def likelihoodAB(cascade, mu=None, B=None, omega=None, omegao=None, model='modelB'):
lhoodA = Cascade(cascade.L)
lhoodB = Cascade(cascade.L)
if model=='modelC':
lhoodC = Cascade(cascade.L)
for j in xrange(cascade.J):
if model=='modelA':
lhoodA.value[j] = cascade.total[j]*nplog(0.5)
lhoodB.value[j] = cascade.value[j]*nplog(B.value[j]) + (cascade.total[j]-cascade.value[j])*nplog(1-B.value[j])
elif model=='modelB':
lhoodA.value[j] = cascade.total[j]*nplog(0.5)
lhoodB.value[j] = gammaln(cascade.value[j]+mu.estim[j]) + gammaln(cascade.total[j]-cascade.value[j]+mu.estim[j]) \
- gammaln(cascade.total[j]+2*mu.estim[j]) + gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j])
elif model=='modelC':
lhoodA.value[j] = gammaln(cascade.value[j]+0.5*omega.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*omega.value[j]) \
- gammaln(cascade.total[j]+omega.value[j]) + gammaln(omega.value[j]) - 2*gammaln(0.5*omega.value[j])
lhoodB.value[j] = gammaln(cascade.value[j]+B.value[j]*omega.value[j]) \
+ gammaln(cascade.total[j]-cascade.value[j]+(1-B.value[j])*omega.value[j]) \
- gammaln(cascade.total[j]+omega.value[j]) + gammaln(omega.value[j]) - gammaln(B.value[j]*omega.value[j]) \
- gammaln((1-B.value[j])*omega.value[j])
lhoodC.value[j] = gammaln(cascade.value[j]+0.5*omegao.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*omegao.value[j]) \
- gammaln(cascade.total[j]+omegao.value[j]) + gammaln(omegao.value[j]) - 2*gammaln(0.5*omegao.value[j])
if model=='modelC':
return lhoodA, lhoodB, lhoodC
else:
return lhoodA, lhoodB
def bayes_optimal_estimator(cascade, pi, mu):
R = Cascade(cascade.L)
for j in range(pi.J):
ratio = nplog(1-pi.estim[j]) - nplog(pi.estim[j]) + gammaln(cascade.value[j].sum(0)+mu.estim[j]) \
+ gammaln(cascade.total[j].sum(0)-cascade.value[j].sum(0)+mu.estim[j]) \
- gammaln(cascade.total[j].sum(0)+2*mu.estim[j]) \
+ gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j]) - cascade.total[j].sum(0)*nplog(0.5)
R.value[j] = 0.5*logistic(ratio) \
+ (cascade.value[j].sum(0)+mu.estim[j])/(cascade.total[j].sum(0)+mu.estim[j])*logistic(-ratio)
return R
def update_Estep(self, cascade, eta, pi, mu=None, B=None, omega=None, omegao=None):
if self.model=='modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=self.model)
elif self.model=='modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=self.model)
elif self.model=='modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade, B=B, omega=omega, omegao=omegao, model=self.model)
for j in xrange(self.J):
log_posterior_odds = nplog(pi.estim[j]) - nplog(1-pi.estim[j]) \
+ outsum(eta.estim[:,1:]*(lhoodA.value[j]-lhoodB.value[j]))/outsum(eta.estim[:,1:])
self.value[j] = newlogistic(-log_posterior_odds)
def update_Estep(self, cascade, scores, alpha, beta, tau, pi, gamma, mu=None, B=None, omega=None, omegao=None):
footprint_logodds = np.zeros((self.N,1),dtype=float)
if gamma.model=='modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=gamma.model)
elif gamma.model=='modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=gamma.model)
elif gamma.model=='modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade, B=B, omega=omega, omegao=omegao, model=gamma.model)
for j in xrange(pi.J):
footprint_logodds += insum((1-gamma.value[j])*(lhoodB.value[j]-lhoodA.value[j]) \
+ gamma.value[j]*(nplog(pi.estim[j])-nplog(gamma.value[j])) \
+ (1-gamma.value[j])*(nplog(1-pi.estim[j])-nplog(1-gamma.value[j])),[1])
self.estim[:,1:] = beta.estim[0] + beta.estim[1]*scores + footprint_logodds \
+ gammaln(self.total+alpha.estim[1]) - gammaln(self.total+alpha.estim[0]) \
+ gammaln(alpha.estim[0]) - gammaln(alpha.estim[1]) \
+ alpha.estim[1]*nplog(tau.estim[1]) - alpha.estim[0]*nplog(tau.estim[0]) \
+ self.total*(nplog(1-tau.estim[1])-nplog(1-tau.estim[0]))
self.estim[:,0] = 0.
