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
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 }
expF = numpy.array([[125.,126.],[126.,126.],[126.,126.],[126.,126.],[126.,126.]])
expS = numpy.array([[84.,84.,84.,84.],[84.,84.,84.,84.]])
expG = numpy.array([[42.,42.,42.,42.],[42.,42.,42.,42.],[42.,42.,42.,42.]])
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_vb_optimised(R,M,K,L,priors)
BNMTF.expF = expF
BNMTF.expS = expS
BNMTF.expG = expG
performances = BNMTF.predict(M_test)
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 }
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.expF = numpy.ones((I,K))
BNMTF.expS = 2*numpy.ones((K,L))
BNMTF.expG = 3*numpy.ones((J,L))
BNMTF.explogtau = 5.
BNMTF.exptau = 3.
# expU*expV.T = [[72.]]
log_likelihood = 3./2.*(5.-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')
assert AIC == BNMTF.quality('AIC')
assert BIC == BNMTF.quality('BIC')
assert MSE == BNMTF.quality('MSE')
with pytest.raises(AssertionError) as error:
BNMTF.quality('FAIL')
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, 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_vb_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_update_F():
for k in range(0,K):
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.muF = numpy.zeros((I,K))
BNMTF.tauF = numpy.zeros((I,K))
BNMTF.expF = 1./lambdaF #[[1./2.]]
BNMTF.expS = 1./lambdaS #[[1./3.]]
BNMTF.expG = 1./lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I,K))*2 #[[2.]]
BNMTF.varS = numpy.ones((K,L))*3 #[[3.]]
BNMTF.varG = numpy.ones((J,L))*4 #[[4.]]
BNMTF.exptau = 3.
BNMTF.update_F(k)
for i in range(0,I):
tauFik = 3. * sum([
sum([BNMTF.expS[k,l]*BNMTF.expG[j,l] for l in range(0,L)])**2 \
+ sum([(BNMTF.varS[k,l]+BNMTF.expS[k,l]**2)*(BNMTF.varG[j,l]+BNMTF.expG[j,l]**2) - BNMTF.expS[k,l]**2*BNMTF.expG[j,l]**2 for l in range(0,L)])
for j in range(0,J) if M[i,j]])
muFik = 1./tauFik * (-lambdaF[i,k] + BNMTF.exptau * sum([
sum([BNMTF.expS[k,l]*BNMTF.expG[j,l] for l in range(0,L)]) * \
(R[i,j] - sum([BNMTF.expF[i,kp]*BNMTF.expS[kp,l]*BNMTF.expG[j,l] for kp,l in itertools.product(xrange(0,K),xrange(0,L)) if kp != k]))
- sum([
BNMTF.expS[k,l] * BNMTF.varG[j,l] * sum([BNMTF.expF[i,kp] * BNMTF.expS[kp,l] for kp in range(0,K) if kp != k])
for l in range(0,L)])
for j in range(0,J) if M[i,j]]))
assert BNMTF.tauF[i,k] == tauFik
assert abs(BNMTF.muF[i,k] - muFik) < 0.00000000000000001
def test_update_G():
for l in range(0, L):
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.muG = numpy.zeros((J, L))
BNMTF.tauG = numpy.zeros((J, L))
BNMTF.expF = 1. / lambdaF #[[1./2.]]
BNMTF.expS = 1. / lambdaS #[[1./3.]]
BNMTF.expG = 1. / lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I, K)) * 2 #[[2.]]
BNMTF.varS = numpy.ones((K, L)) * 3 #[[3.]]
BNMTF.varG = numpy.ones((J, L)) * 4 #[[4.]]
BNMTF.exptau = 3.
BNMTF.update_G(l)
for j in range(0, J):
tauGjl = 3. * sum([
sum([BNMTF.expF[i,k]*BNMTF.expS[k,l] for k in range(0,K)])**2 \
+ sum([(BNMTF.varS[k,l]+BNMTF.expS[k,l]**2)*(BNMTF.varF[i,k]+BNMTF.expF[i,k]**2) - BNMTF.expS[k,l]**2*BNMTF.expF[i,k]**2 for k in range(0,K)])
for i in range(0,I) if M[i,j]])
muGjl = 1./tauGjl * (-lambdaG[j,l] + BNMTF.exptau * sum([
sum([BNMTF.expF[i,k]*BNMTF.expS[k,l] for k in range(0,K)]) * \
(R[i,j] - sum([BNMTF.expF[i,k]*BNMTF.expS[k,lp]*BNMTF.expG[j,lp] for k,lp in itertools.product(xrange(0,K),xrange(0,L)) if lp != l]))
- sum([
BNMTF.varF[i,k] * BNMTF.expS[k,l] * sum([BNMTF.expS[k,lp] * BNMTF.expG[j,lp] for lp in range(0,L) if lp != l])
for k in range(0,K)])
for i in range(0,I) if M[i,j]]))
assert BNMTF.tauG[j, l] == tauGjl
assert BNMTF.muG[j, l] == muGjl
def test_update_G():
for l in range(0,L):
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.muG = numpy.zeros((J,L))
BNMTF.tauG = numpy.zeros((J,L))
BNMTF.expF = 1./lambdaF #[[1./2.]]
BNMTF.expS = 1./lambdaS #[[1./3.]]
BNMTF.expG = 1./lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I,K))*2 #[[2.]]
BNMTF.varS = numpy.ones((K,L))*3 #[[3.]]
BNMTF.varG = numpy.ones((J,L))*4 #[[4.]]
BNMTF.exptau = 3.
BNMTF.update_G(l)
for j in range(0,J):
tauGjl = 3. * sum([
sum([BNMTF.expF[i,k]*BNMTF.expS[k,l] for k in range(0,K)])**2 \
+ sum([(BNMTF.varS[k,l]+BNMTF.expS[k,l]**2)*(BNMTF.varF[i,k]+BNMTF.expF[i,k]**2) - BNMTF.expS[k,l]**2*BNMTF.expF[i,k]**2 for k in range(0,K)])
for i in range(0,I) if M[i,j]])
muGjl = 1./tauGjl * (-lambdaG[j,l] + BNMTF.exptau * sum([
sum([BNMTF.expF[i,k]*BNMTF.expS[k,l] for k in range(0,K)]) * \
(R[i,j] - sum([BNMTF.expF[i,k]*BNMTF.expS[k,lp]*BNMTF.expG[j,lp] for k,lp in itertools.product(xrange(0,K),xrange(0,L)) if lp != l]))
- sum([
BNMTF.varF[i,k] * BNMTF.expS[k,l] * sum([BNMTF.expS[k,lp] * BNMTF.expG[j,lp] for lp in range(0,L) if lp != l])
for k in range(0,K)])
for i in range(0,I) if M[i,j]]))
assert BNMTF.tauG[j,l] == tauGjl
assert BNMTF.muG[j,l] == muGjl
def test_update_S():
for k, l in itertools.product(range(0, K), range(0, L)):
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.muS = numpy.zeros((K, L))
BNMTF.tauS = numpy.zeros((K, L))
BNMTF.expF = 1. / lambdaF #[[1./2.]]
