def test(self):
"""Test for all possible input combinations.
"""
for epsilon in (0.01, 0.1, 0.5):
self.assertEqual(psi(HONEST, GOOD, PLUS, epsilon), 1-epsilon)
self.assertEqual(psi(HONEST, GOOD, MINUS, epsilon), epsilon)
self.assertEqual(psi(HONEST, BAD, PLUS, epsilon), epsilon)
self.assertEqual(psi(HONEST, BAD, MINUS, epsilon), 1-epsilon)
self.assertEqual(psi(FRAUD, GOOD, PLUS, epsilon), 2*epsilon)
self.assertEqual(psi(FRAUD, GOOD, MINUS, epsilon), 1-2*epsilon)
self.assertEqual(psi(FRAUD, BAD, PLUS, epsilon), 1-2*epsilon)
self.assertEqual(psi(FRAUD, BAD, MINUS, epsilon), 2*epsilon)
with self.assertRaises(ValueError):
psi(HONEST, 3, PLUS, 10)
def _update_product_to_user(self, reviewer, product, ulabel):
"""Compute an updated message from a product to a user with a user label.
The updated message is defined as
.. math::
m_{p\\rightarrow u}(y_{i}) \\leftarrow
\\alpha_{3} \\sum_{y_{j} \\in \\cal{L}_{\\cal{P}}}
\\psi_{ij}^{s}(y_{i}, y_{j}) \\phi^{\\cal{P}}_{j}(y_{j})
\\prod_{Y_{k} \\in \\cal{N}_{j} \\cap \\cal{Y}^{\\cal{U}}/u}
m_{k\\rightarrow j}(y_{j}),
where :math:`y_{i} \\in {honest, fraud}`, and
:math:`\\cal{N}_{j} \\cap \\cal{Y}^{\\cal{U}}/u` means a set of users
who review the product :math:`p` but except user :math:`u`,
The :math:`\\psi_{ij}^{s}(y_{i}, y_{j})` takes :math:`\\epsilon` as a
hyper parameter, self.epsilon is used for it.
This method returns a logarithm of the updated message.
Args:
reviewer: Reviewer i.e. a user,
product: Product,
ulabel: user label,
Returns:
a logarithm of the updated message from the given product to the
given reviewer with the given user label.
"""
review = self.retrieve_review(reviewer, product)
res = {}
for plabel in (GOOD, BAD):
res[plabel] = \
np.log(psi(ulabel, plabel, review.evaluation, self.epsilon)) \
+ phi_p(plabel) \
+ self.prod_message_from_users(reviewer, product, plabel)
return np.logaddexp(*res.values())
def _update_user_to_product(self, reviewer, product, plabel):
"""Compute an updated message from a user to a product with a product label.
The updated message is defined as
.. math::
m_{u\\rightarrow p}(y_{j}) \\leftarrow
\\alpha_{1} \\sum_{y_{i} \\in \\cal{L}_{\\cal{U}}}
\\psi_{ij}^{s}(y_{i}, y_{j}) \\phi^{\\cal{U}}_{i}(y_{i})
\\prod_{Y_{k} \\in \\cal{N}_{i} \\cap \\cal{Y}^{\\cal{P}}/p}
m_{k \\rightarrow i}(y_{i}),
where :math:`y_{j} \\in {good, bad}`, and
:math:`\\cal{N}_{i} \\cap \\cal{Y}^{\\cal{P}}/p` means a set of product
the user :math:`u` reviews but except product :math:`p`.
The :math:`\\psi_{ij}^{s}(y_{i}, y_{j})` takes :math:`\\epsilon` as a
hyper parameter, self.epsilon is used for it.
This method returns a logarithm of the updated message.
Args:
reviewer: Reviewer,
product: Product,
plabel: produce label,
Returns:
a logarithm of the updated message from the given reviewer to the
given product with the given product label.