self.estim[self.estim==np.inf] = MAX
self.estim = np.exp(self.estim-np.max(self.estim,1).reshape(self.N,1))
self.estim = self.estim/insum(self.estim,[1])
if np.isnan(self.estim).any():
print "Nan in Eta"
raise ValueError
if np.isinf(self.estim).any():
print "Inf in Eta"
raise ValueError
def likelihood(cascade, scores, eta, gamma, pi, alpha, beta, tau, mu=None, B=None, omega=None, omegao=None):
apriori = beta.estim[0] + beta.estim[1]*scores
if gamma.model=='modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=gamma.model)
elif gamma.model=='modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=gamma.model)
elif gamma.model=='modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade, B=B, omega=omega, omegao=omegao, model=gamma.model)
footprint = np.zeros((cascade.N,1),dtype=float)
for j in xrange(pi.J):
footprint += insum(gamma.value[j]*lhoodA.value[j] + (1-gamma.value[j])*lhoodB.value[j] \
+ gamma.value[j]*(nplog(pi.estim[j])-nplog(gamma.value[j])) \
+ (1-gamma.value[j])*(nplog(1-pi.estim[j])-nplog(1-gamma.value[j])),[1])
P_1 = footprint + gammaln(eta.total+alpha.estim[1]) - gammaln(alpha.estim[1]) \
+ alpha.estim[1]*nplog(tau.estim[1]) + eta.total*nplog(1-tau.estim[1])
P_1[P_1==np.inf] = MAX
P_1[P_1==-np.inf] = -MAX
null = np.zeros((cascade.N,1),dtype=float)
for j in xrange(cascade.J):
if gamma.model=='modelC':
null = null + insum(lhoodC.value[j],[1])
else:
null = null + insum(lhoodA.value[j],[1])
P_0 = null + gammaln(eta.total+alpha.estim[0]) - gammaln(alpha.estim[0]) \
+ alpha.estim[0]*nplog(tau.estim[0]) + eta.total*nplog(1-tau.estim[0])
P_0[P_0==np.inf] = MAX
P_0[P_0==-np.inf] = -MAX
L = P_0*eta.estim[:,:1] + insum(P_1*eta.estim[:,1:],[1]) + apriori*(1-eta.estim[:,:1]) \
- nplog(1+np.exp(apriori)) - insum(eta.estim*nplog(eta.estim),[1])
L = L.sum()
if np.isnan(L):
print "Nan in LogLike"
raise ValueError
if np.isinf(L):
print "Inf in LogLike"
raise ValueError
return L
def F(x):
arg = x[0] + x[1] * scores
func = arg * insum(eta.estim[:, 1:], 1) - nplog(1 + np.exp(arg))
f = -1. * func.sum()
if np.isnan(f) or np.isinf(f):
return np.inf
else:
return f
def F(x):
arg = x[0]+x[1]*scores
func = arg*insum(eta.estim[:,1:],1) - nplog(1+np.exp(arg))
f = -1.*func.sum()
if np.isnan(f) or np.isinf(f):
return np.inf
else:
return f
def loglikelihood(cascade, gamma, pi, B=None, mu=None, tau=None):
L = 0.
for j in xrange(cascade.J):
if gamma.model=='modelA':
lhoodA = cascade.total[j]*nplog(0.5)
lhoodB = cascade.value[j]*nplog(B.value[j]) + (cascade.total[j]-cascade.value[j])*nplog(1-B.value[j])
elif gamma.model=='modelB':
lhoodA = cascade.total[j]*nplog(0.5)
lhoodB = gammaln(cascade.value[j]+mu.estim[j]) + gammaln(cascade.total[j]-cascade.value[j]+mu.estim[j]) \
- gammaln(cascade.total[j]+2*mu.estim[j]) + gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j])
elif gamma.model=='modelC':
lhoodA = gammaln(cascade.value[j]+0.5*tau.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*tau.value[j]) \
- gammaln(cascade.total[j]+tau.value[j]) + gammaln(tau.value[j]) - 2*gammaln(0.5*tau.value[j])
lhoodB = gammaln(cascade.value[j]+B.value[j]*tau.value[j]) \
+ gammaln(cascade.total[j]-cascade.value[j]+(1-B.value[j])*tau.value[j]) \
- gammaln(cascade.total[j]+tau.value[j]) + gammaln(tau.value[j]) - gammaln(B.value[j]*tau.value[j]) \
- gammaln((1-B.value[j])*tau.value[j])
L += np.sum(gamma.value[j]*lhoodA.sum(0) + (1-gamma.value[j])*lhoodB.sum(0) \
+ cascade.N*(gamma.value[j]*nplog(pi.estim[j]) + (1-gamma.value[j])*nplog(1-pi.estim[j]) \
- gamma.value[j]*nplog(gamma.value[j]) - (1-gamma.value[j])*nplog(1-gamma.value[j])))