BNMTF.expS = 1. / lambdaS #[[1./3.]]
BNMTF.expG = 1. / lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I, K)) * 2 #[[2.]]
BNMTF.varS = numpy.ones((K, L)) * 3 #[[3.]]
BNMTF.varG = numpy.ones((J, L)) * 4 #[[4.]]
BNMTF.exptau = 3.
BNMTF.update_S(k, l)
tauSkl = 3. * sum([
BNMTF.expF[i,k]**2 * BNMTF.expG[j,l]**2 \
+ (BNMTF.varF[i,k]+BNMTF.expF[i,k]**2)*(BNMTF.varG[j,l]+BNMTF.expG[j,l]**2) - BNMTF.expF[i,k]**2*BNMTF.expG[j,l]**2
for i,j in itertools.product(xrange(0,I),xrange(0,J)) if M[i,j]])
muSkl = 1. / tauSkl * (-lambdaS[k, l] + BNMTF.exptau * sum([
BNMTF.expF[i, k] * BNMTF.expG[j, l] * (R[i, j] - sum([
BNMTF.expF[i, kp] * BNMTF.expS[kp, lp] * BNMTF.expG[j, lp]
for kp, lp in itertools.product(xrange(0, K), xrange(0, L)) if
(kp != k or lp != l)
])) - BNMTF.varF[i, k] * BNMTF.expG[j, l] * sum([
BNMTF.expS[k, lp] * BNMTF.expG[j, lp]
for lp in range(0, L) if lp != l
]) - BNMTF.expF[i, k] * BNMTF.varG[j, l] * sum([
BNMTF.expF[i, kp] * BNMTF.expS[kp, l]
for kp in range(0, K) if kp != k
]) for i, j in itertools.product(xrange(0, I), xrange(0, J))
if M[i, j]
]))
assert BNMTF.tauS[k, l] == tauSkl
assert abs(BNMTF.muS[k, l] - muSkl) < 0.0000000000000001
def test_update_F():
for k in range(0, K):
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.muF = numpy.zeros((I, K))
BNMTF.tauF = numpy.zeros((I, K))
BNMTF.expF = 1. / lambdaF #[[1./2.]]
BNMTF.expS = 1. / lambdaS #[[1./3.]]
BNMTF.expG = 1. / lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I, K)) * 2 #[[2.]]
BNMTF.varS = numpy.ones((K, L)) * 3 #[[3.]]
BNMTF.varG = numpy.ones((J, L)) * 4 #[[4.]]
BNMTF.exptau = 3.
BNMTF.update_F(k)
for i in range(0, I):
tauFik = 3. * sum([
sum([BNMTF.expS[k,l]*BNMTF.expG[j,l] for l in range(0,L)])**2 \
+ sum([(BNMTF.varS[k,l]+BNMTF.expS[k,l]**2)*(BNMTF.varG[j,l]+BNMTF.expG[j,l]**2) - BNMTF.expS[k,l]**2*BNMTF.expG[j,l]**2 for l in range(0,L)])
for j in range(0,J) if M[i,j]])
muFik = 1./tauFik * (-lambdaF[i,k] + BNMTF.exptau * sum([
sum([BNMTF.expS[k,l]*BNMTF.expG[j,l] for l in range(0,L)]) * \
(R[i,j] - sum([BNMTF.expF[i,kp]*BNMTF.expS[kp,l]*BNMTF.expG[j,l] for kp,l in itertools.product(xrange(0,K),xrange(0,L)) if kp != k]))
- sum([
BNMTF.expS[k,l] * BNMTF.varG[j,l] * sum([BNMTF.expF[i,kp] * BNMTF.expS[kp,l] for kp in range(0,K) if kp != k])
for l in range(0,L)])
for j in range(0,J) if M[i,j]]))
assert BNMTF.tauF[i, k] == tauFik
assert abs(BNMTF.muF[i, k] - muFik) < 0.00000000000000001
def test_update_S():
for k,l in itertools.product(range(0,K),range(0,L)):
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.muS = numpy.zeros((K,L))
BNMTF.tauS = numpy.zeros((K,L))
BNMTF.expF = 1./lambdaF #[[1./2.]]
BNMTF.expS = 1./lambdaS #[[1./3.]]
BNMTF.expG = 1./lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I,K))*2 #[[2.]]
BNMTF.varS = numpy.ones((K,L))*3 #[[3.]]
BNMTF.varG = numpy.ones((J,L))*4 #[[4.]]
BNMTF.exptau = 3.
BNMTF.update_S(k,l)
tauSkl = 3. * sum([
BNMTF.expF[i,k]**2 * BNMTF.expG[j,l]**2 \
+ (BNMTF.varF[i,k]+BNMTF.expF[i,k]**2)*(BNMTF.varG[j,l]+BNMTF.expG[j,l]**2) - BNMTF.expF[i,k]**2*BNMTF.expG[j,l]**2
for i,j in itertools.product(xrange(0,I),xrange(0,J)) if M[i,j]])
muSkl = 1./tauSkl * (-lambdaS[k,l] + BNMTF.exptau * sum([
BNMTF.expF[i,k]*BNMTF.expG[j,l]*(R[i,j] - sum([BNMTF.expF[i,kp]*BNMTF.expS[kp,lp]*BNMTF.expG[j,lp] for kp,lp in itertools.product(xrange(0,K),xrange(0,L)) if (kp != k or lp != l)]))
- BNMTF.varF[i,k] * BNMTF.expG[j,l] * sum([BNMTF.expS[k,lp] * BNMTF.expG[j,lp] for lp in range(0,L) if lp != l])
- BNMTF.expF[i,k] * BNMTF.varG[j,l] * sum([BNMTF.expF[i,kp] * BNMTF.expS[kp,l] for kp in range(0,K) if kp != k])
for i,j in itertools.product(xrange(0,I),xrange(0,J)) if M[i,j]]))
assert BNMTF.tauS[k,l] == tauSkl
assert abs(BNMTF.muS[k,l] - muSkl) < 0.0000000000000001
def test_update_exp_S():
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tauS = 4*numpy.ones((K,L)) # muS = [[1./3.]], tauS = [[4.]]
