMTF.all_G = [3*numpy.ones((J,L)) for i in range(0,iterations)]
BNMTF.all_tau = [3. for i in range(0,iterations)]
# expU*expV.T = [[72.]]
log_likelihood = 3./2.*(math.log(3)-math.log(2*math.pi)) - 3./2. * (71**2 + 70**2 + 68**2)
AIC = -2*log_likelihood + 2*(2*3+3*4+2*4)
BIC = -2*log_likelihood + (2*3+3*4+2*4)*math.log(3)
MSE = (71**2+70**2+68**2)/3.
assert log_likelihood == BNMTF.quality('loglikelihood',burnin,thinning)
assert AIC == BNMTF.quality('AIC',burnin,thinning)
assert BIC == BNMTF.quality('BIC',burnin,thinning)
assert MSE == BNMTF.quality('MSE',burnin,thinning)
with pytest.raises(AssertionError) as error:
BNMTF.quality('FAIL',burnin,thinning)
assert str(error.value) == "Unrecognised metric for model quality: FAIL."
def test_run():
I,J,K,L = 10,5,3,2
R = numpy.ones((I,J))
M = numpy.ones((I,J))
M[0,0], M[2,2], M[3,1] = 0, 0, 0
lambdaF = 2*numpy.ones((I,K))
lambdaS = 3*numpy.ones((K,L))
lambdaG = 4*numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
init = 'exp' #F=1/2,S=1/3,G=1/4
F_prior = numpy.ones((I,K))/2.
S_prior = numpy.ones((K,L))/3.
G_prior = numpy.ones((J,L))/4.
iterations = 15
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init)
(Fs,Ss,Gs,taus) = BNMTF.run(iterations)
assert BNMTF.all_F.shape == (iterations,I,K)
assert BNMTF.all_S.shape == (iterations,K,L)
assert BNMTF.all_G.shape == (iterations,J,L)
assert BNMTF.all_tau.shape == (iterations,)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert Fs[0,i,k] != F_prior[i,k]
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert Ss[0,k,l] != S_prior[k,l]
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert Gs[0,j,l] != G_prior[j,l]
assert taus[1] != alpha/float(beta)
def test_approx_expectation():
burn_in = 2
thinning = 3 # so index 2,5,8 -> m=3,m=6,m=9
(I,J,K,L) = (5,3,2,4)
Fs = [numpy.ones((I,K)) * 3*m**2 for m in range(1,10+1)]
Ss = [numpy.ones((K,L)) * 2*m**2 for m in range(1,10+1)]
Gs = [numpy.ones((J,L)) * 1*m**2 for m in range(1,10+1)] #first is 1's, second is 4's, third is 9's, etc.
taus = [m**2 for m in range(1,10+1)]
expected_exp_tau = (9.+36.+81.)/3.
expected_exp_F = 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_S = 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.),(9.+36.+81.)*(2./3.),(9.+36.+81.)*(2./3.)]])
expected_exp_G = numpy.array([[(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.)],[(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.)],[(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.),(9.+36.+81.)*(1./3.)]])
R = numpy.ones((I,J))
M = numpy.ones((I,J))
lambdaF = 2*numpy.ones((I,K))
lambdaS = 3*numpy.ones((K,L))
lambdaG = 4*numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.all_F = Fs
BNMTF.all_S = Ss
BNMTF.all_G = Gs
BNMTF.all_tau = taus
(exp_F, exp_S, exp_G, exp_tau) = BNMTF.approx_expectation(burn_in,thinning)
assert expected_exp_tau == exp_tau
assert numpy.array_equal(expected_exp_F,exp_F)
assert numpy.array_equal(expected_exp_S,exp_S)
assert numpy.array_equal(expected_exp_G,exp_G)
def test_compute_statistics():
R = numpy.array([[1, 2], [3, 4]], dtype=float)
M = numpy.array([[1, 1], [0, 1]])
I, J, K, L = 2, 2, 3, 4
lambdaF = 2 * numpy.ones((I, K))
lambdaS = 3 * numpy.ones((K, L))
lambdaG = 4 * numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, 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 == BNMTF.compute_MSE(M_pred, R, R_pred)
assert R2_pred == BNMTF.compute_R2(M_pred, R, R_pred)
assert Rp_pred == BNMTF.compute_Rp(M_pred, R, R_pred)
def test_tauG():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
# F*S = [[1/3]], (F*S)^2 = [[1/9]], sum_i F*S = [[4/9]]
tauG = 3.*numpy.array([[4./9.,4./9.,4./9.,4./9.],[4./9.,4./9.,4./9.,4./9.],[4./9.,4./9.,4./9.,4./9.]])
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.tauG(l)[j] == tauG[j,l]
def test_tauS():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
# F outer G = [[1/10]], (F outer G)^2 = [[1/100]], sum (F outer G)^2 = [[12/100]]
tauS = 3.*numpy.array([[3./25.,3./25.,3./25.,3./25.],[3./25.,3./25.,3./25.,3./25.]])