return L
def bayes_optimal_estimator(cascade, pi, mu):
R = Cascade(cascade.L)
for j in range(pi.J):
ratio = (
nplog(1 - pi.estim[j])
- nplog(pi.estim[j])
+ gammaln(cascade.value[j].sum(0) + mu.estim[j])
+ gammaln(cascade.total[j].sum(0) - cascade.value[j].sum(0) + mu.estim[j])
- gammaln(cascade.total[j].sum(0) + 2 * mu.estim[j])
+ gammaln(2 * mu.estim[j])
- 2 * gammaln(mu.estim[j])
- cascade.total[j].sum(0) * nplog(0.5)
)
R.value[j] = 0.5 * logistic(ratio) + (cascade.value[j].sum(0) + mu.estim[j]) / (
cascade.total[j].sum(0) + mu.estim[j]
) * logistic(-ratio)
return R
def __init__(self, cascade, totalreads, scores, gamma=None, beta=None, \
pi=None, mu=None, B=None, omega=None, omegao=None, alpha=None, tau=None):
self.N = cascade.N
self.total = totalreads.reshape(self.N, 1)
self.estim = np.zeros((self.N, 2), dtype=float)
if alpha is None:
indices = np.argsort(self.total.ravel())[:self.N / 2]
self.estim[indices, 1:] = -MAX
indices = np.argsort(self.total.ravel())[self.N / 2:]
self.estim[indices, 1:] = MAX
else:
footprint_logodds = np.zeros((self.N, 1), dtype=float)
if gamma.model == 'modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=gamma.model)
elif gamma.model == 'modelB':
lhoodA, lhoodB = likelihoodAB(cascade,
mu=mu,
model=gamma.model)
elif gamma.model == 'modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade,
B=B,
omega=omega,
omegao=omegao,
model=gamma.model)
for j in xrange(pi.J):
if model == 'modelC':
footprint_logodds += insum(
gamma.value[j] * lhoodA.value[j] - lhoodC.value[j] +
(1 - gamma.value[j]) * lhoodB.value[j], [1])
else:
footprint_logodds += insum(
(1 - gamma.value[j]) *
(lhoodB.value[j] - lhoodA.value[j]), [1])
footprint_logodds += insum(gamma.value[j]*(nplog(pi.estim[j])-nplog(gamma.value[j])) \
+ (1-gamma.value[j])*(nplog(1-pi.estim[j])-nplog(1-gamma.value[j])),[1])
self.estim[:,1:] = beta.estim[0] + beta.estim[1]*scores + footprint_logodds \
+ gammaln(self.total+alpha.estim[1]) - gammaln(self.total+alpha.estim[0]) \
+ gammaln(alpha.estim[0]) - gammaln(alpha.estim[1]) \
+ alpha.estim[1]*nplog(tau.estim[1]) - alpha.estim[0]*nplog(tau.estim[0]) \
+ self.total*(nplog(1-tau.estim[1])-nplog(1-tau.estim[0]))
if alpha is None:
self.estim[self.estim == np.inf] = MAX
self.estim = np.exp(self.estim -
np.max(self.estim, 1).reshape(self.N, 1))
self.estim = self.estim / insum(self.estim, [1])
else:
self.estim[:, 1:] = self.estim[:, 1:] / np.log(10)
def update(self, cascade, pi, mu=None, B=None, tau=None):
for j in xrange(self.J):
if self.model == "modelA":
lhoodA = cascade.total[j] * nplog(0.5)
lhoodB = cascade.value[j] * nplog(B.value[j]) + (cascade.total[j] - cascade.value[j]) * nplog(
1 - B.value[j]
)
elif self.model == "modelB":
lhoodA = cascade.total[j] * nplog(0.5)
lhoodB = (
gammaln(cascade.value[j] + mu.estim[j])
+ gammaln(cascade.total[j] - cascade.value[j] + mu.estim[j])
- gammaln(cascade.total[j] + 2 * mu.estim[j])
+ gammaln(2 * mu.estim[j])
- 2 * gammaln(mu.estim[j])
)
elif self.model == "modelC":
lhoodA = (
gammaln(cascade.value[j] + 0.5 * tau.value[j])
+ gammaln(cascade.total[j] - cascade.value[j] + 0.5 * tau.value[j])
- gammaln(cascade.total[j] + tau.value[j])
+ gammaln(tau.value[j])
- 2 * gammaln(0.5 * tau.value[j])
)
lhoodB = (
gammaln(cascade.value[j] + B.value[j] * tau.value[j])
+ gammaln(cascade.total[j] - cascade.value[j] + (1 - B.value[j]) * tau.value[j])
- gammaln(cascade.total[j] + tau.value[j])
+ gammaln(tau.value[j])
- gammaln(B.value[j] * tau.value[j])
- gammaln((1 - B.value[j]) * tau.value[j])
)
log_posterior_odds = (