"""
review = self.retrieve_review(reviewer, product)
res = {}
for ulabel in (HONEST, FRAUD):
res[ulabel] = \
np.log(psi(ulabel, plabel, review.evaluation, self.epsilon)) \
+ phi_u(ulabel) \
+ self.prod_message_from_products(reviewer, product, ulabel)
return np.logaddexp(*res.values())
def test_update_product_to_user(self):
"""Test updating a message from a product to a user.
In this test, we assume the following review graph,
.. graphviz::
digraph bipartite {
graph [rankdir = LR];
"product-0";
"reviewer-0";
"reviewer-1";
"reviewer-2";
"product-0" -> "reviewer-0" [label="+, m(honest)=0.4, m(fraud)=0.6"];
"reviewer-0" -> "product-0" [label="+, m(good)=0.3, m(bad)=0.7"];
"reviewer-1" -> "product-0" [label="-, m(good)=0.6, m(bad)=0.4"];
"reviewer-2" -> "product-0" [label="+, m(good)=0.8, m(bad)=0.2"];
}
The updated message is defined as
.. math::
m_{p\\rightarrow u}(y_{i}) \\leftarrow
\\alpha_{3} \\sum_{y_{j} \\in \\cal{L}_{\\cal{P}}}
\\psi_{ij}^{s}(y_{i}, y_{j}) \\phi^{\\cal{P}}_{j}(y_{j})
\\prod_{Y_{k} \\in \\cal{N}_{j} \\cap \\cal{Y}^{\\cal{U}}/u}
m_{k\\rightarrow j}(y_{j}),
where :math:`y_{i} \\in {honest, fraud}`, and
:math:`\\cal{N}_{j} \\cap \\cal{Y}^{\\cal{U}}/u` means a set of users
who review the product :math:`p` but except user :math:`u`,
"""
reviewers = [
self.graph.new_reviewer("reviewer-{0}".format(i)) for i in range(3)
]
product = self.graph.new_product("product-0")
reviews = {}
reviews[0] = self.graph.add_review(reviewers[0], product, 1)
reviews[0].update_product_to_user(HONEST, np.log(0.4))
reviews[0].update_product_to_user(FRAUD, np.log(0.6))
reviews[0].update_user_to_product(GOOD, np.log(0.3))
reviews[0].update_user_to_product(BAD, np.log(0.7))
reviews[1] = self.graph.add_review(reviewers[1], product, 0)
reviews[1].update_user_to_product(GOOD, np.log(0.6))
reviews[1].update_user_to_product(BAD, np.log(0.4))
reviews[2] = self.graph.add_review(reviewers[2], product, 1)
reviews[2].update_user_to_product(GOOD, np.log(0.8))
reviews[2].update_user_to_product(BAD, np.log(0.2))
# 0.6*0.8: products of other messages to the product with GOOD.
# 2.0: phi of the label (constant)
# 0.4*0.2: products of other messages to the product with BAD.
ans1 = 0.6 * 0.8 * 2.0 * psi(HONEST, GOOD, PLUS, self.epsilon) \
+ 0.4 * 0.2 * 2.0 * psi(HONEST, BAD, PLUS, self.epsilon)
self.assertAlmostEqual(
np.exp(
self.graph._update_product_to_user( # pylint: disable=protected-access
reviewers[0], product, HONEST)),
ans1)
# 0.6*0.8: products of other messages to the product with GOOD.
# 2.0: phi of the label (constant)
# 0.4*0.2: products of other messages to the product with BAD.
ans2 = 0.6 * 0.8 * 2.0 * psi(FRAUD, GOOD, PLUS, self.epsilon) \
+ 0.4 * 0.2 * 2.0 * psi(FRAUD, BAD, PLUS, self.epsilon)
self.assertAlmostEqual(
np.exp(
self.graph._update_product_to_user( # pylint: disable=protected-access
reviewers[0], product, FRAUD)),
ans2)