BNMTF.update_exp_S(k,l) #-mu*sqrt(tau) = -2./3., lambda(..) = 0.319448 / (1-0.2525) = 0.4273551839464883, gamma =
assert abs(BNMTF.expS[k,l] - (1./3. + 1./2. * 0.4273551839464883)) < 0.00001
assert abs(BNMTF.varS[k,l] - 1./4.*(1. - 0.4675359092102624)) < 0.00001
def test_update_exp_G():
for l in range(0,L):
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tauG = 4*numpy.ones((J,L)) # muG = [[1./4.]], tauG = [[4.]]
BNMTF.update_exp_G(l) #-mu*sqrt(tau) = -0.5., lambda(..) = 0.352065 / (1-0.3085) = 0.5091323210412148, gamma = 0.5137818808494219
for j in range(0,J):
assert abs(BNMTF.expG[j,l] - (1./4. + 1./2. * 0.5091323210412148)) < 0.0001
assert abs(BNMTF.varG[j,l] - 1./4.*(1. - 0.5137818808494219)) < 0.0001
def test_update_exp_F():
for k in range(0,K):
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG)
BNMTF.tauF = 4*numpy.ones((I,K)) # muF = [[0.5]], tauF = [[4.]]
BNMTF.update_exp_F(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(BNMTF.expF[i,k] - (0.5 + 1./2. * 0.2876155949126352)) < 0.00001
assert abs(BNMTF.varF[i,k] - 1./4.*(1.-0.37033832534958433)) < 0.00001
def test_update_tau():
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.expF = 1. / lambdaF #[[1./2.]]
BNMTF.expS = 1. / lambdaS #[[1./3.]]
BNMTF.expG = 1. / lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I, K)) * 2 #[[2.]]
BNMTF.varS = numpy.ones((K, L)) * 3 #[[3.]]
BNMTF.varG = numpy.ones((J, L)) * 4 #[[4.]]
BNMTF.update_tau()
assert BNMTF.alpha_s == alpha + 12. / 2.
assert abs(BNMTF.beta_s - (beta + (2749 + 5. / 6.) / 2.)) < 0.000000000001
def test_update_tau():
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.expF = 1./lambdaF #[[1./2.]]
BNMTF.expS = 1./lambdaS #[[1./3.]]
BNMTF.expG = 1./lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I,K))*2 #[[2.]]
BNMTF.varS = numpy.ones((K,L))*3 #[[3.]]
BNMTF.varG = numpy.ones((J,L))*4 #[[4.]]
BNMTF.update_tau()
assert BNMTF.alpha_s == alpha + 12./2.
assert abs(BNMTF.beta_s - (beta + (2749+5./6.)/2.)) < 0.000000000001
def test_exp_square_diff():
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.expF = 1. / lambdaF #[[1./2.]]
BNMTF.expS = 1. / lambdaS #[[1./3.]]
BNMTF.expG = 1. / lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I, K)) * 2 #[[2.]]
BNMTF.varS = numpy.ones((K, L)) * 3 #[[3.]]
BNMTF.varG = numpy.ones((J, L)) * 4 #[[4.]]
# expF * expS * expV.T = [[1./3.]]. (varF+expF^2)=2.25, (varS+expS^2)=3.+1./9., (varG+expG^2)=4.0625
# 12.*(4./9.) + 12.*(2*4*(2.25*(3.+1./9.)*4.0625-1./4.*1./9.*1./16. + 2./3./4.*((4-1)/3./4.) +4./2./3.*((2-1)/2./3.) ))
exp_square_diff = 2749 + 5. / 6. #
assert abs(BNMTF.exp_square_diff() - exp_square_diff) < 0.000000000001
def test_update_exp_S():
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tauS = 4 * numpy.ones((K, L)) # muS = [[1./3.]], tauS = [[4.]]
BNMTF.update_exp_S(
k, l
) #-mu*sqrt(tau) = -2./3., lambda(..) = 0.319448 / (1-0.2525) = 0.4273551839464883, gamma =
assert abs(BNMTF.expS[k, l] -
(1. / 3. + 1. / 2. * 0.4273551839464883)) < 0.00001
assert abs(BNMTF.varS[k, l] - 1. / 4. *
(1. - 0.4675359092102624)) < 0.00001
def test_exp_square_diff():
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.expF = 1./lambdaF #[[1./2.]]
BNMTF.expS = 1./lambdaS #[[1./3.]]
BNMTF.expG = 1./lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I,K))*2 #[[2.]]
BNMTF.varS = numpy.ones((K,L))*3 #[[3.]]
BNMTF.varG = numpy.ones((J,L))*4 #[[4.]]
# expF * expS * expV.T = [[1./3.]]. (varF+expF^2)=2.25, (varS+expS^2)=3.+1./9., (varG+expG^2)=4.0625
# 12.*(4./9.) + 12.*(2*4*(2.25*(3.+1./9.)*4.0625-1./4.*1./9.*1./16. + 2./3./4.*((4-1)/3./4.) +4./2./3.*((2-1)/2./3.) ))
exp_square_diff = 2749+5./6. #
assert abs(BNMTF.exp_square_diff() - exp_square_diff) < 0.000000000001
def test_update_exp_G():
for l in range(0, L):
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tauG = 4 * numpy.ones((J, L)) # muG = [[1./4.]], tauG = [[4.]]
BNMTF.update_exp_G(
l
) #-mu*sqrt(tau) = -0.5., lambda(..) = 0.352065 / (1-0.3085) = 0.5091323210412148, gamma = 0.5137818808494219
for j in range(0, J):
assert abs(BNMTF.expG[j, l] -
(1. / 4. + 1. / 2. * 0.5091323210412148)) < 0.0001
assert abs(BNMTF.varG[j, l] - 1. / 4. *
(1. - 0.5137818808494219)) < 0.0001
def test_update_exp_F():
for k in range(0, K):
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG)
BNMTF.tauF = 4 * numpy.ones((I, K)) # muF = [[0.5]], tauF = [[4.]]
BNMTF.update_exp_F(
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(BNMTF.expF[i, k] -
(0.5 + 1. / 2. * 0.2876155949126352)) < 0.00001
assert abs(BNMTF.varF[i, k] - 1. / 4. *
(1. - 0.37033832534958433)) < 0.00001
def test_update_exp_tau():
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.initialise()
BNMTF.expF = 1./lambdaF #[[1./2.]]
BNMTF.expS = 1./lambdaS #[[1./3.]]
BNMTF.expG = 1./lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I,K))*2 #[[2.]]
BNMTF.varS = numpy.ones((K,L))*3 #[[3.]]
BNMTF.varG = numpy.ones((J,L))*4 #[[4.]]
