elliot.evaluation.metrics.fairness.reo package

Submodules

elliot.evaluation.metrics.fairness.reo.reo module

This is the implementation of the Ranking-based Equal Opportunity (REO) metric. It proceeds from a user-wise computation, and average the values over the users.

class elliot.evaluation.metrics.fairness.reo.reo.REO(recommendations, config, params, eval_objects, additional_data)

Bases: elliot.evaluation.metrics.base_metric.BaseMetric

Ranking-based Equal Opportunity

This class represents the implementation of the Ranking-based Equal Opportunity (REO) recommendation metric.

For further details, please refer to the paper

\[\mathrm {REO}=\frac{{std}\left(P\left(R @ k \mid g=g_{1}, y=1\right) \ldots P\left(R(a) k=g_{A}, y=1\right)\right)} {{mean}\left(P\left(R @ k \mid g=g_{1}, y=1\right) \ldots P\left(R @ k \mid g=g_{A}, y=1\right)\right)}\]

\(P\left(R @ k \mid g=g_{a}, y=1\right) = \frac{\sum_{u=1}^{N} \sum_{i=1}^{k} G_{g_{a}}\left(R_{u, i}\right) Y\left(u, R_{u, i}\right)} {\sum_{u=1}^{N} \sum_{i \in I \backslash I_{u}^{+}} G_{g_{a}}(i) Y(u, i)}\)

\(Y\left(u, R_{u, i}\right)\) identifies the ground-truth label of a user-item pair left(u, R_{u, i}right), if item R_{u, i} is liked by user 𝑢, returns 1, otherwise 0

\(\sum_{i=1}^{k} G_{g_{a}}\left(R_{u, i}\right) Y\left(u, R_{u, i}\right)\) counts how many items in test set from group {g_a} are ranked in top-𝑘 for user u

\(\sum_{i \in I \backslash I_{u}^{+}} G_{g_{a}}(i) Y(u, i)\) counts the total number of items from group {g_a} 𝑎 in test set for user u

To compute the metric, add it to the config file adopting the following pattern:

complex_metrics:
 - metric: REO
  clustering_name: ItemPopularity
  clustering_file: ../data/movielens_1m/i_pop.tsv

eval()

get()

name()

Metric Name Getter :return: returns the public name of the metric

process()

Evaluation function :return: the overall value of Ranking-based Equal Opportunity (REO)

Module contents