nplog(pi.estim[j]) - nplog(1 - pi.estim[j]) + 1.0 / cascade.N * (lhoodA.sum(0) - lhoodB.sum(0))
)
self.value[j] = logistic(-log_posterior_odds)
def update(self, cascade, pi, mu=None, B=None, tau=None):
for j in xrange(self.J):
if self.model=='modelA':
lhoodA = cascade.total[j]*nplog(0.5)
lhoodB = cascade.value[j]*nplog(B.value[j]) + (cascade.total[j]-cascade.value[j])*nplog(1-B.value[j])
elif self.model=='modelB':
lhoodA = cascade.total[j]*nplog(0.5)
lhoodB = gammaln(cascade.value[j]+mu.estim[j]) + gammaln(cascade.total[j]-cascade.value[j]+mu.estim[j]) \
- gammaln(cascade.total[j]+2*mu.estim[j]) + gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j])
elif self.model=='modelC':
lhoodA = gammaln(cascade.value[j]+0.5*tau.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*tau.value[j]) \
- gammaln(cascade.total[j]+tau.value[j]) + gammaln(tau.value[j]) - 2*gammaln(0.5*tau.value[j])
lhoodB = gammaln(cascade.value[j]+B.value[j]*tau.value[j]) \
+ gammaln(cascade.total[j]-cascade.value[j]+(1-B.value[j])*tau.value[j]) \
- gammaln(cascade.total[j]+tau.value[j]) + gammaln(tau.value[j]) - gammaln(B.value[j]*tau.value[j]) \
- gammaln((1-B.value[j])*tau.value[j])
log_posterior_odds = nplog(pi.estim[j]) - nplog(1-pi.estim[j]) + 1./cascade.N*(lhoodA.sum(0) - lhoodB.sum(0))
self.value[j] = logistic(-log_posterior_odds)
def update_Estep(self,
cascade,
scores,
alpha,
beta,
tau,
pi,
gamma,
mu=None,
B=None,
omega=None,
omegao=None):
footprint_logodds = np.zeros((self.N, 1), dtype=float)
if gamma.model == 'modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=gamma.model)
elif gamma.model == 'modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=gamma.model)
elif gamma.model == 'modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade,
B=B,
omega=omega,
omegao=omegao,
model=gamma.model)
for j in xrange(pi.J):
footprint_logodds += insum((1-gamma.value[j])*(lhoodB.value[j]-lhoodA.value[j]) \
+ gamma.value[j]*(nplog(pi.estim[j])-nplog(gamma.value[j])) \
+ (1-gamma.value[j])*(nplog(1-pi.estim[j])-nplog(1-gamma.value[j])),[1])
self.estim[:,1:] = beta.estim[0] + beta.estim[1]*scores + footprint_logodds \
+ gammaln(self.total+alpha.estim[1]) - gammaln(self.total+alpha.estim[0]) \
+ gammaln(alpha.estim[0]) - gammaln(alpha.estim[1]) \
+ alpha.estim[1]*nplog(tau.estim[1]) - alpha.estim[0]*nplog(tau.estim[0]) \
+ self.total*(nplog(1-tau.estim[1])-nplog(1-tau.estim[0]))
self.estim[:, 0] = 0.
self.estim[self.estim == np.inf] = MAX
self.estim = np.exp(self.estim -
np.max(self.estim, 1).reshape(self.N, 1))
self.estim = self.estim / insum(self.estim, [1])
if np.isnan(self.estim).any():
print "Nan in Eta"
raise ValueError
if np.isinf(self.estim).any():
print "Inf in Eta"
raise ValueError
def logposteriorodds_poissonbinomial(reads, gamma, pi, parameters):
N, L = reads.shape
cascade = Cascade(L)
cascade.setreads(reads)
logodds = np.zeros((N,), dtype=float)
if gamma.model == "modelA":
B = parameters
elif gamma.model == "modelB":
mu = parameters
elif gamma.model == "modelC":
B, tau = parameters
for j in xrange(pi.J):
if gamma.model == "modelA":
lhoodA = cascade.total[j] * nplog(0.5)
lhoodB = cascade.value[j] * nplog(B.value[j]) + (cascade.total[j] - cascade.value[j]) * nplog(
1 - B.value[j]
)
elif gamma.model == "modelB":
lhoodA = cascade.total[j] * nplog(0.5)
lhoodB = (
gammaln(cascade.value[j] + mu.estim[j])
+ gammaln(cascade.total[j] - cascade.value[j] + mu.estim[j])
- gammaln(cascade.total[j] + 2 * mu.estim[j])
+ gammaln(2 * mu.estim[j])
- 2 * gammaln(mu.estim[j])
)
elif gamma.model == "modelC":