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert abs(BNMTF.tauS(k,l) - tauS[k,l]) < 0.000000000000001
def test_tauF():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
# S*G.T = [[4/15]], (S*G.T)^2 = [[16/225]], sum_j S*G.T = [[32/225,32/225],[48/225,48/225],[32/225,32/225],[32/225,32/225],[48/225,48/225]]
tauF = 3.*numpy.array([[32./225.,32./225.],[48./225.,48./225.],[32./225.,32./225.],[32./225.,32./225.],[48./225.,48./225.]])
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert abs(BNMTF.tauF(k)[i] - tauF[i,k]) < 0.000000000000001
def test_tauS():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
# F outer G = [[1/10]], (F outer G)^2 = [[1/100]], sum (F outer G)^2 = [[12/100]]
tauS = 3. * numpy.array([[3. / 25., 3. / 25., 3. / 25., 3. / 25.],
[3. / 25., 3. / 25., 3. / 25., 3. / 25.]])
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert abs(BNMTF.tauS(k, l) - tauS[k, l]) < 0.000000000000001
def test_predict():
burn_in = 2
thinning = 3 # so index 2,5,8 -> m=3,m=6,m=9
(I, J, K, L) = (5, 3, 2, 4)
Fs = [numpy.ones((I, K)) * 3 * m**2 for m in range(1, 10 + 1)]
Ss = [numpy.ones((K, L)) * 2 * m**2 for m in range(1, 10 + 1)]
Gs = [numpy.ones((J, L)) * 1 * m**2 for m in range(1, 10 + 1)
] #first is 1's, second is 4's, third is 9's, etc.
Fs[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))
lambdaF = 2 * numpy.ones((I, K))
lambdaS = 3 * numpy.ones((K, L))
lambdaG = 5 * numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
#expected_exp_F = numpy.array([[125.,126.],[126.,126.],[126.,126.],[126.,126.],[126.,126.]])
#expected_exp_S = numpy.array([[84.,84.,84.,84.],[84.,84.,84.,84.]])
#expected_exp_G = numpy.array([[42.,42.,42.,42.],[42.,42.,42.,42.],[42.,42.,42.,42.]])
#R_pred = numpy.array([[ 3542112., 3542112., 3542112.],[ 3556224., 3556224., 3556224.],[ 3556224., 3556224., 3556224.],[ 3556224., 3556224., 3556224.],[ 3556224., 3556224., 3556224.]])
M_test = numpy.array(
[[0, 0, 1], [0, 1, 0], [0, 0, 0], [1, 1, 0],
[0, 0, 0]]) #R->3,5,10,11, R_pred->3542112,3556224,3556224,3556224
MSE = ((3. - 3542112.)**2 + (5. - 3556224.)**2 + (10. - 3556224.)**2 +
(11. - 3556224.)**2) / 4.
R2 = 1. - ((3. - 3542112.)**2 + (5. - 3556224.)**2 + (10. - 3556224.)**2 +
(11. - 3556224.)**2) / (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=3552696,var_pred=5292, corr=(-4.25*-63 + -2.25*21 + 2.75*21 + 3.75*21)
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.all_F = Fs
BNMTF.all_S = Ss
BNMTF.all_G = Gs
BNMTF.all_tau = taus
performances = BNMTF.predict(M_test, burn_in, thinning)
assert performances['MSE'] == MSE
assert performances['R^2'] == R2
assert performances['Rp'] == Rp
def test_tauG():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
# F*S = [[1/3]], (F*S)^2 = [[1/9]], sum_i F*S = [[4/9]]
tauG = 3. * numpy.array([[4. / 9., 4. / 9., 4. / 9., 4. / 9.],
[4. / 9., 4. / 9., 4. / 9., 4. / 9.],
[4. / 9., 4. / 9., 4. / 9., 4. / 9.]])
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.tauG(l)[j] == tauG[j, l]
def test_muG():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
tauG = 3.*numpy.array([[4./9.,4./9.,4./9.,4./9.],[4./9.,4./9.,4./9.,4./9.],[4./9.,4./9.,4./9.,4./9.]])
# Rij - Fi*S*Gj + Gjl*(Fi*Sl)) = 11/15 + 1/5 * 1/3 = 12/15 = 4/5
# (Rij - Fi*S*Gj + Gjl*(Fi*Sl)) * (Fi*Sl) = 4/5 * 1/3 = 4/15
muG = 1./tauG * ( 3. * numpy.array([[4.*4./15.,4.*4./15.,4.*4./15.,4.*4./15.],[4.*4./15.,4.*4./15.,4.*4./15.,4.*4./15.],[4.*4./15.,4.*4./15.,4.*4./15.,4.*4./15.]]) - lambdaG )
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert abs(BNMTF.muG(tauG[:,l],l)[j] - muG[j,l]) < 0.000000000000001
def test_muS():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
tauS = 3.*numpy.array([[3./25.,3./25.,3./25.,3./25.],[3./25.,3./25.,3./25.,3./25.]])
