#!/usr/bin/python
# -*- coding: utf-8 -*-
##
# score.py: Provides mixins which compute the score numerically with a
# central difference.
##
# © 2017, Chris Ferrie (csferrie@gmail.com) and
# Christopher Granade (cgranade@cgranade.com).
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its
# contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
##
## FEATURES ###################################################################
from __future__ import absolute_import
from __future__ import division
## IMPORTS ####################################################################
from builtins import range
import numpy as np
## CLASSES ####################################################################
[docs]class ScoreMixin(object):
r"""
A mixin which includes a method ``score`` that numerically estimates the
score of the likelihood function. Any class which mixes in this class
should be equipped with a property ``n_modelparams`` and a method
``likelihood`` to satisfy dependency.
"""
_h = 1e-10
@property
def h(self):
r"""
Returns the step size to be used in numerical differentiation with
respect to the model parameters.
The step size is given as a vector with length ``n_modelparams`` so
that each model parameter can be weighted independently.
"""
if np.size(self._h) > 1:
assert np.size(self._h) == self.n_modelparams
return self._h
else:
return self._h * np.ones(self.n_modelparams)
[docs] def score(self, outcomes, modelparams, expparams, return_L=False):
r"""
Returns the numerically computed score of the likelihood
function, defined as:
.. math::
q(d, \vec{x}; \vec{e}) = \vec{\nabla}_{\vec{x}} \log \Pr(d | \vec{x}; \vec{e}).
Calls are represented as a four-index tensor
``score[idx_modelparam, idx_outcome, idx_model, idx_experiment]``.
The left-most index may be suppressed for single-parameter models.
The numerical gradient is computed using the central difference method,
with step size given by the property `~ScoreMixin.h`.
If return_L is True, both `q` and the likelihood `L` are returned as `q, L`.
"""
if len(modelparams.shape) == 1:
modelparams = modelparams[:, np.newaxis]
# compute likelihood at central point
L0 = self.likelihood(outcomes, modelparams, expparams)
# allocate space for the score
q = np.empty([self.n_modelparams,
outcomes.shape[0],
modelparams.shape[0],
expparams.shape[0]])
h_perturb = np.empty(modelparams.shape)
# just loop over the model parameter as there usually won't be so many
# of them that vectorizing would be worth the effort.
for mp_idx in range(self.n_modelparams):
h_perturb[:] = np.zeros(modelparams.shape)
h_perturb[:, mp_idx] = self.h[mp_idx]
# use the chain rule since taking the numerical derivative of a
# logarithm is unstable
q[mp_idx, :] = (
self.likelihood(outcomes, modelparams + h_perturb, expparams) -
self.likelihood(outcomes, modelparams - h_perturb, expparams)
) / (2 * self.h[mp_idx] * L0)
if return_L:
return q, L0
else:
return q