def estimate_nll(X, f_nll_z, f_nll_x_given_z, f_nll_z_given_x,
f_sample_z_given_x, n_samples):
if X.ndim == 2:
log_prior = np.empty((n_samples, X.shape[0]))
log_posterior = np.empty((n_samples, X.shape[0]))
log_recog = np.empty((n_samples, X.shape[0]))
elif X.ndim == 3:
log_prior = np.empty((n_samples, X.shape[0], X.shape[1]))
log_posterior = np.empty((n_samples, X.shape[0], X.shape[1]))
log_recog = np.empty((n_samples, X.shape[0], X.shape[1]))
else:
raise ValueError('unexpected ndim for X, can be 2 or 3')
for i in range(n_samples):
Z = f_sample_z_given_x(X)
log_prior[i] = ma.assert_numpy(-f_nll_z(Z))
log_posterior[i] = ma.assert_numpy(-f_nll_x_given_z(X, Z))
log_recog[i] = ma.assert_numpy(-f_nll_z_given_x(Z, X))
d = log_prior + log_posterior - log_recog
while d.ndim > 1:
d = d.sum(-1)
ll = logsumexp(d, 0) - np.log(n_samples)
# Normalize to average.
ll /= X.shape[0]
if X.ndim == 3:
ll /= X.shape[1]
return -ll
def estimate_nll(X, f_nll_z, f_nll_x_given_z, f_nll_z_given_x,
f_sample_z_given_x, n_samples):
if X.ndim == 2:
log_prior = np.empty((n_samples, X.shape[0]))
log_posterior = np.empty((n_samples, X.shape[0]))
log_recog = np.empty((n_samples, X.shape[0]))
elif X.ndim == 3:
log_prior = np.empty((n_samples, X.shape[0], X.shape[1]))
log_posterior = np.empty((n_samples, X.shape[0], X.shape[1]))
log_recog = np.empty((n_samples, X.shape[0], X.shape[1]))
else:
raise ValueError('unexpected ndim for X, can be 2 or 3')
for i in range(n_samples):
Z = f_sample_z_given_x(X)
log_prior[i] = ma.assert_numpy(-f_nll_z(Z))
log_posterior[i] = ma.assert_numpy(-f_nll_x_given_z(X, Z))
log_recog[i] = ma.assert_numpy(-f_nll_z_given_x(Z, X))
d = log_prior + log_posterior - log_recog
while d.ndim > 1:
d = d.sum(-1)
ll = logsumexp(d, 0) - np.log(n_samples)
# Normalize to average.
ll /= X.shape[0]
if X.ndim == 3:
ll /= X.shape[1]
return -ll
def bound_spectral_radius(arr, bound=1.2):
"""Set the spectral radius of the square matrix ``arr`` to ``bound``.
This is performed by making an Eigendecomposition of ``arr``, rescale all
Eigenvalues such that the absolute value of the greatest matches ``bound``
and recompose it again.
Parameters
----------
arr : array_like, two dimensional
Array to work upon in place.
bound : float, optional, default: 1.2
Examples
--------
>>> import numpy as np
>>> from climin.initialize import bound_spectral_radius
>>> arr = np.arange(9).reshape((3, 3)).astype('float64')
>>> bound_spectral_radius(arr, 1.1)
>>> arr # doctest: +SKIP
array([[ -7.86816957e-17, 8.98979486e-02, 1.79795897e-01],
[ 2.69693846e-01, 3.59591794e-01, 4.49489743e-01],
[ 5.39387691e-01, 6.29285640e-01, 7.19183588e-01]])
"""
vals, vecs = np.linalg.eig(ma.assert_numpy(arr))
vals /= abs(vals).max()
vals *= 1.2
arr[...] = np.dot(vecs, np.dot(np.diag(vals), np.linalg.inv(vecs)))
