"""Defines estimators which estimate a model's ability to represent the data.
All estimators have to implement the `.Estimator` interface.
"""
from __future__ import annotations
from typing import TYPE_CHECKING, Callable, Iterable, Mapping
import numpy as np
from tensorwaves.data.transform import SympyDataTransformer
from tensorwaves.function._backend import find_function, raise_missing_module_error
from tensorwaves.function.sympy import create_parametrized_function, prepare_caching
from tensorwaves.interface import (
DataSample,
DataTransformer,
Estimator,
ParameterValue,
ParametrizedFunction,
)
if TYPE_CHECKING:
import sympy as sp
[docs]def create_cached_function(
expression: sp.Expr,
parameters: Mapping[sp.Symbol, ParameterValue],
backend: str,
free_parameters: Iterable[sp.Symbol],
use_cse: bool = True,
) -> tuple[ParametrizedFunction, DataTransformer]:
"""Create a function and data transformer for cached computations.
Once it is known which parameters in an expression are to be optimized, this
function makes it easy to cache constant sub-trees.
Args:
expression: The `~sympy.core.expr.Expr` that should be expressed in a
computational backend.
parameters: Symbols in the :code:`expression` that should be
interpreted as parameters. The values in this mapping will be used in the
returned :attr:`.ParametrizedFunction.parameters`.
backend: The computational backend to which in which to express the
input :code:`expression`.
use_cse: See :func:`.create_parametrized_function`.
Returns:
A 'cached' `.ParametrizedFunction` with only the free
`~.ParametrizedFunction.parameters` that are to be optimized and a
`.DataTransformer` that needs to be used to transform a data sample for the
original expresion to the cached function.
.. seealso:: This function is an extension of :func:`.prepare_caching` and
:func:`.create_parametrized_function`. :doc:`/usage/caching` shows how
to use this function.
"""
cache_expression, transformer_expressions = prepare_caching(
expression, parameters, free_parameters
)
free_parameter_values = {
par: value for par, value in parameters.items() if par in free_parameters
}
cached_function = create_parametrized_function(
cache_expression, free_parameter_values, backend, use_cse=use_cse
)
cache_transformer = SympyDataTransformer.from_sympy(
transformer_expressions, backend, use_cse=use_cse
)
return cached_function, cache_transformer
[docs]def gradient_creator(
function: Callable[[Mapping[str, ParameterValue]], ParameterValue],
backend: str,
) -> Callable[[Mapping[str, ParameterValue]], dict[str, ParameterValue]]:
# pylint: disable=import-outside-toplevel
if backend == "jax":
try:
import jax
from jax.config import config
except ImportError: # pragma: no cover
raise_missing_module_error("jax", extras_require="jax")
config.update("jax_enable_x64", True)
return jax.grad(function)
def raise_gradient_not_implemented(
parameters: Mapping[str, ParameterValue]
) -> dict[str, ParameterValue]:
raise NotImplementedError(f"Gradient not implemented for back-end {backend}.")
return raise_gradient_not_implemented
[docs]class ChiSquared(Estimator):
r"""Chi-squared test estimator.
.. math:: \chi^2 = \sum_{i=1}^n w_i\left(y_i - f_\mathbf{p}(x_i)\right)^2
Args:
function: A `.ParametrizedFunction` :math:`f_\mathbf{p}` with
a set of free `~.ParametrizedFunction.parameters` :math:`\mathbf{p}`.
domain: Input data-set :math:`\mathbf{x}` of :math:`n` events
:math:`x_i` over which to compute :code:`function` :math:`f_\mathbf{p}`.
observed_values: Observed values :math:`y_i`.
weights: Optional weights :math:`w_i`. Default: :math:`w_i=1`
(unweighted). A common choice is :math:`w_i = 1/\sigma_i^2`, with
:math:`\sigma_i` the uncertainty in each measured value of :math:`y_i`.
backend: Computational backend with which to compute the sum
:math:`\sum_{i=1}^n`.
