def sample_features(model, data, state):
K, D = state.Z.shape[1], state.X.shape[1]
Lambda = np.dot(state.Z.T, state.Z) / state.sigma_sq_n + np.eye(K) / state.sigma_sq_f
h = np.dot(state.Z.T, state.X) / state.sigma_sq_n
# we can ignore the constant factors because they don't depend on Z
pot = gaussians.Potential(h.T, psd_matrices.FullMatrix(Lambda[nax, :, :]), 0.)
return pot.to_distribution().sample().T
def evidence(model, data, state):
K, D = state.Z.shape[1], state.X.shape[1]
Lambda = np.dot(state.Z.T, state.Z) / state.sigma_sq_n + np.eye(K) / state.sigma_sq_f
h = np.dot(state.Z.T, state.X) / state.sigma_sq_n
# we can ignore the constant factors because they don't depend on Z
pot = gaussians.Potential(h.T, psd_matrices.FullMatrix(Lambda[nax, :, :]), 0.)
return pot.integral().sum()
def cond_U(X, obs, V, ssq_U, ssq_N):
N, K, D = X.shape[0], V.shape[0], X.shape[1]
if np.all(obs):
Lambda = np.diag(1. / ssq_U) + np.dot(V, V.T) / ssq_N
Lambda = Lambda[nax, :, :]
else:
Lambda = np.zeros((N, K, K))
for i in range(N):
idxs = np.where(obs[i, :])[0]
V_curr = V[:, idxs]
Lambda[i, :, :] = np.diag(1. / ssq_U) + np.dot(V_curr, V_curr.T) / ssq_N
h = np.dot(X * obs, V.T) / ssq_N
return gaussians.Potential(h, psd_matrices.FullMatrix(Lambda), 0.)
def from_moments_diag(mu, sigma_sq, Z=0.):
return Distribution(mu, psd_matrices.FullMatrix(np.diag(sigma_sq)), Z)
def from_moments_full(mu, Sigma, Z=0.):
return Distribution(mu, psd_matrices.FullMatrix(Sigma), Z)
def from_moments_full(mu, Sigma):
return Distribution(mu, psd_matrices.FullMatrix(Sigma)).to_potential()