BNMTF.update_tau()
BNMTF.update_exp_tau()
print BNMTF.alpha_s, BNMTF.beta_s
assert abs(BNMTF.exptau - 9./1375.91666667) < 0.0000000000001
assert abs(BNMTF.explogtau - (2.14064147795560999 - math.log(1375.91666667))) < 0.00000000001
def test_update_exp_tau():
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.initialise()
BNMTF.expF = 1. / lambdaF #[[1./2.]]
BNMTF.expS = 1. / lambdaS #[[1./3.]]
BNMTF.expG = 1. / lambdaG #[[1./4.]]
BNMTF.varF = numpy.ones((I, K)) * 2 #[[2.]]
BNMTF.varS = numpy.ones((K, L)) * 3 #[[3.]]
BNMTF.varG = numpy.ones((J, L)) * 4 #[[4.]]
BNMTF.update_tau()
BNMTF.update_exp_tau()
print BNMTF.alpha_s, BNMTF.beta_s
assert abs(BNMTF.exptau - 9. / 1375.91666667) < 0.0000000000001
assert abs(BNMTF.explogtau -
(2.14064147795560999 - math.log(1375.91666667))) < 0.00000000001
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
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
}
expF = numpy.array([[125., 126.], [126., 126.], [126., 126.], [126., 126.],
[126., 126.]])
expS = numpy.array([[84., 84., 84., 84.], [84., 84., 84., 84.]])
expG = numpy.array([[42., 42., 42., 42.], [42., 42., 42., 42.],
[42., 42., 42., 42.]])
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_vb_optimised(R, M, K, L, priors)
BNMTF.expF = expF
BNMTF.expS = expS
BNMTF.expG = expG
performances = BNMTF.predict(M_test)
assert performances['MSE'] == MSE
assert performances['R^2'] == R2
assert performances['Rp'] == Rp
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
R[0, 1], R[0, 2] = 2., 3.
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 = 2
BNMF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMF.initialise()
BNMF.run(iterations)
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMF.muF[i, k] != 1. / lambdaF[i, k]
assert BNMF.tauF[i, k] != 1.
assert BNMF.expF[i, k] != numpy.inf and not math.isnan(BNMF.expF[i, k])
assert BNMF.tauF[i, k] != numpy.inf and not math.isnan(BNMF.tauF[i, k])
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMF.muS[k, l] != 1. / lambdaS[k, l]
assert BNMF.tauS[k, l] != 1.
assert BNMF.expS[k, l] != numpy.inf and not math.isnan(BNMF.expS[k, l])
assert BNMF.tauS[k, l] != numpy.inf and not math.isnan(BNMF.tauS[k, l])
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMF.muG[j, l] != 1. / lambdaG[j, l]
assert BNMF.tauG[j, l] != 1.
assert BNMF.expG[j, l] != numpy.inf and not math.isnan(BNMF.expG[j, l])
assert BNMF.tauG[j, l] != numpy.inf and not math.isnan(BNMF.tauG[j, l])
assert BNMF.alpha_s != alpha
assert BNMF.beta_s != beta
assert BNMF.exptau != numpy.inf and not math.isnan(BNMF.exptau)
assert BNMF.explogtau != numpy.inf and not math.isnan(BNMF.explogtau)
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_vb_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_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
R[0,1], R[0,2] = 2., 3.
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 = 2
BNMF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMF.initialise()
BNMF.run(iterations)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMF.muF[i,k] != 1./lambdaF[i,k]
assert BNMF.tauF[i,k] != 1.
assert BNMF.expF[i,k] != numpy.inf and not math.isnan(BNMF.expF[i,k])
assert BNMF.tauF[i,k] != numpy.inf and not math.isnan(BNMF.tauF[i,k])
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMF.muS[k,l] != 1./lambdaS[k,l]
assert BNMF.tauS[k,l] != 1.
assert BNMF.expS[k,l] != numpy.inf and not math.isnan(BNMF.expS[k,l])
assert BNMF.tauS[k,l] != numpy.inf and not math.isnan(BNMF.tauS[k,l])
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMF.muG[j,l] != 1./lambdaG[j,l]
assert BNMF.tauG[j,l] != 1.
assert BNMF.expG[j,l] != numpy.inf and not math.isnan(BNMF.expG[j,l])
assert BNMF.tauG[j,l] != numpy.inf and not math.isnan(BNMF.tauG[j,l])
assert BNMF.alpha_s != alpha
assert BNMF.beta_s != beta
assert BNMF.exptau != numpy.inf and not math.isnan(BNMF.exptau)
assert BNMF.explogtau != numpy.inf and not math.isnan(BNMF.explogtau)
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
}
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.expF = numpy.ones((I, K))
BNMTF.expS = 2 * numpy.ones((K, L))
BNMTF.expG = 3 * numpy.ones((J, L))
BNMTF.explogtau = 5.
BNMTF.exptau = 3.
# expU*expV.T = [[72.]]
log_likelihood = 3. / 2. * (5. - 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')
assert AIC == BNMTF.quality('AIC')
assert BIC == BNMTF.quality('BIC')
assert MSE == BNMTF.quality('MSE')
with pytest.raises(AssertionError) as error:
BNMTF.quality('FAIL')
assert str(error.value) == "Unrecognised metric for model quality: FAIL."
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_vb_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_vb_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_vb_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_vb_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_vb_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_vb_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_vb_optimised(R4,M1,K,L,priors)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmtf_vb_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_vb_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.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_vb_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_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
}
# Initialisation using expectation
init_S, init_FG = 'exp', 'exp'
BNMTF = bnmtf_vb_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.tauF[i, k] == 1.
assert BNMTF.muF[i, k] == 1. / lambdaF[i, k]
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.tauS[k, l] == 1.
assert BNMTF.muS[k, l] == 1. / lambdaS[k, l]
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.tauG[j, l] == 1.
assert BNMTF.muG[j, l] == 1. / lambdaG[j, l]
assert BNMTF.alpha_s == alpha + I * J / 2.
#assert BNMTF.alpha_s == alpha
assert BNMTF.beta_s == beta + BNMTF.exp_square_diff() / 2.
#assert BNMTF.beta_s == beta
assert BNMTF.exptau == (alpha +
I * J / 2.) / (beta + BNMTF.exp_square_diff() / 2.)
