"""
This is the implementation of the Popularity-based Ranking-based Statistical Parity (RSP) metric.
It proceeds from a user-wise computation, and average the values over the users.
"""
__version__ = '0.3.1'
__author__ = 'Vito Walter Anelli, Claudio Pomo'
__email__ = 'vitowalter.anelli@poliba.it, claudio.pomo@poliba.it'
import operator
import numpy as np
from elliot.evaluation.metrics.base_metric import BaseMetric
[docs]class PopRSP(BaseMetric):
r"""
Popularity-based Ranking-based Statistical Parity
This class represents the implementation of the Popularity-based Ranking-based Statistical Parity (RSP) recommendation metric.
For further details, please refer to the `paper <https://dl.acm.org/doi/abs/10.1145/3397271.3401177>`_
.. math::
\mathrm {RSP}=\frac{{std}\left(P\left(R @ k \mid g=g_{1}\right), \ldots, P\left(R @ k \mid g=g_{A}\right)\right)}
{{mean}\left(P\left(R @ k \mid g=g_{1}\right), \ldots, P\left(R @ k \mid g=g_{A}\right)\right)}
:math `P(R @ k \mid g=g_{A})) = \frac{\sum_{u=1}^{N} \sum_{i=1}^{k} G_{g_{a}}(R_{u, i})}
{\sum_{u=1}^{N} \sum_{i \in I \backslash I_{u}^{+}} G_{g_{a}}(i)}`
:math:`\sum_{i=1}^{k} G_{g_{a}}\left(R_{u, i}\right)` calculates how many un-interacted items
from group `{g_a}` are ranked in top-đ for user u.
:math:`\sum_{i \in I \backslash I_{u}^{+}} G_{g_{a}}(i)`
calculates how many un-interacted items belong to group `{g_a}` for u
To compute the metric, add it to the config file adopting the following pattern:
.. code:: yaml
simple_metrics: [PopRSP]
"""
def __init__(self, recommendations, config, params, eval_objects):
"""
Constructor
:param recommendations: list of recommendations in the form {user: [(item1,value1),...]}
:param config: SimpleNameSpace that represents the configuration of the experiment
:param params: Parameters of the model
:param eval_objects: list of objects that may be useful for the computation of the different metrics
"""
super().__init__(recommendations, config, params, eval_objects)
self._cutoff = self._evaluation_objects.cutoff
self._short_head = set(self._evaluation_objects.pop.get_short_head())
self._long_tail = set(self._evaluation_objects.pop.get_long_tail())
self._train = self._evaluation_objects.data.train_dict
self._num = []
self._den = []
[docs] @staticmethod
def name():
"""
Metric Name Getter
:return: returns the public name of the metric
"""
return "PopRSP"
def __user_pop_rsp(self, user_recommendations, cutoff, long_tail, short_head, u_train):
"""
Per User Popularity-based Ranking-based Statistical Parity (RSP)
:param user_recommendations: list of user recommendation in the form [(item1,value1),...]
:param cutoff: numerical threshold to limit the recommendation list
:param user_relevant_items: list of user relevant items in the form [item1,...]
:return: the value of the Average Recommendation Popularity metric for the specific user
"""
recommended_items = set([i for i, _ in user_recommendations[:cutoff]])
num_h = len(recommended_items & short_head)
num_t = len(recommended_items & long_tail)
den_h = len(short_head-u_train)
den_t = len(long_tail-u_train)
return num_h, num_t, den_h, den_t
[docs] def eval(self):
"""
Evaluation function
:return: the overall averaged value of PopRSP
"""
for u, u_r in self._recommendations.items():
num_h, num_t, den_h, den_t = self.__user_pop_rsp(u_r, self._cutoff, self._long_tail, self._short_head, set(self._train[u].keys()))
self._num.append([num_h, num_t])
self._den.append([den_h, den_t])
self._num = np.sum(np.array(self._num), axis = 0)
self._den = np.sum(np.array(self._den), axis = 0)
pr = self._num / self._den
return np.std(pr)/np.mean(pr)