def logprior(var_par, draw, k):
# Log of prior probabilities
d = int((len(var_par) / 2 - k) / k)
l = int(len(var_par) / 2)
alpha = np.ones(k) # Prior for mixture probabilities
beta = np.ones(d) # Prior for multinomials
mu, cov = var_par[:l], np.exp(var_par[l:])
samples = draw * cov + mu
pi = softmax(samples[:k])
thetas = softmax(samples[k:].reshape([k, d]), axis=1)
return dirichlet.logpdf(pi, alpha) + np.sum(
[dirichlet.logpdf(theta, beta) + ldt(theta)
for theta in thetas]) + ldt(pi)
def log_prior(self):
lp = 0
for k in range(self.nb_states):
alpha = self.prior['alpha'] * np.ones(self.nb_states)\
+ self.prior['kappa'] * (np.arange(self.nb_states) == k)
lp += dirichlet.logpdf(self.matrix[k], alpha)
return lp
def logprior(var_par, draw, k, a=None, b=None, d=None):
# Log of prior probabilities
l = int(len(var_par) / 2)
q = ((l + 1) / k - 2 - d) / (d + 1)
q = int(q)
mu, cov = var_par[:l], np.exp(var_par[l:])
samples = draw * cov + mu
pars = get_pars(samples, k, d, q)
#pi = softmax(pars['pi'])
pi = stick_backward(pars['pi'])
mus = pars['mu'].reshape([k, d])
alphas = pars['alpha'].reshape([k, q])
tau = pars['tau']
W = pars['W'].reshape([k, d * q])
logp = 0
for j, W_ in enumerate(W):
W_ = W_.reshape([d, q])
tau_ = tau[j]
logp += multi_lpdf(
mus[j], mean=np.zeros(d), cov=1e3 * np.eye(d)) + sum([
multi_lpdf(W_[:, i], mean=np.zeros(d), cov=np.eye(d) / alpha)
for i, alpha in enumerate(np.exp(alphas[j]))
]) + sum(lgamma(np.exp(alphas[j]), 1e-3, 1e3) +
alphas[j]) + lgamma(np.exp(tau_), 1e-3, 1e3) + tau_
#return logp + dirichlet.logpdf(pi, np.ones(k)) + ldt(pi)
return logp + dirichlet.logpdf(pi, np.ones(k)) + np.log(
np.abs(stick_jacobian_det(pars['pi'])))
def log_prior(self):
K = self.K
Ps = np.exp(self.log_Ps - logsumexp(self.log_Ps, axis=1, keepdims=True))
lp = 0
for k in range(K):
alpha = self.alpha * np.ones(K) + self.kappa * (np.arange(K) == k)
lp += dirichlet.logpdf(Ps[k], alpha)
return lp
def logprior(sample, k):
pi = softmax(sample[:k])
a = np.ones(pi.shape[0])
mvnpar = sample[k:]
mus = mvnpar[:-k].reshape([k, int((mvnpar.shape[0] - k) / k)])
taus = mvnpar[-k:]
logp = 0
for i, tau in enumerate(taus):
logp += linvgamma(np.exp(tau), alpha, beta) + tau - k / 2 * np.log(
2 * np.pi) - 0.5 * np.dot(mus[i], mus[i])
return logp + dirichlet.logpdf(pi, a) + ldt(pi)
def p_log_prob(self, idx, z):
x = self.data[idx]
mu, tau, pi = z['mu'], softplus(z['tau']), stick_breaking(z['pi'])
matrix = []
log_prior = 0.
log_prior += np.sum(gamma_logpdf(tau, 1e-5, 1e-5) + np.log(jacobian_softplus(z['tau'])))
log_prior += np.sum(norm.logpdf(mu, 0, 1.))
log_prior += dirichlet.logpdf(pi, 1e3 * np.ones(self.clusters)) + np.log(jacobian_stick_breaking(z['pi']))
for k in range(self.clusters):
matrix.append(np.log(pi[k]) + np.sum(norm.logpdf(x, mu[(k * self.D):((k + 1) * self.D)],
np.full([self.D], 1./np.sqrt(tau[k]))), 1))
matrix = np.vstack(matrix)
vector = logsumexp(matrix, axis=0)
log_lik = np.sum(vector)
return self.scale * log_lik + log_prior
def logprior(var_par, draw, k): # Log of prior probabilities l = int(len(var_par)/2) d = (l-2*k+1)/k d = int(d) mu, cov = var_par[:l], np.exp(var_par[l:]) samples = draw*cov + mu pars = get_pars(samples, k, d) pi = stick_backward(pars['pi']) mus = pars['mu'].reshape([k,d]) taus = pars['tau'] logp = 0 for i, tau in enumerate(taus): logp += linvgamma(np.exp(tau), alpha, beta) + tau + multi_lpdf(mus[i], np.zeros(d), 1) return logp + dirichlet.logpdf(pi, np.ones(k)) + np.log(np.abs(stick_jacobian_det(pars['pi'])))