#assert BNMTF.exptau == alpha / beta
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert abs(BNMTF.expF[i, k] - (0.5 + 0.352065 / (1 - 0.3085))) < 0.0001
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert abs(BNMTF.expS[k, l] - (1. / 3. + 0.377383 /
(1 - 0.3694))) < 0.0001
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert abs(BNMTF.expG[j, l] - (1. / 4. + 0.386668 /
(1 - 0.4013))) < 0.0001
# Initialisation of S using random draws from prior
init_S, init_FG = 'random', 'exp'
BNMTF = bnmtf_vb_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.tauF[i, k] == 1.
assert BNMTF.muF[i, k] == 1. / lambdaF[i, k]
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.tauS[k, l] == 1.
assert BNMTF.muS[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.tauG[j, l] == 1.
assert BNMTF.muG[j, l] == 1. / lambdaG[j, l]
# Initialisation of F and G using random draws from prior
init_S, init_FG = 'exp', 'random'
BNMTF = bnmtf_vb_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.tauF[i, k] == 1.
assert BNMTF.muF[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.tauS[k, l] == 1.
assert BNMTF.muS[k, l] == 1. / lambdaS[k, l]
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.tauG[j, l] == 1.
assert BNMTF.muG[j, l] != 1. / lambdaG[j, l]
# Initialisation of F and G using Kmeans
init_S, init_FG = 'exp', 'kmeans'
BNMTF = bnmtf_vb_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.tauF[i, k] == 1.
assert BNMTF.muF[i, k] == 0 or BNMTF.muF[i, k] == 1
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.tauG[j, l] == 1.
assert BNMTF.muG[j, l] == 0 or BNMTF.muG[j, l] == 1
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.tauS[k, l] == 1.
assert BNMTF.muS[k, l] == 1. / lambdaS[k, l]
# Initialise tauF, tauS, tauG using predefined values
tauFSG = {
'tauF': 2 * numpy.ones((I, K)),
'tauS': 3 * numpy.ones((K, L)),
'tauG': 4 * numpy.ones((J, L))
}
init_S, init_FG = 'exp', 'exp'
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.initialise(init_S, init_FG, tauFSG)
for i, k in itertools.product(xrange(0, I), xrange(0, K)):
assert BNMTF.tauF[i, k] == 2.
for k, l in itertools.product(xrange(0, K), xrange(0, L)):
assert BNMTF.tauS[k, l] == 3.
for j, l in itertools.product(xrange(0, J), xrange(0, L)):
assert BNMTF.tauG[j, l] == 4.
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 }
# Initialisation using expectation
init_S, init_FG = 'exp', 'exp'
BNMTF = bnmtf_vb_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.tauF[i,k] == 1.
assert BNMTF.muF[i,k] == 1./lambdaF[i,k]
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.tauS[k,l] == 1.
assert BNMTF.muS[k,l] == 1./lambdaS[k,l]
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.tauG[j,l] == 1.
assert BNMTF.muG[j,l] == 1./lambdaG[j,l]
assert BNMTF.alpha_s == alpha + I*J/2.
#assert BNMTF.alpha_s == alpha
assert BNMTF.beta_s == beta + BNMTF.exp_square_diff()/2.
#assert BNMTF.beta_s == beta
assert BNMTF.exptau == (alpha + I*J/2.)/(beta + BNMTF.exp_square_diff()/2.)
#assert BNMTF.exptau == alpha / beta
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert abs(BNMTF.expF[i,k] - (0.5 + 0.352065 / (1-0.3085))) < 0.0001
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert abs(BNMTF.expS[k,l] - (1./3. + 0.377383 / (1-0.3694))) < 0.0001
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert abs(BNMTF.expG[j,l] - (1./4. + 0.386668 / (1-0.4013))) < 0.0001
# Initialisation of S using random draws from prior
init_S, init_FG = 'random', 'exp'
BNMTF = bnmtf_vb_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.tauF[i,k] == 1.
assert BNMTF.muF[i,k] == 1./lambdaF[i,k]
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.tauS[k,l] == 1.
assert BNMTF.muS[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.tauG[j,l] == 1.
assert BNMTF.muG[j,l] == 1./lambdaG[j,l]
# Initialisation of F and G using random draws from prior
init_S, init_FG = 'exp', 'random'
BNMTF = bnmtf_vb_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.tauF[i,k] == 1.
assert BNMTF.muF[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.tauS[k,l] == 1.
assert BNMTF.muS[k,l] == 1./lambdaS[k,l]
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.tauG[j,l] == 1.
assert BNMTF.muG[j,l] != 1./lambdaG[j,l]
# Initialisation of F and G using Kmeans
init_S, init_FG = 'exp', 'kmeans'
BNMTF = bnmtf_vb_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.tauF[i,k] == 1.
assert BNMTF.muF[i,k] == 0 or BNMTF.muF[i,k] == 1
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.tauG[j,l] == 1.
assert BNMTF.muG[j,l] == 0 or BNMTF.muG[j,l] == 1
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.tauS[k,l] == 1.
assert BNMTF.muS[k,l] == 1./lambdaS[k,l]
# Initialise tauF, tauS, tauG using predefined values
tauFSG = {
'tauF' : 2*numpy.ones((I,K)),
'tauS' : 3*numpy.ones((K,L)),
'tauG' : 4*numpy.ones((J,L))
}
init_S, init_FG = 'exp', 'exp'
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.initialise(init_S,init_FG,tauFSG)
for i,k in itertools.product(xrange(0,I),xrange(0,K)):
assert BNMTF.tauF[i,k] == 2.
for k,l in itertools.product(xrange(0,K),xrange(0,L)):
assert BNMTF.tauS[k,l] == 3.
for j,l in itertools.product(xrange(0,J),xrange(0,L)):
assert BNMTF.tauG[j,l] == 4.
def test_elbo():
I,J,K,L = 5,3,2,4
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
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 }
expF = 5*numpy.ones((I,K))
expS = 6*numpy.ones((K,L))
expG = 7*numpy.ones((J,L))
varF = 11*numpy.ones((I,K))
varS = 12*numpy.ones((K,L))
varG = 13*numpy.ones((J,L))
exptau = 8.
explogtau = 9.
muF = 14*numpy.ones((I,K))
muS = 15*numpy.ones((K,L))
muG = 16*numpy.ones((J,L))
tauF = numpy.ones((I,K))/100.
tauS = numpy.ones((K,L))/101.
tauG = numpy.ones((J,L))/102.
alpha_s = 20.
beta_s = 21.