lhoodA = (
gammaln(cascade.value[j] + 0.5 * tau.value[j])
+ gammaln(cascade.total[j] - cascade.value[j] + 0.5 * tau.value[j])
- gammaln(cascade.total[j] + tau.value[j])
+ gammaln(tau.value[j])
- 2 * gammaln(0.5 * tau.value[j])
)
lhoodB = (
gammaln(cascade.value[j] + B.value[j] * tau.value[j])
+ gammaln(cascade.total[j] - cascade.value[j] + (1 - B.value[j]) * tau.value[j])
- gammaln(cascade.total[j] + tau.value[j])
+ gammaln(tau.value[j])
- gammaln(B.value[j] * tau.value[j])
- gammaln((1 - B.value[j]) * tau.value[j])
)
logratio = nplog(1 - pi.estim[j]) + lhoodB - nplog(pi.estim[j]) - lhoodA
logodds += np.sum(nplog(pi.estim[j]) - nplog(logistic(logratio)), 1)
return logodds
def likelihoodAB(cascade,
mu=None,
B=None,
omega=None,
omegao=None,
model='modelB'):
lhoodA = Cascade(cascade.L)
lhoodB = Cascade(cascade.L)
if model == 'modelC':
lhoodC = Cascade(cascade.L)
for j in xrange(cascade.J):
if model == 'modelA':
lhoodA.value[j] = cascade.total[j] * nplog(0.5)
lhoodB.value[j] = cascade.value[j] * nplog(B.value[j]) + (
cascade.total[j] - cascade.value[j]) * nplog(1 - B.value[j])
elif model == 'modelB':
lhoodA.value[j] = cascade.total[j] * nplog(0.5)
lhoodB.value[j] = gammaln(cascade.value[j]+mu.estim[j]) + gammaln(cascade.total[j]-cascade.value[j]+mu.estim[j]) \
- gammaln(cascade.total[j]+2*mu.estim[j]) + gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j])
elif model == 'modelC':
lhoodA.value[j] = gammaln(cascade.value[j]+0.5*omega.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*omega.value[j]) \
- gammaln(cascade.total[j]+omega.value[j]) + gammaln(omega.value[j]) - 2*gammaln(0.5*omega.value[j])
lhoodB.value[j] = gammaln(cascade.value[j]+B.value[j]*omega.value[j]) \
+ gammaln(cascade.total[j]-cascade.value[j]+(1-B.value[j])*omega.value[j]) \
- gammaln(cascade.total[j]+omega.value[j]) + gammaln(omega.value[j]) - gammaln(B.value[j]*omega.value[j]) \
- gammaln((1-B.value[j])*omega.value[j])
lhoodC.value[j] = gammaln(cascade.value[j]+0.5*omegao.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*omegao.value[j]) \
- gammaln(cascade.total[j]+omegao.value[j]) + gammaln(omegao.value[j]) - 2*gammaln(0.5*omegao.value[j])
if model == 'modelC':
return lhoodA, lhoodB, lhoodC
else:
return lhoodA, lhoodB
def update_Estep(self,
cascade,
eta,
pi,
mu=None,
B=None,
omega=None,
omegao=None):
if self.model == 'modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=self.model)
elif self.model == 'modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=self.model)
elif self.model == 'modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade,
B=B,
omega=omega,
omegao=omegao,
model=self.model)
for j in xrange(self.J):
log_posterior_odds = nplog(pi.estim[j]) - nplog(1-pi.estim[j]) \
+ outsum(eta.estim[:,1:]*(lhoodA.value[j]-lhoodB.value[j]))/outsum(eta.estim[:,1:])
self.value[j] = newlogistic(-log_posterior_odds)
def loglikelihood(cascade, gamma, pi, B=None, mu=None, tau=None):
L = 0.0
for j in xrange(cascade.J):
if gamma.model == "modelA":
lhoodA = cascade.total[j] * nplog(0.5)
lhoodB = cascade.value[j] * nplog(B.value[j]) + (cascade.total[j] - cascade.value[j]) * nplog(
1 - B.value[j]
)
elif gamma.model == "modelB":
lhoodA = cascade.total[j] * nplog(0.5)
lhoodB = (
gammaln(cascade.value[j] + mu.estim[j])
+ gammaln(cascade.total[j] - cascade.value[j] + mu.estim[j])
- gammaln(cascade.total[j] + 2 * mu.estim[j])
+ gammaln(2 * mu.estim[j])
- 2 * gammaln(mu.estim[j])
)
elif gamma.model == "modelC":
lhoodA = (
gammaln(cascade.value[j] + 0.5 * tau.value[j])
+ gammaln(cascade.total[j] - cascade.value[j] + 0.5 * tau.value[j])