# Rij - Fi*S*Gj + Fik*Skl*Gjk = 11/15 + 1/2*1/3*1/5 = 23/30
# (Rij - Fi*S*Gj + Fik*Skl*Gjk) * Fik*Gjk = 23/30 * 1/10 = 23/300
muS = 1./tauS * ( 3. * numpy.array([[12*23./300.,12*23./300.,12*23./300.,12*23./300.],[12*23./300.,12*23./300.,12*23./300.,12*23./300.]]) - lambdaS )
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert abs(BNMTF.muS(tauS[k,l],k,l) - muS[k,l]) < 0.000000000000001
def test_muF():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
tauF = 3.*numpy.array([[32./225.,32./225.],[48./225.,48./225.],[32./225.,32./225.],[32./225.,32./225.],[48./225.,48./225.]])
# Rij - Fi*S*Gj + Fik(Sk*Gj) = 11/15 + 1/2 * 4/15 = 13/15
# (Rij - Fi*S*Gj + Fik(Sk*Gj)) * (Sk*Gj) = 13/15 * 4/15 = 52/225
muF = 1./tauF * ( 3. * numpy.array([[2*(52./225.),2*(52./225.)],[3*(52./225.),3*(52./225.)],[2*(52./225.),2*(52./225.)],[2*(52./225.),2*(52./225.)],[3*(52./225.),3*(52./225.)]]) - lambdaF )
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert abs(BNMTF.muF(tauF[:,k],k)[i] - muF[i,k]) < 0.000000000000001
def test_tauF():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
# S*G.T = [[4/15]], (S*G.T)^2 = [[16/225]], sum_j S*G.T = [[32/225,32/225],[48/225,48/225],[32/225,32/225],[32/225,32/225],[48/225,48/225]]
tauF = 3. * numpy.array([[32. / 225., 32. / 225.], [
48. / 225., 48. / 225.
], [32. / 225., 32. / 225.], [32. / 225., 32. / 225.],
[48. / 225., 48. / 225.]])
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert abs(BNMTF.tauF(k)[i] - tauF[i, k]) < 0.000000000000001
def test_muS():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
tauS = 3. * numpy.array([[3. / 25., 3. / 25., 3. / 25., 3. / 25.],
[3. / 25., 3. / 25., 3. / 25., 3. / 25.]])
# Rij - Fi*S*Gj + Fik*Skl*Gjk = 11/15 + 1/2*1/3*1/5 = 23/30
# (Rij - Fi*S*Gj + Fik*Skl*Gjk) * Fik*Gjk = 23/30 * 1/10 = 23/300
muS = 1. / tauS * (3. * numpy.array([[
12 * 23. / 300., 12 * 23. / 300., 12 * 23. / 300., 12 * 23. / 300.
], [12 * 23. / 300., 12 * 23. / 300., 12 * 23. / 300., 12 * 23. / 300.]]) -
lambdaS)
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert abs(BNMTF.muS(tauS[k, l], k, l) - muS[k, l]) < 0.000000000000001
def test_muG():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
tauG = 3. * numpy.array([[4. / 9., 4. / 9., 4. / 9., 4. / 9.],
[4. / 9., 4. / 9., 4. / 9., 4. / 9.],
[4. / 9., 4. / 9., 4. / 9., 4. / 9.]])
# Rij - Fi*S*Gj + Gjl*(Fi*Sl)) = 11/15 + 1/5 * 1/3 = 12/15 = 4/5
# (Rij - Fi*S*Gj + Gjl*(Fi*Sl)) * (Fi*Sl) = 4/5 * 1/3 = 4/15
muG = 1. / tauG * (3. * numpy.array(
[[4. * 4. / 15., 4. * 4. / 15., 4. * 4. / 15., 4. * 4. / 15.],
[4. * 4. / 15., 4. * 4. / 15., 4. * 4. / 15., 4. * 4. / 15.],
[4. * 4. / 15., 4. * 4. / 15., 4. * 4. / 15., 4. * 4. / 15.]]) -
lambdaG)
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert abs(BNMTF.muG(tauG[:, l], l)[j] - muG[j, l]) < 0.000000000000001
def test_muF():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
tauF = 3. * numpy.array([[32. / 225., 32. / 225.], [
48. / 225., 48. / 225.
], [32. / 225., 32. / 225.], [32. / 225., 32. / 225.],
[48. / 225., 48. / 225.]])