# expF * expS * expG.T = [[1680]]
# (R - expF*expS*expG.T)^2 = 12*1679^2 = 33828492
# Var[F*S*G.T] = 12*K*L*((11+5^2)*(12+6^2)*(13+7^2)-5^2*6^2*7^2
# + 11*6*7*((4-1)*6*7) + 13*5*6*((2-1)*5*6))
# = 12*2*4*(63036 + 58212 + 11700) = 12763008
# -muF*sqrt(tauF) = -14*math.sqrt(1./100.) = -1.4
# -muS*sqrt(tauS) = -15*math.sqrt(1./101.) = -1.4925557853149838
# -muG*sqrt(tauG) = -16*math.sqrt(1./102.) = -1.5842360687626789
# cdf(-1.4) = 0.080756659233771066
# cdf(-1.4925557853149838) = 0.067776752211548219
# cdf(-1.5842360687626789) = 0.056570004076003155
ELBO = 12./2.*(explogtau - math.log(2*math.pi)) - 8./2.*(33828492+12763008) \
+ 5*2*(math.log(2.) - 2.*5.) + 2*4*(math.log(3.) - 3.*6.) + 3*4*(math.log(4.) - 4.*7.) \
+ 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*4*2*math.log(1./101.) + 0.5*4*2*math.log(2*math.pi) + 4*2*math.log(1.-0.067776752211548219) \
+ 0.5*4*2*1./101.*(12.+81.) \
- 0.5*4*3*math.log(1./102.) + 0.5*4*3*math.log(2*math.pi) + 4*3*math.log(1.-0.056570004076003155) \
+ 0.5*4*3*1./102.*(13.+81.)
BNMTF = bnmtf_vb_optimised(R,M,K,L,priors)
BNMTF.expF = expF
BNMTF.expS = expS
BNMTF.expG = expG
BNMTF.varF = varF
BNMTF.varS = varS
BNMTF.varG = varG
BNMTF.exptau = exptau
BNMTF.explogtau = explogtau
BNMTF.muF = muF
BNMTF.muS = muS
BNMTF.muG = muG
BNMTF.tauF = tauF
BNMTF.tauS = tauS
BNMTF.tauG = tauG
BNMTF.alpha_s = alpha_s
BNMTF.beta_s = beta_s
assert BNMTF.elbo() == ELBO
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_vb_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_vb_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_vb_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_vb_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_vb_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_vb_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_vb_optimised(R4, M1, K, L, priors)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
bnmtf_vb_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_vb_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.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_vb_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_elbo():
I, J, K, L = 5, 3, 2, 4
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
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
}
expF = 5 * numpy.ones((I, K))
expS = 6 * numpy.ones((K, L))
expG = 7 * numpy.ones((J, L))
varF = 11 * numpy.ones((I, K))
varS = 12 * numpy.ones((K, L))
varG = 13 * numpy.ones((J, L))
exptau = 8.
explogtau = 9.
muF = 14 * numpy.ones((I, K))
muS = 15 * numpy.ones((K, L))
muG = 16 * numpy.ones((J, L))
tauF = numpy.ones((I, K)) / 100.
tauS = numpy.ones((K, L)) / 101.
tauG = numpy.ones((J, L)) / 102.
alpha_s = 20.
beta_s = 21.
# expF * expS * expG.T = [[1680]]
# (R - expF*expS*expG.T)^2 = 12*1679^2 = 33828492
# Var[F*S*G.T] = 12*K*L*((11+5^2)*(12+6^2)*(13+7^2)-5^2*6^2*7^2
# + 11*6*7*((4-1)*6*7) + 13*5*6*((2-1)*5*6))
# = 12*2*4*(63036 + 58212 + 11700) = 12763008
# -muF*sqrt(tauF) = -14*math.sqrt(1./100.) = -1.4
# -muS*sqrt(tauS) = -15*math.sqrt(1./101.) = -1.4925557853149838
# -muG*sqrt(tauG) = -16*math.sqrt(1./102.) = -1.5842360687626789
# cdf(-1.4) = 0.080756659233771066
# cdf(-1.4925557853149838) = 0.067776752211548219
# cdf(-1.5842360687626789) = 0.056570004076003155
ELBO = 12./2.*(explogtau - math.log(2*math.pi)) - 8./2.*(33828492+12763008) \
+ 5*2*(math.log(2.) - 2.*5.) + 2*4*(math.log(3.) - 3.*6.) + 3*4*(math.log(4.) - 4.*7.) \
+ 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*4*2*math.log(1./101.) + 0.5*4*2*math.log(2*math.pi) + 4*2*math.log(1.-0.067776752211548219) \
+ 0.5*4*2*1./101.*(12.+81.) \
- 0.5*4*3*math.log(1./102.) + 0.5*4*3*math.log(2*math.pi) + 4*3*math.log(1.-0.056570004076003155) \
+ 0.5*4*3*1./102.*(13.+81.)
BNMTF = bnmtf_vb_optimised(R, M, K, L, priors)
BNMTF.expF = expF
BNMTF.expS = expS
BNMTF.expG = expG
BNMTF.varF = varF
BNMTF.varS = varS
BNMTF.varG = varG
BNMTF.exptau = exptau
BNMTF.explogtau = explogtau
BNMTF.muF = muF
BNMTF.muS = muS
BNMTF.muG = muG
BNMTF.tauF = tauF
BNMTF.tauS = tauS
BNMTF.tauG = tauG
BNMTF.alpha_s = alpha_s
BNMTF.beta_s = beta_s
assert BNMTF.elbo() == ELBO
'tauG': numpy.ones((J, L)) * 1.