.. seealso:: :doc:`/usage/chi-squared`
"""
def __init__(
self,
function: ParametrizedFunction,
domain: DataSample,
observed_values: np.ndarray,
weights: np.ndarray | None = None,
backend: str = "numpy",
) -> None:
self.__function = function
self.__domain = domain
self.__observed_values = observed_values
if weights is None:
ones = find_function("ones", backend)
self.__weights = ones(len(self.__observed_values))
else:
self.__weights = weights
self.__gradient = gradient_creator(self.__call__, backend)
self.__sum = find_function("sum", backend)
def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:
self.__function.update_parameters(parameters)
computed_values = self.__function(self.__domain)
chi_squared = self.__weights * (computed_values - self.__observed_values) ** 2
return self.__sum(chi_squared)
[docs] def gradient(
self, parameters: Mapping[str, ParameterValue]
) -> dict[str, ParameterValue]:
return self.__gradient(parameters)
[docs]class UnbinnedNLL(Estimator): # pylint: disable=too-many-instance-attributes
r"""Unbinned negative log likelihood estimator.
The **log likelihood** :math:`\log\mathcal{L}` for a given function
:math:`f_\mathbf{p}: X^m \rightarrow \mathbb{R}` over :math:`N` data points
:math:`\mathbf{x}` and over a (phase space) domain of :math:`n_\mathrm{phsp}` points
:math:`\mathbf{x}_\mathrm{phsp}`, is given by:
.. math::
-\log\mathcal{L} = N\log\lambda -\sum_{i=1}^N \log\left(f_\mathbf{p}(x_i)\right)
with :math:`\lambda` the normalization integral over :math:`f_\mathbf{p}`. The
integral is computed numerically by averaging over a significantly large (phase
space) domain sample :math:`\mathbf{x}_\mathrm{phsp}` of size :math:`n`:
.. math::
\lambda = \frac{\sum_{j=1}^n V f_\mathbf{p}(x_{\mathrm{phsp},j})}{n}.
Args:
function: A `.ParametrizedFunction` :math:`f_\mathbf{p}` that describes
a distribution over a certain domain.
data: The `.DataSample` :math:`\mathbf{x}` over which to compute
:math:`f_\mathbf{p}`.
phsp: The domain (phase space) with which the likelihood is normalized.
When correcting for the detector efficiency, use a phase space sample that
passed the detector reconstruction.
phsp_volume: Optional phase space volume :math:`V`, used in the
normalization factor. Default: :math:`V=1`.
backend: The computational back-end with which the sums and averages
should be computed.
.. seealso:: :doc:`/usage/unbinned-fit`
"""
def __init__( # pylint: disable=too-many-arguments
self,
function: ParametrizedFunction,
data: DataSample,
phsp: DataSample,
phsp_volume: float = 1.0,
backend: str = "numpy",
) -> None:
self.__data = dict(data) # shallow copy
self.__phsp = {k: v for k, v in phsp.items() if k != "weights"}
self.__phsp_weights = phsp.get("weights")
self.__function = function
self.__gradient = gradient_creator(self.__call__, backend)
self.__mean_function = find_function("mean", backend)
self.__sum_function = find_function("sum", backend)
self.__log_function = find_function("log", backend)
self.__phsp_volume = phsp_volume
def __call__(self, parameters: Mapping[str, ParameterValue]) -> float:
self.__function.update_parameters(parameters)
bare_intensities = self.__function(self.__data)
phsp_intensities = self.__function(self.__phsp)
if self.__phsp_weights is not None:
phsp_intensities *= self.__phsp_weights
normalization_factor = 1.0 / (
self.__phsp_volume * self.__mean_function(phsp_intensities)
)
likelihoods = normalization_factor * bare_intensities
return -self.__sum_function(self.__log_function(likelihoods))
[docs] def gradient(
self, parameters: Mapping[str, ParameterValue]
) -> dict[str, ParameterValue]:
return self.__gradient(parameters)