# Rij - Fi*S*Gj + Fik(Sk*Gj) = 11/15 + 1/2 * 4/15 = 13/15
# (Rij - Fi*S*Gj + Fik(Sk*Gj)) * (Sk*Gj) = 13/15 * 4/15 = 52/225
muF = 1. / tauF * (3. * numpy.array(
[[2 * (52. / 225.), 2 *
(52. / 225.)], [3 * (52. / 225.), 3 *
(52. / 225.)], [2 * (52. / 225.), 2 * (52. / 225.)],
[2 * (52. / 225.), 2 *
(52. / 225.)], [3 * (52. / 225.), 3 * (52. / 225.)]]) - lambdaF)
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert abs(BNMTF.muF(tauF[:, k], k)[i] - muF[i, k]) < 0.000000000000001
def test_run():
I, J, K, L = 10, 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
lambdaF = 2 * numpy.ones((I, K))
lambdaS = 3 * numpy.ones((K, L))
lambdaG = 4 * numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
init = 'exp' #F=1/2,S=1/3,G=1/4
F_prior = numpy.ones((I, K)) / 2.
S_prior = numpy.ones((K, L)) / 3.
G_prior = numpy.ones((J, L)) / 4.
iterations = 15
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init)
(Fs, Ss, Gs, taus) = BNMTF.run(iterations)
assert BNMTF.all_F.shape == (iterations, I, K)
assert BNMTF.all_S.shape == (iterations, K, L)
assert BNMTF.all_G.shape == (iterations, J, L)
assert BNMTF.all_tau.shape == (iterations, )
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert Fs[0, i, k] != F_prior[i, k]
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert Ss[0, k, l] != S_prior[k, l]
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert Gs[0, j, l] != G_prior[j, l]
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, L = 2, 2, 3, 4
lambdaF = 2*numpy.ones((I,K))
lambdaS = 3*numpy.ones((K,L))
lambdaG = 4*numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,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 == BNMTF.compute_MSE(M_pred,R,R_pred)
assert R2_pred == BNMTF.compute_R2(M_pred,R,R_pred)
assert Rp_pred == BNMTF.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,L) = (5,3,2,4)
Fs = [numpy.ones((I,K)) * 3*m**2 for m in range(1,10+1)]
Ss = [numpy.ones((K,L)) * 2*m**2 for m in range(1,10+1)]
Gs = [numpy.ones((J,L)) * 1*m**2 for m in range(1,10+1)] #first is 1's, second is 4's, third is 9's, etc.
Fs[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))
lambdaF = 2*numpy.ones((I,K))
lambdaS = 3*numpy.ones((K,L))
lambdaG = 5*numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
#expected_exp_F = numpy.array([[125.,126.],[126.,126.],[126.,126.],[126.,126.],[126.,126.]])
#expected_exp_S = numpy.array([[84.,84.,84.,84.],[84.,84.,84.,84.]])
#expected_exp_G = numpy.array([[42.,42.,42.,42.],[42.,42.,42.,42.],[42.,42.,42.,42.]])
#R_pred = numpy.array([[ 3542112., 3542112., 3542112.],[ 3556224., 3556224., 3556224.],[ 3556224., 3556224., 3556224.],[ 3556224., 3556224., 3556224.],[ 3556224., 3556224., 3556224.]])
M_test = numpy.array([[0,0,1],[0,1,0],[0,0,0],[1,1,0],[0,0,0]]) #R->3,5,10,11, R_pred->3542112,3556224,3556224,3556224
MSE = ((3.-3542112.)**2 + (5.-3556224.)**2 + (10.-3556224.)**2 + (11.-3556224.)**2) / 4.
R2 = 1. - ((3.-3542112.)**2 + (5.-3556224.)**2 + (10.-3556224.)**2 + (11.-3556224.)**2) / (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=3552696,var_pred=5292, corr=(-4.25*-63 + -2.25*21 + 2.75*21 + 3.75*21)
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.all_F = Fs
BNMTF.all_S = Ss
BNMTF.all_G = Gs
BNMTF.all_tau = taus
performances = BNMTF.predict(M_test,burn_in,thinning)
assert performances['MSE'] == MSE
assert performances['R^2'] == R2
assert performances['Rp'] == Rp
def test_log_likelihood():
R = numpy.array([[1, 2], [3, 4]], dtype=float)
M = numpy.array([[1, 1], [0, 1]])
I, J, K, L = 2, 2, 3, 4
lambdaF = 2 * numpy.ones((I, K))
lambdaS = 3 * numpy.ones((K, L))
lambdaG = 4 * numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
iterations = 10
burnin, thinning = 4, 2
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.all_F = [numpy.ones((I, K)) for i in range(0, iterations)]
BNMTF.all_S = [2 * numpy.ones((K, L)) for i in range(0, iterations)]
BNMTF.all_G = [3 * numpy.ones((J, L)) for i in range(0, iterations)]
BNMTF.all_tau = [3. for i in range(0, iterations)]
# expU*expV.T = [[72.]]
log_likelihood = 3. / 2. * (math.log(3) - math.log(
2 * math.pi)) - 3. / 2. * (71**2 + 70**2 + 68**2)
AIC = -2 * log_likelihood + 2 * (2 * 3 + 3 * 4 + 2 * 4)
BIC = -2 * log_likelihood + (2 * 3 + 3 * 4 + 2 * 4) * math.log(3)
MSE = (71**2 + 70**2 + 68**2) / 3.