}
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_vb_optimised(X_min, M, K, L, priors)
BNMTF.initialise(init_S=init_S, init_FG=init_FG, tauFSG=tauFSG)
BNMTF.run(iterations)
# Plot the tau expectation values to check convergence
plt.plot(BNMTF.all_exp_tau)
# Print the performances across iterations (MSE)
print "vb_all_performances = %s" % BNMTF.all_performances['MSE']
'''
vb_all_performances = [3.6560497805224408, 3.0813292661709162, 3.0645411707818879, 3.0525658578677146, 3.0432294800433217, 3.0353147079925389, 3.0281758341302782, 3.0226092485114404, 3.0180924608167805, 3.0139127030767114, 3.0099122667795863, 3.0059787264911373, 3.0020059059602895, 2.9979235848542376, 2.9939857310808189, 2.9898185953423795, 2.9854832227763319, 2.9809603527304036, 2.97624979475611, 2.9711907503274269, 2.9658176056612779, 2.9601355444227435, 2.9541278594520368, 2.9477835971072976, 2.9412314889174089, 2.9352617225772626, 2.9292177423085928, 2.9227155371535689, 2.9155856674515941, 2.9076653346542143, 2.8987801998468714, 2.8887613557725276, 2.877929867013683, 2.8664188240201112, 2.853946443672462, 2.8404561369103098, 2.8264738197741579, 2.8126534805321883, 2.7994240587681447, 2.7867394981258542, 2.7738704133811085, 2.7607088513751723, 2.7472492349120992, 2.7335579408151376, 2.7199102127498063, 2.7068352201855417, 2.6940848737391012, 2.6817269337924143, 2.669756858405901, 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2.0656349178501046, 2.0655903784404739, 2.0655466359287962, 2.0655036735599346, 2.0654614747528526, 2.065420023087007, 2.0653793022945823, 2.0653392962577488, 2.0652999890099597, 2.0652613647407372, 2.0652234078032614, 2.0651861027238825, 2.0651494342134122, 2.0651133871793879, 2.0650779467393616, 2.0650430982345553, 2.0650088272437648, 2.0649751195968293, 2.0649419613883917, 2.0649093389901045, 2.0648772390621692, 2.0648456485629825, 2.0648145547573113, 2.0647839452219094, 2.0647538078487897, 2.0647241308459026, 2.0646949027351678, 2.0646661123479935, 2.064637748818853, 2.0646098015767103, 2.0645822603351376, 2.0645551150816517, 2.0645283560664227, 2.0645019737912063, 2.0644759589982531, 2.0644503026603527, 2.0644249959710841, 2.0644000303367642, 2.0643753973687557, 2.0643510888768875, 2.0643270968639622, 2.0643034135208893, 2.0642800312225478, 2.0642569425239086, 2.064234140157184, 2.0642116170286977, 2.0641893662162922, 2.0641673809666861, 2.064145654693081, 2.064124180972684, 2.0641029535442228, 2.0640819663052685, 2.0640612133098393, 2.0640406887654827, 2.0640203870306579, 2.0640003026119396, 2.0639804301608775, 2.0639607644713394, 2.0639413004762699, 2.0639220332447663, 2.0639029579789785, 2.0638840700111167, 2.063865364800348, 2.0638468379295998, 2.0638284851027602, 2.063810302141476, 2.0637922849823296, 2.0637744296738081, 2.0637567323734647, 2.0637391893450054, 2.0637217969557007, 2.0637045516734358, 2.0636874500641227, 2.0636704887891191, 2.0636536646026435, 2.0636369743494054, 2.0636204149618651, 2.0636039834582971, 2.0635876769400618, 2.0635714925896531, 2.0635554276683785, 2.0635394795141315, 2.0635236455395578, 2.0635079232298534, 2.0634923101407097, 2.0634768038966458, 2.0634614021888349, 2.0634461027735993, 2.0634309034703899, 2.063415802160165, 2.0634007967836601, 2.0633858853398639, 2.0633710658842541, 2.0633563365274092, 2.0633416954333872, 2.0633271408183127, 2.0633126709489185, 2.06329828414118, 2.0632839787589816, 2.0632697532126452, 2.0632556059579281, 2.063241535494547, 2.0632275403650278, 2.0632136191536676, 2.0631997704851193, 2.0631859930237861, 2.0631722854723051, 2.0631586465709493, 2.0631450750965512, 2.0631315698617732, 2.0631181297145313, 2.0631047535373077, 2.0630914402470868, 2.0630781887950036, 2.0630649981669564, 2.063051867383872, 2.0630387955035605, 2.063025781622037, 2.0630128248764934, 2.0629999244491191, 2.0629870795720264, 2.0629742895336221, 2.062961553686506, 2.0629488714573831, 2.0629362423582061, 2.0629236659997883, 2.0629111421060697, 2.0628986705296599, 2.0628862512668289, 2.0628738844717494, 2.0628615704666089, 2.0628493097471154, 2.0628371029802772, 2.0628249509929959, 2.0628128547495805, 2.0628008153183295, 2.0627888338278382, 2.0627769114151255, 2.0627650491703253, 2.062753248080901, 2.0627415089809578, 2.062729832509667, 2.0627182190807036, 2.0627066688649784, 2.0626951817861765, 2.0626837575284358, 2.0626723955545798, 2.0626610951335165, 2.0626498553771673, 2.0626386752883952, 2.0626275538222316]
'''
# Load in data
R = numpy.loadtxt(input_folder+"R.txt")
M = numpy.ones((I,J))
# 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_vb_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
vb_all_times_average = list(numpy.average(times_repeats, axis=0))
vb_all_performances = performances_repeats[0]
print "vb_all_times_average = %s" % vb_all_times_average
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_vb_optimised(R, M, K, L, priors)
BNMF.initialise(init_S, init_FG)
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 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)
init_S = 'random' #'exp' #
init_FG = 'kmeans' #'exp' #
tauFSG = {
'tauF' : numpy.ones((I,K))*1.,
'tauS' : numpy.ones((K,L))*1.,
'tauG' : numpy.ones((J,L))*1.
}
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_vb_optimised(X_min,M,K,L,priors)
BNMTF.initialise(init_S=init_S,init_FG=init_FG,tauFSG=tauFSG)
BNMTF.run(iterations)
# Plot the tau expectation values to check convergence
plt.plot(BNMTF.all_exp_tau)
# Print the performances across iterations (MSE)
print "vb_all_performances = %s" % BNMTF.all_performances['MSE']
'''