- gammaln(cascade.total[j] + tau.value[j])
+ gammaln(tau.value[j])
- 2 * gammaln(0.5 * tau.value[j])
)
lhoodB = (
gammaln(cascade.value[j] + B.value[j] * tau.value[j])
+ gammaln(cascade.total[j] - cascade.value[j] + (1 - B.value[j]) * tau.value[j])
- gammaln(cascade.total[j] + tau.value[j])
+ gammaln(tau.value[j])
- gammaln(B.value[j] * tau.value[j])
- gammaln((1 - B.value[j]) * tau.value[j])
)
L += np.sum(
gamma.value[j] * lhoodA.sum(0)
+ (1 - gamma.value[j]) * lhoodB.sum(0)
+ cascade.N
* (
gamma.value[j] * nplog(pi.estim[j])
+ (1 - gamma.value[j]) * nplog(1 - pi.estim[j])
- gamma.value[j] * nplog(gamma.value[j])
- (1 - gamma.value[j]) * nplog(1 - gamma.value[j])
)
)
return L
def __init__(self, cascade, totalreads, scores, gamma=None, beta=None, \
pi=None, mu=None, B=None, omega=None, omegao=None, alpha=None, tau=None):
self.N = cascade.N
self.total = totalreads.reshape(self.N,1)
self.estim = np.zeros((self.N, 2),dtype=float)
if alpha is None:
indices = np.argsort(self.total.ravel())[:self.N/2]
self.estim[indices,1:] = -MAX
indices = np.argsort(self.total.ravel())[self.N/2:]
self.estim[indices,1:] = MAX
else:
footprint_logodds = np.zeros((self.N,1),dtype=float)
if gamma.model=='modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=gamma.model)
elif gamma.model=='modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=gamma.model)
elif gamma.model=='modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade, B=B, omega=omega, omegao=omegao, model=gamma.model)
for j in xrange(pi.J):
if model=='modelC':
footprint_logodds += insum(gamma.value[j]*lhoodA.value[j]-lhoodC.value[j]+(1-gamma.value[j])*lhoodB.value[j],[1])
else:
footprint_logodds += insum((1-gamma.value[j])*(lhoodB.value[j]-lhoodA.value[j]),[1])
footprint_logodds += insum(gamma.value[j]*(nplog(pi.estim[j])-nplog(gamma.value[j])) \
+ (1-gamma.value[j])*(nplog(1-pi.estim[j])-nplog(1-gamma.value[j])),[1])
self.estim[:,1:] = beta.estim[0] + beta.estim[1]*scores + footprint_logodds \
+ gammaln(self.total+alpha.estim[1]) - gammaln(self.total+alpha.estim[0]) \
+ gammaln(alpha.estim[0]) - gammaln(alpha.estim[1]) \
+ alpha.estim[1]*nplog(tau.estim[1]) - alpha.estim[0]*nplog(tau.estim[0]) \
+ self.total*(nplog(1-tau.estim[1])-nplog(1-tau.estim[0]))
if alpha is None:
self.estim[self.estim==np.inf] = MAX
self.estim = np.exp(self.estim-np.max(self.estim,1).reshape(self.N,1))
self.estim = self.estim/insum(self.estim,[1])
else:
self.estim[:,1:] = self.estim[:,1:]/np.log(10)
def update_Mstep(self, eta, tau):
etaestim = np.zeros((eta.estim.shape[0], 2), dtype=float)
etaestim[:, 0] = eta.estim[:, 0]
etaestim[:, 1] = eta.estim[:, 1:].sum(1)
C = nplog(tau.estim) * outsum(etaestim)
def F(x):
func = outsum(gammaln(eta.total+x)*etaestim) \
- gammaln(x)*outsum(etaestim) + C*x
f = -1. * func.sum()
if np.isnan(f) or np.isinf(f):
return np.inf
else:
return f
def Fprime(x):
df = outsum(digamma(eta.total+x)*etaestim) \
- digamma(x)*outsum(etaestim) + C
Df = -1. * df.ravel()
if np.isnan(Df).any() or np.isinf(Df).any():
return np.array([np.inf, np.inf])
else:
return Df
bounds = [(0, None), (0, None)]
xo = self.estim.copy()
solution = opt.fmin_l_bfgs_b(F,
xo,
fprime=Fprime,
bounds=bounds,
disp=0)
self.estim = solution[0]
if np.isnan(self.estim).any():
print "Nan in Alpha"
raise ValueError
if np.isinf(self.estim).any():
print "Inf in Alpha"
raise ValueError
def bayes_optimal_estimator(cascade, eta, pi, B=None, mu=None, model='modelA'):
"""
computes the posterior mean conditional on the most likely
set of states for gamma.