assert log_likelihood == BNMTF.quality('loglikelihood', burnin, thinning)
assert AIC == BNMTF.quality('AIC', burnin, thinning)
assert BIC == BNMTF.quality('BIC', burnin, thinning)
assert MSE == BNMTF.quality('MSE', burnin, thinning)
with pytest.raises(AssertionError) as error:
BNMTF.quality('FAIL', burnin, thinning)
assert str(error.value) == "Unrecognised metric for model quality: FAIL."
def test_initialise():
I, J, K, L = 5, 3, 2, 4
R = numpy.ones((I, J))
M = numpy.ones((I, J))
lambdaF = 2 * numpy.ones((I, K))
lambdaS = 3 * numpy.ones((K, L))
lambdaG = 4 * numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
# First do a random initialisation - we can then only check whether values are correctly initialised
init_S = 'random'
init_FG = 'random'
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
assert BNMTF.tau >= 0.0
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMTF.F[i, k] >= 0.0
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.S[k, l] >= 0.0
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.G[j, l] >= 0.0
# Initialisation of S using random draws from prior
init_S, init_FG = 'random', 'exp'
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMTF.F[i, k] == 1. / lambdaF[i, k]
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.S[k, l] != 1. / lambdaS[
k, l] # test whether we overwrote the expectation
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.G[j, l] == 1. / lambdaG[j, l]
# Initialisation of F and G using random draws from prior
init_S, init_FG = 'exp', 'random'
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMTF.F[i, k] != 1. / lambdaF[
i, k] # test whether we overwrote the expectation
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.S[k, l] == 1. / lambdaS[k, l]
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.G[j, l] != 1. / lambdaG[
j, l] # test whether we overwrote the expectation
# Initialisation of F and G using Kmeans
init_S, init_FG = 'exp', 'kmeans'
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMTF.F[i, k] == 0.2 or BNMTF.F[i, k] == 1.2
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.G[j, l] == 0.2 or BNMTF.G[j, l] == 1.2
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.S[k, l] == 1. / lambdaS[k, l]
def test_approx_expectation():
burn_in = 2
thinning = 3 # so index 2,5,8 -> m=3,m=6,m=9
(I, J, K, L) = (5, 3, 2, 4)
Fs = [numpy.ones((I, K)) * 3 * m**2 for m in range(1, 10 + 1)]
Ss = [numpy.ones((K, L)) * 2 * m**2 for m in range(1, 10 + 1)]
Gs = [numpy.ones((J, L)) * 1 * m**2 for m in range(1, 10 + 1)
] #first is 1's, second is 4's, third is 9's, etc.
taus = [m**2 for m in range(1, 10 + 1)]
expected_exp_tau = (9. + 36. + 81.) / 3.
expected_exp_F = 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_S = 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.),
(9. + 36. + 81.) * (2. / 3.),
(9. + 36. + 81.) * (2. / 3.)]])
expected_exp_G = numpy.array([[(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.)],
[(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.)],
[(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.),
(9. + 36. + 81.) * (1. / 3.)]])
R = numpy.ones((I, J))
M = numpy.ones((I, J))
lambdaF = 2 * numpy.ones((I, K))
lambdaS = 3 * numpy.ones((K, L))
lambdaG = 4 * numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.all_F = Fs
BNMTF.all_S = Ss
BNMTF.all_G = Gs
BNMTF.all_tau = taus
(exp_F, exp_S, exp_G,
exp_tau) = BNMTF.approx_expectation(burn_in, thinning)
assert expected_exp_tau == exp_tau
assert numpy.array_equal(expected_exp_F, exp_F)
assert numpy.array_equal(expected_exp_S, exp_S)
assert numpy.array_equal(expected_exp_G, exp_G)
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,L = 5,3,1,2
lambdaF = numpy.ones((I,K))
lambdaS = numpy.ones((K,L))
lambdaG = numpy.ones((J,L))
alpha, beta = 3, 1
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R1,M,K,L,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:
bnmtf_gibbs_optimised(R2,M,K,L,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:
bnmtf_gibbs_optimised(R3,M,K,L,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 lambdaF, lambdaS, lambdaG
I,J,K,L = 2,3,1,2
R4 = numpy.ones((2,3))
lambdaF = numpy.ones((2+1,1))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4,M,K,L,priors)
assert str(error.value) == "Prior matrix lambdaF has the wrong shape: (3, 1) instead of (2, 1)."
lambdaF = numpy.ones((2,1))
lambdaS = numpy.ones((1+1,2+1))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4,M,K,L,priors)
assert str(error.value) == "Prior matrix lambdaS has the wrong shape: (2, 3) instead of (1, 2)."
lambdaS = numpy.ones((1,2))
lambdaG = numpy.ones((3,2+1))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4,M,K,L,priors)
assert str(error.value) == "Prior matrix lambdaG has the wrong shape: (3, 3) instead of (3, 2)."
