#
# likelihood.py
#
# Copyright (c) 2016-2023 Junpei Kawamoto
#
# This file is part of rgmining-fraud-eagle.
#
# rgmining-fraud-eagle is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# rgmining-fraud-eagle is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with rgmining-fraud-eagle. If not, see <http://www.gnu.org/licenses/>.
"""Define likelihood functions.
This module defines a likelihood of a pair of user and product.
See :meth:`psi` for the detailed definition of the likelihood.
"""
from fraud_eagle.labels import ProductLabel, ReviewLabel, UserLabel
# pylint: disable=too-many-branches
[docs]def psi(u_label: UserLabel, p_label: ProductLabel, r_label: ReviewLabel, epsilon: float) -> float:
"""Likelihood of a pair of user and product.
The likelihood is dependent on the review of the user gives the product.
The review is one of {+, -}. We defined constant representing "+" and "-",
thus the review is one of the {:data:`PLUS<fraud_eagle.labels.PLUS>`,
:data:`MINUS<fraud_eagle.labels.MINUS>`}.
On the other hand, epsilon is a given parameter.
The likelihood :math:`\\psi_{ij}^{s}`, where :math:`i` and :math:`j` are
indexes of user and produce, respectively, and :math:`s` is a review
i.e. :math:`s \\in {+, -}`, is given as following tables.
If the review is :data:`PLUS<fraud_eagle.labels.PLUS>`,
.. csv-table::
:header: review: +, Product: Good, Product: Bad
User: Honest, 1 - :math:`\\epsilon`, :math:`\\epsilon`
User: Fraud, 2 :math:`\\epsilon`, 1 - 2 :math:`\\epsilon`
If the review is :data:`MINUS<fraud_eagle.labels.MINUS>`,
.. csv-table::
:header: review: -, Product: Good, Product: Bad
User: Honest, :math:`\\epsilon`, 1 - :math:`\\epsilon`
User: Fraud, 1 - 2 :math:`\\epsilon`, 2 :math:`\\epsilon`
Args:
u_label: user label which must be one of the { \
:data:`UserLabel.HONEST<fraud_eagle.labels.UserLabel.HONEST>`, \
:data:`UserLabel.FRAUD<fraud_eagle.labels.UserLabel.FRAUD>`}.
p_label: product label which must be one of the \
{:data:`ProductLabel.GOOD<fraud_eagle.labels.ProductLabel.GOOD>`, \
:data:`ProductLabel.BAD<fraud_eagle.labels.ProductLabel.BAD>`}.
r_label: review label which must be one of the \
{:data:`ReviewLabel.PLUS<fraud_eagle.labels.ReviewLabel.PLUS>`, \
:data:`ReviewLabel.MINUS<fraud_eagle.labels.ReviewLabel.MINUS>`}.
epsilon: a float parameter in :math:`[0,1]`.
Returns:
Float value representing a likelihood of the given values.
"""
if r_label == ReviewLabel.PLUS:
if u_label == UserLabel.HONEST:
if p_label == ProductLabel.GOOD:
return 1 - epsilon
elif p_label == ProductLabel.BAD:
return epsilon
elif u_label == UserLabel.FRAUD:
if p_label == ProductLabel.GOOD:
return 2 * epsilon
elif p_label == ProductLabel.BAD:
return 1 - 2 * epsilon
elif r_label == ReviewLabel.MINUS:
if u_label == UserLabel.HONEST:
if p_label == ProductLabel.GOOD:
return epsilon
elif p_label == ProductLabel.BAD:
return 1 - epsilon
elif u_label == UserLabel.FRAUD:
if p_label == ProductLabel.GOOD:
return 1 - 2 * epsilon
elif p_label == ProductLabel.BAD:
return 2 * epsilon
raise ValueError("arguments are invalid")