"""Implementation of log-normal likelihood
"""
from typing import Optional, Union
import numpy as np
from beetroots.modelling.likelihoods.abstract_likelihood import Likelihood
[docs]
class LogNormalLikelihood(Likelihood):
"""Class implementing a log-normal likelihood model."""
__slots__ = (
"forward_map",
"D",
"L",
"N",
"y",
"logy",
"sigma",
)
def __init__(
self,
forward_map,
D: int,
L: int,
N: int,
y: np.ndarray,
sigma: Union[float, np.ndarray],
) -> None:
"""Constructor of the LogNormalLikelihood object.
Parameters
----------
forward_map : ForwardMap instance
forward map, involved in the mean of the distribution.
D : int
number of disinct physical parameters in input space.
L : int
number of distinct observed physical parameters.
N : int
number of pixels in each physical dimension
y : np.ndarray of shape (N, L)
parameter of the log-normal distribution
sigma : float or np.ndarray of shape (N, L)
variance of the log-normal distribution
Raises
------
ValueError
y must have the shape (N, L)
Note
----
* Derivatives and Hessians are taken with respect of the mean of the distribution.
* y provided in log space already? (saving computations)
"""
# TODO: add method to update y? (instead of having to reinstantiate the full object any time y is updated?)
super().__init__(forward_map, D, L, N, y)
self.logy = np.log(self.y)
# ! trigger an error is the mean y contains less than N elements
if not y.shape == (N, L):
raise ValueError(
"y must have the shape (N, L) = ({}, {}) elements".format(
self.N, self.L
)
)
if isinstance(sigma, (float, int)):
self.sigma = sigma * np.ones(
(N, L)
) # ! P.-A.: not sure this is actually needed... (unless broadcast is not enough here)
else:
assert sigma.shape == (N, L)
self.sigma = sigma
def _update_observations(self, y):
"""Update the parameters on which the distribution is defined (if
updated within the solver).
Parameters
----------
y : np.ndarray of shape (N, L)
parameter of the log-normal distribution
Raises
------
ValueError
y must have the shape (N, L)
"""
# ! trigger an error is the mean y contains less than N elements
if not y.shape == (self.N, self.L):
raise ValueError(
"y must have the shape (N, L) = ({}, {}) elements".format(
self.N, self.L
)
)
self.y = y
self.logy = np.log(self.y)
[docs]
def neglog_pdf(
self,
forward_map_evals: dict,
nll_utils: dict,
pixelwise: bool = False,
full: bool = False,
idx: Optional[np.ndarray] = None,
) -> Union[float, np.ndarray]:
# TODO: there are a few steps to be clarified in there
# TODO: (what is the point of the reformatting step in here)
# a priori, sam echange expected
if idx is None:
N_pix = self.N * 1
logy = self.logy * 1
sigma = self.sigma * 1
else:
n_pix = idx.size
k_mtm = forward_map_evals["f_Theta"].shape[0] // n_pix
N_pix = forward_map_evals["f_Theta"].shape[0]
logy = np.zeros((n_pix, k_mtm, self.L))
sigma = np.zeros((n_pix, k_mtm, self.L))
for i_pix in range(n_pix):
logy[i_pix, :, :] = self.logy[idx[i_pix], :][None, :] * np.ones(
(k_mtm, self.L)
)
sigma[i_pix, :, :] = self.sigma[idx[i_pix], :][None, :] * np.ones(
(k_mtm, self.L)
)
logy = logy.reshape((N_pix, self.L))
sigma = sigma.reshape((N_pix, self.L))
nlpdf = logy + (logy - forward_map_evals["log_f_Theta"]) ** 2 / (
2 * sigma**2
) # (N_pix, L)
if full:
return nlpdf # (N_pix, L)
if pixelwise:
return np.sum(nlpdf, axis=1) # (N_pix,)
return np.sum(nlpdf) # float
[docs]
def gradient_neglog_pdf(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
grad_ = (
forward_map_evals["grad_log_f_Theta"]
* ((forward_map_evals["log_f_Theta"] - self.logy) / self.sigma**2)[
:, None, :
]
) # (N, D, L)
# ! issue: do not sum over L if L = D (i.e. identity forward_map)
if not self.D == self.L:
grad_ = np.sum(grad_, axis=2) # (N, D)
return grad_
[docs]
def hess_diag_neglog_pdf(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
r"""Hessian w.r.t to the parameter of the log-normal distribution.
Parameters
----------
x : np.ndarray of shape (N, D)
[description]
f_Theta : np.ndarray of shape (N, L), optional
[description], by default None
grad_f_Theta : np.ndarray of shape (N, D, L), optional
[description], by default None
hess_diag_f_Theta : np.ndarray of shape (N, D, L), optional
[description], by default None
Returns
-------
np.ndarray of shape (N, D)
[description]
"""
hess_diag = (1 / self.sigma**2)[:, None, :] * (
forward_map_evals["grad_log_f_Theta"] ** 2
+ forward_map_evals["hess_diag_log_f_Theta"]
* (forward_map_evals["f_Theta"] - self.logy)[:, None, :]
)
# ! issue: do not sum over L if L = D (i.e. identity forward_map)
if not self.D == self.L:
hess_diag = np.sum(hess_diag, axis=2) # (N, D)
return hess_diag
[docs]
def evaluate_all_forward_map(
self,
Theta: np.ndarray,
compute_derivatives: bool,
compute_derivatives_2nd_order: bool = True,
) -> dict:
assert len(Theta.shape) == 2 and Theta.shape[1] == self.D
forward_map_evals = self.forward_map.compute_all(
Theta, True, True, compute_derivatives, compute_derivatives_2nd_order
)
return forward_map_evals
[docs]
def evaluate_all_nll_utils(
self,
forward_map_evals: dict,
idx: Optional[int] = None,
compute_derivatives: bool = False,
compute_derivatives_2nd_order: bool = True,
) -> dict:
nll_utils = {}
return nll_utils