# Test getting an exception if a row or column is entirely unknown
lambdaF = numpy.ones((I,K))
lambdaS = numpy.ones((K,L))
lambdaG = numpy.ones((J,L))
M1 = [[1,1,1],[0,0,0]]
M2 = [[1,1,0],[1,0,0]]
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4,M1,K,L,priors)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4,M2,K,L,priors)
assert str(error.value) == "Fully unobserved column in R, column 2."
# Finally, a successful case
I,J,K,L = 3,2,2,2
R5 = 2*numpy.ones((I,J))
lambdaF = numpy.ones((I,K))
lambdaS = numpy.ones((K,L))
lambdaG = numpy.ones((J,L))
M = numpy.ones((I,J))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
BNMTF = bnmtf_gibbs_optimised(R5,M,K,L,priors)
assert numpy.array_equal(BNMTF.R,R5)
assert numpy.array_equal(BNMTF.M,M)
assert BNMTF.I == I
assert BNMTF.J == J
assert BNMTF.K == K
assert BNMTF.L == L
assert BNMTF.size_Omega == I*J
assert BNMTF.alpha == alpha
assert BNMTF.beta == beta
assert numpy.array_equal(BNMTF.lambdaF,lambdaF)
assert numpy.array_equal(BNMTF.lambdaS,lambdaS)
assert numpy.array_equal(BNMTF.lambdaG,lambdaG)
# Test when lambdaF S G are integers
I,J,K,L = 3,2,2,2
R5 = 2*numpy.ones((I,J))
lambdaF = 3
lambdaS = 4
lambdaG = 5
M = numpy.ones((I,J))
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
BNMTF = bnmtf_gibbs_optimised(R5,M,K,L,priors)
assert numpy.array_equal(BNMTF.R,R5)
assert numpy.array_equal(BNMTF.M,M)
assert BNMTF.I == I
assert BNMTF.J == J
assert BNMTF.K == K
assert BNMTF.L == L
assert BNMTF.size_Omega == I*J
assert BNMTF.alpha == alpha
assert BNMTF.beta == beta
assert numpy.array_equal(BNMTF.lambdaF,3*numpy.ones((I,K)))
assert numpy.array_equal(BNMTF.lambdaS,4*numpy.ones((K,L)))
assert numpy.array_equal(BNMTF.lambdaG,5*numpy.ones((J,L)))
R = numpy.loadtxt(input_folder + "R.txt")
M = numpy.ones((I, J))
#M = numpy.loadtxt(input_folder+"M.txt")
M_test = calc_inverse_M(numpy.loadtxt(input_folder + "M.txt"))
# Run the VB algorithm, <repeats> times
times_repeats = []
performances_repeats = []
for i in range(0, repeats):
# Set all the seeds
numpy.random.seed(3)
random.seed(4)
scipy.random.seed(5)
# Run the classifier
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.run(iterations)
# Extract the performances and timestamps across all iterations
times_repeats.append(BNMTF.all_times)
performances_repeats.append(BNMTF.all_performances)
# Check whether seed worked: all performances should be the same
assert all([numpy.array_equal(performances, performances_repeats[0]) for performances in performances_repeats]), \
"Seed went wrong - performances not the same across repeats!"
# Print out the performances, and the average times
gibbs_all_times_average = list(numpy.average(times_repeats, axis=0))
gibbs_all_performances = performances_repeats[0]
print "gibbs_all_times_average = %s" % gibbs_all_times_average
lambdaF = numpy.ones((I, K)) / 10.
lambdaS = numpy.ones((K, L)) / 10.
lambdaG = numpy.ones((J, L)) / 10.
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
# Load in data
(_, X_min, M, _, _, _, _) = load_Sanger(standardised=standardised)
# Run the Gibbs sampler
BNMTF = bnmtf_gibbs_optimised(X_min, M, K, L, priors)
BNMTF.initialise(init_S=init_S, init_FG=init_FG)
BNMTF.run(iterations)
# Also measure the performances on the training data
performances = BNMTF.predict(M, burnin, thinning)
print performances
# Plot the tau expectation values to check convergence
plt.plot(BNMTF.all_tau)
# Print the performances across iterations (MSE)
print "all_performances = %s" % BNMTF.all_performances['MSE']
'''
all_performances = [21.421197768547213, 6.3583912411769443, 4.1905150872867791, 3.5061419879402549, 3.2401904945288589, 3.1061034167609085, 3.0317883467556381, 2.9898304967466904, 2.9597551532537403, 2.9383503871636449, 2.9254205069284884, 2.9174938663203092, 2.9099499161449942, 2.9062570985645522, 2.9031497813762694, 2.8996412733085539, 2.8933585834560027, 2.8895195553715656, 2.8857902380755402, 2.8826893976014194, 2.8818869316601061, 2.879167497739882, 2.8810542681772024, 2.8774833883780992, 2.8764204742423538, 2.8690108092204154, 2.8725197104371101, 2.8674899173730819, 2.8647480905877538, 2.8626898729711101, 2.8593806833372533, 2.8565979156668497, 2.8534557000365472, 2.8486892736477119, 2.8442410993582907, 2.8424692916558705, 2.8381512986523192, 2.8355096495142504, 2.8377105511241458, 2.8331943900354211, 2.8304945163441682, 2.8222371793873791, 2.8187736926904341, 2.8142125953486694, 2.8123009163914499, 2.8141234880524757, 2.8117717085995619, 2.8059703725159513, 2.8066421988610086, 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2.2797202598380553]
'''
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, L = 5, 3, 1, 2
lambdaF = numpy.ones((I, K))
lambdaS = numpy.ones((K, L))
lambdaG = numpy.ones((J, L))
alpha, beta = 3, 1
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R1, M, K, L, 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:
bnmtf_gibbs_optimised(R2, M, K, L, 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:
bnmtf_gibbs_optimised(R3, M, K, L, 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 lambdaF, lambdaS, lambdaG
I, J, K, L = 2, 3, 1, 2
R4 = numpy.ones((2, 3))
lambdaF = numpy.ones((2 + 1, 1))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4, M, K, L, priors)
assert str(
error.value
) == "Prior matrix lambdaF has the wrong shape: (3, 1) instead of (2, 1)."
