def _set_initial_values(self, alpha0, nu0, Phi0, mu0, Sigma0, weights0,
alpha_a0, alpha_b0):
if nu0 is None:
nu0 = 3
if Phi0 is None:
Phi0 = np.empty((self.ncomp, self.ndim, self.ndim))
Phi0[:] = np.eye(self.ndim) * (nu0 - 1)
if Sigma0 is None:
# draw from prior
Sigma0 = np.empty((self.ncomp, self.ndim, self.ndim))
for j in xrange(self.ncomp):
Sigma0[j] = pm.rinverse_wishart_prec(nu0 + 2 + self.ncomp, Phi0[j])
# starting values, are these sensible?
if mu0 is None:
mu0 = np.empty((self.ncomp, self.ndim))
for j in xrange(self.ncomp):
mu0[j] = pm.rmv_normal_cov(self.mu_prior_mean,
self.gamma[j] * Sigma0[j])
if weights0 is None:
_, weights0 = stick_break_proc(1, 1, size=self.ncomp - 1)
self._alpha0 = alpha0
self._alpha_a0 = alpha_a0
self._alpha_b0 = alpha_b0
self._weights0 = weights0
self._mu0 = mu0
self._Sigma0 = Sigma0
self._nu0 = nu0 # prior degrees of freedom
self._Phi0 = Phi0 # prior location for Sigma_j's
def _update_mu_Sigma(self, Sigma, component_mask):
mu_output = np.zeros((self.ncomp, self.ndim))
Sigma_output = np.zeros((self.ncomp, self.ndim, self.ndim))
for j in xrange(self.ncomp):
mask = component_mask[j]
Xj = self.data[mask]
nj = len(Xj)
# TODO: sample from prior if nj == 0
sumxj = Xj.sum(0)
gam = self.gamma[j]
mu_hyper = self.mu_prior_mean
post_mean = (mu_hyper / gam + sumxj) / (1 / gam + nj)
post_cov = 1 / (1 / gam + nj) * Sigma[j]
new_mu = pm.rmv_normal_cov(post_mean, post_cov)
Xj_demeaned = Xj - new_mu
mu_SS = np.outer(new_mu - mu_hyper, new_mu - mu_hyper) / gam
data_SS = np.dot(Xj_demeaned.T, Xj_demeaned)
post_Phi = data_SS + mu_SS + self._nu0 * self._Phi0[j]
# symmetrize
post_Phi = (post_Phi + post_Phi.T) / 2
# P(Sigma) ~ IW(nu + 2, nu * Phi)
# P(Sigma | theta, Y) ~
post_nu = nj + self.ncomp + self._nu0 + 3
# pymc rinverse_wishart takes
new_Sigma = pm.rinverse_wishart_prec(post_nu, post_Phi)
mu_output[j] = new_mu
Sigma_output[j] = new_Sigma
return mu_output, Sigma_output
