# Source code for fraud_eagle.prior

```
#
# prior.py
#
# Copyright (c) 2016-2017 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 prior beliefs of users and products.
"""
from __future__ import absolute_import
import numpy as np
from fraud_eagle.constants import HONEST, FRAUD, GOOD, BAD
_LOG_2 = np.log(2.)
"""Precomputed value, the logarithm of 2.0."""
[docs]def phi_u(user):
"""Logarithm of a prior belief of a user.
The definition is
.. math::
\\phi_{i}^{\\cal{U}}: \\cal{L}_{\\cal{U}} \\rightarrow \\mathbb{R}_{\\geq 0},
where :math:`\\cal{U}` is a set of user nodes, :math:`\\cal{L}_{\\cal{U}}`
is a set of user labels, and :math:`\\mathbb{R}_{\\geq 0}` is a set of real
numbers grater or equals to :math:`0`.
The implementation of this mapping is given as
.. math::
\\phi_{i}^{\\cal{U}}(y_{i}) \\leftarrow \\|\\cal{L}_{\\cal{U}}\\|.
On the other hand, :math:`\\cal{L}_{\\cal{U}}` is given as {honest, fraud}.
It means the mapping returns :math:`\\phi_{i} = 2` for any user.
This function returns the logarithm of such :math:`\\phi_{i}`, i.e.
:math:`\\log(\\phi_{i}(u))` for any user :math:`u`.
Args:
user: User object.
Returns:
The logarithm of the prior belief of the label of the given user.
However, it returns :math:`\\log 2` whatever the given user is.
"""
if user in (HONEST, FRAUD):
return _LOG_2
raise ValueError("Invalid user label:", user)
[docs]def phi_p(product):
"""Logarithm of a prior belief of a product.
The definition is
.. math::
\\phi_{j}^{\\cal{P}}: \\cal{L}_{\\cal{P}} \\rightarrow \\mathbb{R}_{\\geq 0},
where :math:`\\cal{P}` is a set of produce nodes, :math:`\\cal{L}_{\\cal{P}}`
is a set of product labels, and :math:`\\mathbb{R}_{\\geq 0}` is a set of real
numbers grater or equals to :math:`0`.
The implementation of this mapping is given as
.. math::
\\phi_{j}^{\\cal{P}}(y_{j}) \\leftarrow \\|\\cal{L}_{\\cal{P}}\\|.
On the other hand, :math:`\\cal{L}_{\\cal{P}}` is given as {good, bad}.
It means the mapping returns :math:`2` despite the given product.
This function returns the logarithm of such :math:`\\phi_{j}`, i.e.
:math:`\\log(\\phi_{j}(p))` for any product :math:`p`.
Args:
user: Product object.
Returns:
The logarithm of the prior belief of the label of the given product.
However, it returns :math:`\\log 2` whatever the given product is.
"""
if product in (GOOD, BAD):
return _LOG_2
raise ValueError("Invalid product label:", product)
```