lambdaF = numpy.ones((2, 1))
lambdaS = numpy.ones((1 + 1, 2 + 1))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4, M, K, L, priors)
assert str(
error.value
) == "Prior matrix lambdaS has the wrong shape: (2, 3) instead of (1, 2)."
lambdaS = numpy.ones((1, 2))
lambdaG = numpy.ones((3, 2 + 1))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4, M, K, L, priors)
assert str(
error.value
) == "Prior matrix lambdaG has the wrong shape: (3, 3) instead of (3, 2)."
# Test getting an exception if a row or column is entirely unknown
lambdaF = numpy.ones((I, K))
lambdaS = numpy.ones((K, L))
lambdaG = numpy.ones((J, L))
M1 = [[1, 1, 1], [0, 0, 0]]
M2 = [[1, 1, 0], [1, 0, 0]]
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4, M1, K, L, priors)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmtf_gibbs_optimised(R4, M2, K, L, priors)
assert str(error.value) == "Fully unobserved column in R, column 2."
# Finally, a successful case
I, J, K, L = 3, 2, 2, 2
R5 = 2 * numpy.ones((I, J))
lambdaF = numpy.ones((I, K))
lambdaS = numpy.ones((K, L))
lambdaG = numpy.ones((J, L))
M = numpy.ones((I, J))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
BNMTF = bnmtf_gibbs_optimised(R5, M, K, L, priors)
assert numpy.array_equal(BNMTF.R, R5)
assert numpy.array_equal(BNMTF.M, M)
assert BNMTF.I == I
assert BNMTF.J == J
assert BNMTF.K == K
assert BNMTF.L == L
assert BNMTF.size_Omega == I * J
assert BNMTF.alpha == alpha
assert BNMTF.beta == beta
assert numpy.array_equal(BNMTF.lambdaF, lambdaF)
assert numpy.array_equal(BNMTF.lambdaS, lambdaS)
assert numpy.array_equal(BNMTF.lambdaG, lambdaG)
# Test when lambdaF S G are integers
I, J, K, L = 3, 2, 2, 2
R5 = 2 * numpy.ones((I, J))
lambdaF = 3
lambdaS = 4
lambdaG = 5
M = numpy.ones((I, J))
priors = {
'alpha': alpha,
'beta': beta,
'lambdaF': lambdaF,
'lambdaS': lambdaS,
'lambdaG': lambdaG
}
BNMTF = bnmtf_gibbs_optimised(R5, M, K, L, priors)
assert numpy.array_equal(BNMTF.R, R5)
assert numpy.array_equal(BNMTF.M, M)
assert BNMTF.I == I
assert BNMTF.J == J
assert BNMTF.K == K
assert BNMTF.L == L
assert BNMTF.size_Omega == I * J
assert BNMTF.alpha == alpha
assert BNMTF.beta == beta
assert numpy.array_equal(BNMTF.lambdaF, 3 * numpy.ones((I, K)))
assert numpy.array_equal(BNMTF.lambdaS, 4 * numpy.ones((K, L)))
assert numpy.array_equal(BNMTF.lambdaG, 5 * numpy.ones((J, L)))
def test_alpha_s():
BNMTF = bnmtf_gibbs_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tau = 3.
alpha_s = alpha + 6.
assert BNMTF.alpha_s() == alpha_s
I, J, K, L = 622,139,10,5
init_S = 'random' #'exp' #
init_FG = 'kmeans' #'exp' #
alpha, beta = 1., 1.
lambdaF = numpy.ones((I,K))/10.
lambdaS = numpy.ones((K,L))/10.
lambdaG = numpy.ones((J,L))/10.
