"""Implementation of LogNormal likelihood with censorship (with a lower limit)
"""
from typing import Optional, Union
import numpy as np
from scipy.stats import norm as statsnorm
from beetroots.modelling.likelihoods import utils
from beetroots.modelling.likelihoods.abstract_likelihood import Likelihood
[docs]
class CensoredLogNormalLikelihood(Likelihood):
r"""Class implementing a LogNormal likelihood model with lower censorship"""
__slots__ = (
"forward_map",
"D",
"L",
"N",
"y",
"logy",
"sigma",
"omega",
"log_omega",
)
def __init__(
self,
forward_map,
D: int,
L: int,
N: int,
y: np.ndarray,
sigma: Union[float, np.ndarray],
omega: Union[float, np.ndarray],
) -> None:
"""Constructor of the LogNormalLikelihood object.
Parameters
----------
forward_map : ForwardMap instance
forward map
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)
mean of the LogNormal distribution
bias : float or np.ndarray of shape (N, L)
variance of the LogNormal distribution
sigma : float or np.ndarray of shape (N, L)
variance of the LogNormal distribution
omega : float or np.ndarray of shape (N, L)
censorship threshold
Raises
------
ValueError
y must have the shape (N, L)
"""
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))
else:
assert sigma.shape == (N, L)
self.sigma = sigma
if isinstance(omega, (float, int)):
self.omega = omega * np.ones((N, L))
else:
assert omega.shape == (N, L)
self.omega = omega
self.log_omega = np.log(self.omega)
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,
idx: Optional[np.ndarray] = None,
) -> Union[float, np.ndarray]:
r"""[summary]
.. math::
p(y_{n,\ell} \vert x) \propto \exp \left\{- [y_{n,\ell} = \omega] \Phi( \frac{\omega - f_{\ell}(x_n)}{\sigma^2} \right) - [y_{n,\ell} > \omega] \frac{\omega - f_{\ell}(x_n)}{\sigma^2} \right\}
"""
if idx is None:
N_pix = self.N * 1
logy = self.logy * 1
sigma = self.sigma * 1
log_omega = self.omega * 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))
log_omega = 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)
)
log_omega[i_pix, :, :] = self.log_omega[idx[i_pix], :][
None, :
] * np.ones((k_mtm, self.L))
logy = logy.reshape((N_pix, self.L))
sigma = sigma.reshape((N_pix, self.L))
log_omega = log_omega.reshape((N_pix, self.L))
nlpdf = np.where(
logy == log_omega,
self.neglog_pdf_ac(
forward_map_evals,
nll_utils,
logy,
sigma,
log_omega,
),
self.neglog_pdf_au(
forward_map_evals,
nll_utils,
logy,
sigma,
log_omega,
),
) # (N_pix, L)
if pixelwise:
return np.sum(nlpdf, axis=1) # (N_pix,)
return np.sum(nlpdf)
[docs]
def neglog_pdf_ac(
self,
forward_map_evals: dict,
nll_utils: dict,
log_y: np.ndarray,
sigma: np.ndarray,
log_omega: np.ndarray,
) -> np.ndarray:
return -statsnorm.logcdf((log_omega - forward_map_evals["f_Theta"]) / sigma)
[docs]
def neglog_pdf_au(
self,
forward_map_evals: dict,
nll_utils: dict,
log_y: np.ndarray,
sigma: np.ndarray,
log_omega: np.ndarray,
) -> np.ndarray:
return log_y + (forward_map_evals["f_Theta"] - log_y) ** 2 / (2 * sigma**2)
[docs]
def gradient_neglog_pdf(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
"""[summary]
[extended_summary]
Parameters
----------
x : np.ndarray of shape (N, D)
[description]
f_Theta : np.ndarray of shape (N, L), optional
image of x via forward map, by default None
grad_f_Theta : np.ndarray of shape (N, D, L), optional
[description], by default None
Returns
-------
np.ndarray of shape (N, D)
[description]
"""
grad_ = np.where(
(self.y == self.omega)[:, None, :],
self.gradient_neglog_pdf_ac(forward_map_evals, nll_utils),
self.gradient_neglog_pdf_au(forward_map_evals, nll_utils),
) # (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 gradient_neglog_pdf_ac(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
grad_ = (
forward_map_evals["grad_f_Theta"]
* (
utils.norm_pdf_cdf_ratio(
(self.log_omega - forward_map_evals["f_Theta"]) / self.sigma
)
/ self.sigma
)[:, None, :]
)
return grad_ # (N, D, L)
[docs]
def gradient_neglog_pdf_au(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
grad_ = (
forward_map_evals["grad_f_Theta"]
* ((forward_map_evals["f_Theta"] - self.logy) / self.sigma**2)[:, None, :]
)
return grad_ # (N, D, L)
[docs]
def hess_diag_neglog_pdf(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
r"""[summary]
[extended_summary]
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, L)
[description]
"""
hess_diag = np.where(
(self.y == self.omega)[:, None, :],
self.hess_diag_neglog_pdf_ac(forward_map_evals, nll_utils),
self.hess_diag_neglog_pdf_au(forward_map_evals, nll_utils),
) # (N, D, L)
# ! 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 hess_diag_neglog_pdf_ac(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
hess_diag = (
utils.norm_pdf_cdf_ratio(
(self.log_omega - forward_map_evals["f_Theta"]) / self.sigma
)
/ self.sigma
)[:, None, :] * (
forward_map_evals["hess_diag_f_Theta"]
+ forward_map_evals["grad_f_Theta"] ** 2
* (
(
(self.log_omega - forward_map_evals["f_Theta"]) / self.sigma
+ utils.norm_pdf_cdf_ratio(
(self.log_omega - forward_map_evals["f_Theta"]) / self.sigma
)
)
/ self.sigma
)[:, None, :]
)
return hess_diag # (N, D, L)
[docs]
def hess_diag_neglog_pdf_au(
self, forward_map_evals: dict, nll_utils: dict
) -> np.ndarray:
return (1 / self.sigma**2)[:, None, :] * (
forward_map_evals["grad_f_Theta"] ** 2
+ forward_map_evals["hess_diag_f_Theta"]
* (forward_map_evals["f_Theta"] - self.logy)[:, None, :]
) # (N, D, L)
[docs]
def evaluate_all_forward_map(
self,
Theta: np.ndarray,
compute_derivatives: bool,
compute_derivatives_2nd_order: bool,
) -> dict:
assert len(Theta.shape) == 2 and Theta.shape[1] == self.D
forward_map_evals = self.forward_map.compute_all(
Theta, True, False, compute_derivatives, compute_derivatives_2nd_order
)
return forward_map_evals
[docs]
def evaluate_all_nll_utils(
self,
forward_map_evals: dict,
idx: Optional[np.ndarray] = None,
compute_derivatives: bool = True,
compute_derivatives_2nd_order: bool = True,
) -> dict:
nll_utils = {}
return nll_utils