vb_all_performances = [3.6560497805224408, 3.0813292661709162, 3.0645411707818879, 3.0525658578677146, 3.0432294800433217, 3.0353147079925389, 3.0281758341302782, 3.0226092485114404, 3.0180924608167805, 3.0139127030767114, 3.0099122667795863, 3.0059787264911373, 3.0020059059602895, 2.9979235848542376, 2.9939857310808189, 2.9898185953423795, 2.9854832227763319, 2.9809603527304036, 2.97624979475611, 2.9711907503274269, 2.9658176056612779, 2.9601355444227435, 2.9541278594520368, 2.9477835971072976, 2.9412314889174089, 2.9352617225772626, 2.9292177423085928, 2.9227155371535689, 2.9155856674515941, 2.9076653346542143, 2.8987801998468714, 2.8887613557725276, 2.877929867013683, 2.8664188240201112, 2.853946443672462, 2.8404561369103098, 2.8264738197741579, 2.8126534805321883, 2.7994240587681447, 2.7867394981258542, 2.7738704133811085, 2.7607088513751723, 2.7472492349120992, 2.7335579408151376, 2.7199102127498063, 2.7068352201855417, 2.6940848737391012, 2.6817269337924143, 2.669756858405901, 2.6578316000013333, 2.6457385873537937, 2.6352039707814567, 2.6263373139507173, 2.6184511925159919, 2.611199879564492, 2.6044738437438752, 2.598200830592627, 2.5923243952235322, 2.5867990838311168, 2.5815867196158364, 2.5766545339890716, 2.5719729771397386, 2.5675132996735486, 2.563247301129044, 2.5591499223735945, 2.5552190232426533, 2.5514961756469443, 2.5479492727489572, 2.5445153560246223, 2.5411652671113889, 2.5378835587917732, 2.5346580967152756, 2.5314784647321011, 2.5283355753788883, 2.5252212175519877, 2.5221279788671471, 2.5190493573826367, 2.5159796537672854, 2.5129135330412247, 2.5098453426257246, 2.5067809227272497, 2.5037614603826319, 2.5007199273377827, 2.4976126544675603, 2.4944331098992083, 2.4911782709979646, 2.4878440708469833, 2.4844260739733337, 2.4809257035614043, 2.4773577135594618, 2.4737540989267566, 2.4701792139920662, 2.4666095633314615, 2.4630112926416063, 2.4593711122874291, 2.4556838142082782, 2.4519491165965084, 2.4481697200140573, 2.4443486552141542, 2.440487093172842, 2.4365839756035839, 2.4326371149794848, 2.4286446046552457, 2.4246059042360666, 2.4205223328853833, 2.4163969111727042, 2.4122338970306205, 2.4080382794948063, 2.403815130964206, 2.3995689988120903, 2.3953037201324006, 2.3910227364882082, 2.3867298159103272, 2.3824301769542031, 2.3781314718043607, 2.3738432998122976, 2.3695719276547158, 2.3653150625629031, 2.3610921489770931, 2.3569375784395401, 2.3528612189229094, 2.3488605113009573, 2.3449337782904451, 2.3410816686800642, 2.3373051211829856, 2.3336042769123884, 2.3299819419611127, 2.3264475393113844, 2.3230099146884546, 2.3196605347440284, 2.3163699005757441, 2.3131041171384816, 2.3098388634347544, 2.3065539242858808, 2.3033182263003829, 2.3000289882953253, 2.2965245371922194, 2.2930851183528502, 2.2898203348285544, 2.2867324823351622, 2.2837843562781512, 2.2809502521712557, 2.2782062737714202, 2.2755378060435718, 2.2729396825035399, 2.2704080121247978, 2.2679387349034092, 2.2655280687098336, 2.2631727111787008, 2.2608697941416125, 2.2586167584042793, 2.2564112368206284, 2.254250984534973, 2.2521338765877226, 2.250057965504205, 2.2480215350797716, 2.2460230719295247, 2.2440611613506314, 2.2421343925244104, 2.2402413320282495, 2.2383805592443196, 2.2365507290126176, 2.2347506305141955, 2.232979222000008, 2.2312356325229965, 2.2295191334064701, 2.2278290893503025, 2.2261649009982198, 2.2245259495991418, 2.222911550479524, 2.2213209195038264, 2.219753165351348, 2.2182073376733249, 2.2166825473541953, 2.215178094736681, 2.2136934856905413, 2.2122283166960508, 2.2107821486213015, 2.209354463389662, 2.2079446889741581, 2.2065522409149985, 2.2051765521555708, 2.2038170869594369, 2.2024733459888894, 2.2011448733806449, 2.1998312747526425, 2.1985322449522573, 2.1972475797369087, 2.1959771319675045, 2.194720719235236, 2.1934780512787668, 2.1922487251394505, 2.1910322832835596, 2.1898283248750485, 2.1886366514269846, 2.1874573625907296, 2.1862907927433848, 2.1851372956078143, 2.183997017604661, 2.1828697926704992, 2.1817551789542744, 2.1806525675723059, 2.1795612867988021, 2.1784806694500398, 2.1774100934866407, 2.1763490189402912, 2.1752970207839977, 2.1742537894982745, 2.1732190943775671, 2.1721927482306129, 2.17117460349484, 2.1701645748079788, 2.1691626704416147, 2.1681690060993568, 2.1671837699916541, 2.1662071553377249, 2.165239317699867, 2.1642803747659212, 2.1633304223621033, 2.1623895478325323, 2.1614578394239365, 2.160535366187109, 2.1596218197695309, 2.1587145439898645, 2.1578056502100114, 2.1568879340850122, 2.1559726215284307, 2.1551056253483334, 2.1542746101358072, 2.1534404402323051, 2.1525993041660749, 2.1517561584321103, 2.1509150437345674, 2.1500787162545856, 2.1492492151721208, 2.1484283145915981, 2.1476178021736683, 2.1468194857244884, 2.1460349218231851, 2.1452650897659691, 2.1445101226509506, 2.1437690938284462, 2.1430405522961848, 2.1423242449256037, 2.1416221856203941, 2.1409374721553371, 2.1402713044080666, 2.1396198614575352, 2.1389760884528934, 2.1383354233837659, 2.1376932399624575, 2.1370418213462887, 2.1363793365679227, 2.1357133715635195, 2.1350496403275354, 2.1343915499008133, 2.1337243753358086, 2.1329527133461808, 2.1320179346951926, 2.130885502597692, 2.1297321288744033, 2.1286240275667652, 2.1275867942879882, 2.1266190943573107, 2.1257067168890456, 2.1248347248152322, 2.1239927818589335, 2.1231748637492012, 2.122377466885379, 2.1215983129292937, 2.1208357263777908, 2.1200883843801508, 2.1193552099589841, 2.1186353104891724, 2.1179279331651579, 2.1172324316629489, 2.1165482419951904, 2.1158748655662318, 2.1152118576238927, 2.1145588196153025, 2.1139153940176132, 2.1132812603385824, 2.112656131649004, 2.1120397517949656, 2.1114318931760558, 2.1108323539466678, 2.1102409542026872, 2.1096575336277557, 2.109081953808432, 2.1085141039804625, 2.1079539038972306, 2.107401298505835, 2.1068562454962438, 2.1063187016213183, 2.1057886130265806, 2.1052659111426655, 2.1047505128643307, 2.1042423229771159, 2.1037412372475819, 2.1032471452983805, 2.1027599330047582, 2.102279484773951, 2.1018056868763209, 2.1013384336598295, 2.1008776374101426, 2.1004232377285974, 2.0999752000245073, 2.0995334945992252, 2.0990980606620084, 2.0986687662763095, 2.0982453638946161, 2.0978274373718824, 2.0974143751939884, 2.0970054516638381, 2.0966000377298912, 2.0961978102650844, 2.0957988080934156, 2.0954033306649356, 2.095011782094351, 2.0946245496203377, 2.0942419451514835, 2.0938642011479094, 2.0934915113974411, 2.0931241123753681, 2.0927623462470444, 2.0924065667449052, 2.0920569203865305, 2.091713290608086, 2.0913754400625306, 2.0910431212397969, 2.0907160958372661, 2.0903941341961971, 2.0900770250138629, 2.0897645859366505, 2.0894566660728118, 2.0891531411339734, 2.0888539059167908, 2.0885588677257365, 2.0882679419023589, 2.0879810490711423, 2.0876981133598838, 2.0874190611290881, 2.0871438200878565, 2.086872318843338, 2.0866044869635965, 2.0863402556298412, 2.0860795589658592, 2.0858223361346075, 2.0855685342274177, 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