priors = { 'alpha':alpha, 'beta':beta, 'lambdaF':lambdaF, 'lambdaS':lambdaS, 'lambdaG':lambdaG }
# Load in data
(_,X_min,M,_,_,_,_) = load_Sanger(standardised=standardised)
# Run the Gibbs sampler
BNMTF = bnmtf_gibbs_optimised(X_min,M,K,L,priors)
BNMTF.initialise(init_S=init_S,init_FG=init_FG)
BNMTF.run(iterations)
# Also measure the performances on the training data
performances = BNMTF.predict(M,burnin,thinning)
print performances
# Plot the tau expectation values to check convergence
plt.plot(BNMTF.all_tau)
# Print the performances across iterations (MSE)
print "all_performances = %s" % BNMTF.all_performances['MSE']
'''
all_performances = [21.421197768547213, 6.3583912411769443, 4.1905150872867791, 3.5061419879402549, 3.2401904945288589, 3.1061034167609085, 3.0317883467556381, 2.9898304967466904, 2.9597551532537403, 2.9383503871636449, 2.9254205069284884, 2.9174938663203092, 2.9099499161449942, 2.9062570985645522, 2.9031497813762694, 2.8996412733085539, 2.8933585834560027, 2.8895195553715656, 2.8857902380755402, 2.8826893976014194, 2.8818869316601061, 2.879167497739882, 2.8810542681772024, 2.8774833883780992, 2.8764204742423538, 2.8690108092204154, 2.8725197104371101, 2.8674899173730819, 2.8647480905877538, 2.8626898729711101, 2.8593806833372533, 2.8565979156668497, 2.8534557000365472, 2.8486892736477119, 2.8442410993582907, 2.8424692916558705, 2.8381512986523192, 2.8355096495142504, 2.8377105511241458, 2.8331943900354211, 2.8304945163441682, 2.8222371793873791, 2.8187736926904341, 2.8142125953486694, 2.8123009163914499, 2.8141234880524757, 2.8117717085995619, 2.8059703725159513, 2.8066421988610086, 2.8055944223940736, 2.7997620244475629, 2.7982321373971564, 2.7983070728647377, 2.7970005782459055, 2.7979642884735307, 2.7950424452772769, 2.7929941875296747, 2.7881670598714097, 2.7871400065172396, 2.7816411365618094, 2.7818833625205426, 2.7744479857150077, 2.7730558648870067, 2.7711438261741677, 2.7718152242946443, 2.766961470633531, 2.7654244826300469, 2.7648775450099472, 2.759830401256282, 2.7604965970646158, 2.7565190544527352, 2.751721901129716, 2.7499851477712034, 2.7486851571379924, 2.7485557659818927, 2.7456710521803371, 2.7432921691336118, 2.7401237642034371, 2.7331482067432695, 2.7312389506051078, 2.7296576766624039, 2.7291115245357629, 2.7293278854136069, 2.7256303034532081, 2.7189792815582186, 2.7242246054550825, 2.7207063083185834, 2.7200853566998937, 2.7126052328111712, 2.7104206931618524, 2.7081642594411091, 2.7073972104837329, 2.7086208242493455, 2.7063489671878553, 2.7045511903566073, 2.700216589322828, 2.6985049679557624, 2.6985730146085505, 2.6962894918501195, 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2.2835538965411621, 2.2805643086175853, 2.2816775531981648, 2.2825254787572318, 2.2811948782264153, 2.2825146344990497, 2.282754111903103, 2.2830908596699824, 2.2812709387001231, 2.2819972410443086, 2.2818875430567309, 2.2825457949765755, 2.2824629557105252, 2.2838960229814922, 2.2803418045361354, 2.2826600731156175, 2.2813350704033679, 2.2807526587456661, 2.2828164394800421, 2.2851422417793446, 2.2809753873876679, 2.2812822991999315, 2.2823394535889605, 2.2835923142160741, 2.2829732001482363, 2.2796921617443617, 2.2841529004742158, 2.2799784011382194, 2.2820589274177463, 2.2813805541757177, 2.280464881304062, 2.2807335174580259, 2.2818007471503763, 2.2816039765172125, 2.2782487208983784, 2.2781263239720144, 2.2820882923159114, 2.2821401768336869, 2.2789695945552166, 2.2791322615876193, 2.2797851108479716, 2.2819833638823281, 2.2821960942913475, 2.2809085038292123, 2.2799407423350004, 2.2814388033860018, 2.2775334764834683, 2.2816922200030416, 2.2811528164968875, 2.2801223657401284, 2.2797202598380553]
def test_alpha_s():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
alpha_s = alpha + 6.
assert BNMTF.alpha_s() == alpha_s
all_R.append(R)
# We now run the VB 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 = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMF.initialise(init_S,init_FG)
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)
def test_beta_s():
BNMTF = bnmtf_gibbs_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tau = 3.
beta_s = beta + .5*(12*(11./15.)**2) #F*S = [[1/6+1/6=1/3,..]], F*S*G^T = [[1/15*4=4/15,..]]
assert abs(BNMTF.beta_s() - beta_s) < 0.00000000000001
