def variance(self, n_s):
"""
Stochastic approximator of predictive variance.
Follows "Massively Scalable GPs"
Args:
n_s (int): Number of iterations to run stochastic approximation
Returns: Approximate predictive variance at grid points
"""
if self.root_eigdecomp is None:
self.sqrt_eig()
if self.obs_idx is not None:
root_K = self.root_eigdecomp[self.obs_idx, :]
else:
root_K = self.root_eigdecomp
diag = kron_list_diag(self.Ks)
samples = []
for i in range(n_s):
g_m = np.random.normal(size=self.m)
g_n = np.random.normal(size=self.n)
right_side = np.sqrt(self.W).dot(np.dot(root_K, g_m)) +\
np.sqrt(self.noise) * g_n
r = self.opt.cg(self.Ks, right_side)
if self.obs_idx is not None:
Wr = np.zeros(self.m)
Wr[self.obs_idx] = np.multiply(np.sqrt(self.W), r)
else:
Wr = np.multiply(np.sqrt(self.W), r)
samples.append(kron_mvp(self.Ks, Wr))
var = np.var(samples, axis=0)
return np.clip(diag - var, 0, 1e12).flatten(), var
def __init__(self, X, y, kernels, likelihood, mu=None, obs_idx=None):
"""
Args:
kernel (): kernel function
likelihood (): likelihood function. Requires log_like() function
X (): data
y (): responses
mu (): prior mean
noise (): noise variance
obs_idx (): if dealing with partial grid, indices of grid that are observed
verbose (): print or not
"""
super(MFSVI, self).__init__(X, y, kernels, likelihood, mu, obs_idx)
self.q_S = np.log(kron_list_diag(self.Ks))
self.mu_params, self.s_params = (None, None)
def marginal(self):
"""
Calculates marginal likelihood
Returns: marginal likelihood
"""
if self.alpha is None:
self.solve()
if self.eigvals is None:
self.eig_decomp()
mu = self.mu
if self.obs_idx is not None:
mu = self.mu[self.obs_idx]
det = 0.5 * np.sum(np.log(kron_list_diag(self.eigvals) + self.noise))
fit = 0.5 * np.dot(self.y - mu, self.alpha)
prior = 0
for kern in self.kernels:
prior += kern.log_prior(kern.params)
return -det - fit - prior
def variance_pmap(self, n_s=30):
"""
Stochastic approximator of predictive variance.
Follows "Massively Scalable GPs"
Args:
n_s (int): Number of iterations to run stochastic approximation
Returns: Approximate predictive variance at grid points
"""
if self.eigvals or self.eigvecs is None:
self.eig_decomp()
Q = self.eigvecs
Q_t = [v.T for v in self.eigvecs]
Vr = [np.nan_to_num(np.sqrt(e)) for e in self.eigvals]
diag = kron_list_diag(self.Ks) + self.noise
samples = []
for i in range(n_s):
g_m = np.random.normal(size=self.m)
g_n = np.random.normal(size=self.n)
Kroot_g = kron_mvp(Q, kron_mvp(Vr, kron_mvp(Q_t, g_m)))
if self.obs_idx is not None:
Kroot_g = Kroot_g[self.obs_idx]
right_side = Kroot_g + np.sqrt(self.noise) * g_n
r = self.cg_opt.cg(self.Ks, right_side)
if self.obs_idx is not None:
Wr = np.zeros(self.m)
Wr[self.obs_idx] = r
else:
Wr = r
samples.append(kron_mvp(self.Ks, Wr))
est = np.var(samples, axis=0)
return np.clip(diag - est, 0, a_max=None).flatten()
def construct_Ks(self, kernels=None, noise=1e-2):
super(SVIBase, self).construct_Ks()
self.Ks = [K + np.diag(np.ones(K.shape[0])) * noise for K in self.Ks]
self.K_invs = [np.linalg.inv(K) for K in self.Ks]
self.k_inv_diag = kron_list_diag(self.K_invs)
self.det_K = self.log_det_K()