"""
M1 = Cascade(cascade.L)
M2 = Cascade(cascade.L)
if isinstance(eta, Eta):
states = eta.estim[:, 1:] > 0.5
else:
states = eta[:, 1:]
if not isinstance(pi, Pi):
pitmp = Pi(cascade.J)
pitmp.estim = pi
pi = pitmp
if model == 'modelA':
for j in range(pi.J):
ratio = nplog(1-pi.estim[j]) - nplog(pi.estim[j]) + (cascade.value[j]*states).sum(0)*nplog(B.value[j]) \
+ ((cascade.total[j]-cascade.value[j])*states).sum(0)*nplog(1-B.value[j]) \
- (cascade.total[j]*states).sum(0)*nplog(0.5)
M1.value[j] = 0.5 * newlogistic(ratio) + B.value[j] * newlogistic(
-ratio)
M2.value[j] = 0.25 * newlogistic(
ratio) + B.value[j]**2 * newlogistic(-ratio)
elif model == 'modelB':
if not isinstance(mu, Mu):
mutmp = Mu(cascade.J)
mutmp.estim = mu
mu = mutmp
for j in range(pi.J):
ratio = nplog(1-pi.estim[j]) - nplog(pi.estim[j]) + gammaln((cascade.value[j]*states).sum(0)+mu.estim[j]) \
+ gammaln((cascade.total[j]*states).sum(0)-(cascade.value[j]*states).sum(0)+mu.estim[j]) \
- gammaln((cascade.total[j]*states).sum(0)+2*mu.estim[j]) \
+ gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j]) - (cascade.total[j]*states).sum(0)*nplog(0.5)
M1.value[j] = 0.5*newlogistic(ratio) \
+ ((cascade.value[j]*states).sum(0)+mu.estim[j])/((cascade.total[j]*states).sum(0)+mu.estim[j])*newlogistic(-ratio)
M2.value[j] = 0.25*newlogistic(ratio) \
+ ((cascade.value[j]*states).sum(0)+mu.estim[j]+1)/((cascade.total[j]*states).sum(0)+mu.estim[j]+1) \
* ((cascade.value[j]*states).sum(0)+mu.estim[j])/((cascade.total[j]*states).sum(0)+mu.estim[j])*newlogistic(-ratio)
elif model == 'modelC':
raise NotImplementedError
return M1, M2
def update_Mstep(self, eta, tau):
etaestim = np.zeros((eta.estim.shape[0],2),dtype=float)
etaestim[:,0] = eta.estim[:,0]
etaestim[:,1] = eta.estim[:,1:].sum(1)
C = nplog(tau.estim)*outsum(etaestim)
def F(x):
func = outsum(gammaln(eta.total+x)*etaestim) \
- gammaln(x)*outsum(etaestim) + C*x
f = -1.*func.sum()
if np.isnan(f) or np.isinf(f):
return np.inf
else:
return f
def Fprime(x):
df = outsum(digamma(eta.total+x)*etaestim) \
- digamma(x)*outsum(etaestim) + C
Df = -1.*df.ravel()
if np.isnan(Df).any() or np.isinf(Df).any():
return np.array([np.inf, np.inf])
else:
return Df
bounds = [(0, None), (0, None)]
xo = self.estim.copy()
solution = opt.fmin_l_bfgs_b(F, xo, fprime=Fprime, bounds=bounds, disp=0)
self.estim = solution[0]
if np.isnan(self.estim).any():
print "Nan in Alpha"
raise ValueError
if np.isinf(self.estim).any():
print "Inf in Alpha"
raise ValueError
def bayes_optimal_estimator(cascade, eta, pi, B=None, mu=None, model='modelA'):
"""
computes the posterior mean conditional on the most likely
set of states for gamma.
"""
M1 = Cascade(cascade.L)
M2 = Cascade(cascade.L)
if isinstance(eta, Eta):
states = eta.estim[:,1:]>0.5
else:
states = eta[:,1:]
if not isinstance(pi, Pi):
pitmp = Pi(cascade.J)
pitmp.estim = pi
pi = pitmp
if model=='modelA':
for j in range(pi.J):
ratio = nplog(1-pi.estim[j]) - nplog(pi.estim[j]) + (cascade.value[j]*states).sum(0)*nplog(B.value[j]) \
+ ((cascade.total[j]-cascade.value[j])*states).sum(0)*nplog(1-B.value[j]) \
- (cascade.total[j]*states).sum(0)*nplog(0.5)
M1.value[j] = 0.5*newlogistic(ratio) + B.value[j]*newlogistic(-ratio)
M2.value[j] = 0.25*newlogistic(ratio) + B.value[j]**2*newlogistic(-ratio)
elif model=='modelB':
if not isinstance(mu, Mu):
mutmp = Mu(cascade.J)
mutmp.estim = mu
mu = mutmp
for j in range(pi.J):
ratio = nplog(1-pi.estim[j]) - nplog(pi.estim[j]) + gammaln((cascade.value[j]*states).sum(0)+mu.estim[j]) \
+ gammaln((cascade.total[j]*states).sum(0)-(cascade.value[j]*states).sum(0)+mu.estim[j]) \
- gammaln((cascade.total[j]*states).sum(0)+2*mu.estim[j]) \
+ gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j]) - (cascade.total[j]*states).sum(0)*nplog(0.5)
M1.value[j] = 0.5*newlogistic(ratio) \
+ ((cascade.value[j]*states).sum(0)+mu.estim[j])/((cascade.total[j]*states).sum(0)+mu.estim[j])*newlogistic(-ratio)
M2.value[j] = 0.25*newlogistic(ratio) \
+ ((cascade.value[j]*states).sum(0)+mu.estim[j]+1)/((cascade.total[j]*states).sum(0)+mu.estim[j]+1) \
* ((cascade.value[j]*states).sum(0)+mu.estim[j])/((cascade.total[j]*states).sum(0)+mu.estim[j])*newlogistic(-ratio)
elif model=='modelC':
raise NotImplementedError
return M1, M2
def logposteriorodds_poissonbinomial(reads, gamma, pi, parameters):
N,L = reads.shape
cascade = Cascade(L)
cascade.setreads(reads)
logodds = np.zeros((N,),dtype=float)
if gamma.model=='modelA':
B = parameters
elif gamma.model=='modelB':
mu = parameters
elif gamma.model=='modelC':
B, tau = parameters
for j in xrange(pi.J):
if gamma.model=='modelA':
lhoodA = cascade.total[j]*nplog(0.5)
lhoodB = cascade.value[j]*nplog(B.value[j]) + (cascade.total[j]-cascade.value[j])*nplog(1-B.value[j])
elif gamma.model=='modelB':
lhoodA = cascade.total[j]*nplog(0.5)
lhoodB = gammaln(cascade.value[j]+mu.estim[j]) + gammaln(cascade.total[j]-cascade.value[j]+mu.estim[j]) \
- gammaln(cascade.total[j]+2*mu.estim[j]) + gammaln(2*mu.estim[j]) - 2*gammaln(mu.estim[j])
elif gamma.model=='modelC':
lhoodA = gammaln(cascade.value[j]+0.5*tau.value[j]) + gammaln(cascade.total[j]-cascade.value[j]+0.5*tau.value[j]) \
- gammaln(cascade.total[j]+tau.value[j]) + gammaln(tau.value[j]) - 2*gammaln(0.5*tau.value[j])
lhoodB = gammaln(cascade.value[j]+B.value[j]*tau.value[j]) \
+ gammaln(cascade.total[j]-cascade.value[j]+(1-B.value[j])*tau.value[j]) \
- gammaln(cascade.total[j]+tau.value[j]) + gammaln(tau.value[j]) - gammaln(B.value[j]*tau.value[j]) \
- gammaln((1-B.value[j])*tau.value[j])
logratio = nplog(1-pi.estim[j]) + lhoodB - nplog(pi.estim[j]) - lhoodA
logodds += np.sum(nplog(pi.estim[j]) - nplog(logistic(logratio)),1)
return logodds
def logposteriorodds_multinomial(reads, footprint, null):
logodds = insum(reads*nplog(footprint.ravel()),[1]) - insum(reads*nplog(null),[1])
return logodds.ravel()
def logposteriorodds_multinomial(reads, footprint, null):
logodds = insum(reads * nplog(footprint.ravel()), [1]) - insum(reads * nplog(null), [1])
return logodds.ravel()
def likelihood(cascade,
scores,
eta,
gamma,
pi,
alpha,
beta,
tau,
mu=None,
B=None,
omega=None,
omegao=None):
apriori = beta.estim[0] + beta.estim[1] * scores
if gamma.model == 'modelA':
lhoodA, lhoodB = likelihoodAB(cascade, B=B, model=gamma.model)
elif gamma.model == 'modelB':
lhoodA, lhoodB = likelihoodAB(cascade, mu=mu, model=gamma.model)
elif gamma.model == 'modelC':
lhoodA, lhoodB, lhoodC = likelihoodAB(cascade,
B=B,
omega=omega,
omegao=omegao,
model=gamma.model)
footprint = np.zeros((cascade.N, 1), dtype=float)
for j in xrange(pi.J):
footprint += insum(gamma.value[j]*lhoodA.value[j] + (1-gamma.value[j])*lhoodB.value[j] \
+ gamma.value[j]*(nplog(pi.estim[j])-nplog(gamma.value[j])) \
+ (1-gamma.value[j])*(nplog(1-pi.estim[j])-nplog(1-gamma.value[j])),[1])
P_1 = footprint + gammaln(eta.total+alpha.estim[1]) - gammaln(alpha.estim[1]) \
+ alpha.estim[1]*nplog(tau.estim[1]) + eta.total*nplog(1-tau.estim[1])
P_1[P_1 == np.inf] = MAX
P_1[P_1 == -np.inf] = -MAX
null = np.zeros((cascade.N, 1), dtype=float)
for j in xrange(cascade.J):
if gamma.model == 'modelC':
null = null + insum(lhoodC.value[j], [1])
else:
null = null + insum(lhoodA.value[j], [1])
P_0 = null + gammaln(eta.total+alpha.estim[0]) - gammaln(alpha.estim[0]) \
+ alpha.estim[0]*nplog(tau.estim[0]) + eta.total*nplog(1-tau.estim[0])
P_0[P_0 == np.inf] = MAX
P_0[P_0 == -np.inf] = -MAX
L = P_0*eta.estim[:,:1] + insum(P_1*eta.estim[:,1:],[1]) + apriori*(1-eta.estim[:,:1]) \
- nplog(1+np.exp(apriori)) - insum(eta.estim*nplog(eta.estim),[1])
L = L.sum()
if np.isnan(L):
print "Nan in LogLike"
raise ValueError
if np.isinf(L):
print "Inf in LogLike"
raise ValueError
return L
