Methods for explaining Top-N recommendations through subgroup discovery

Abstract

Explainable Artificial Intelligence (XAI) has received a lot of attention over the past decade, with the proposal of many methods explaining black box classifiers such as neural networks. Despite the ubiquity of recommender systems in the digital world, only few researchers have attempted to explain their functioning, whereas one major obstacle to their use is the problem of societal acceptability and trustworthiness. Indeed, recommender systems direct user choices to a large extent and their impact is important as they give access to only a small part of the range of items (e.g., products and/or services), as the submerged part of the iceberg. Consequently, they limit access to other resources. The potentially negative effects of these systems have been pointed out as phenomena like echo chambers and winner-take-all effects, because the internal logic of these systems is to likely enclose the consumer in a “déjà vu” loop. Therefore, it is crucial to provide explanations of such recommender systems and to identify the user data that led the respective system to make the individual recommendations. This then makes it possible to evaluate recommender systems not only regarding their effectiveness (i.e., their capability to recommend an item that was actually chosen by the user), but also with respect to the diversity, relevance and timeliness of the active data used for the recommendation. In this paper, we propose a deep analysis of two state-of-the-art models learnt on four datasets based on the identification of the items or the sequences of items actively used by the models. Our proposed methods are based on subgroup discovery with different pattern languages (i.e., itemsets and sequences). Specifically, we provide interpretable explanations of the recommendations of the Top-N items, which are useful to compare different models. Ultimately, these can then be used to present simple and understandable patterns to explain the reasons behind a generated recommendation to the user.

A Appendix

Hit rate (Hit@N):

$$\begin{aligned} Hit@N = \frac{1}{|U|} \sum _{u \in U} \sum _{i\in GT^u} \frac{\mathbb {1}(R_{i} \le N)}{|GT^u|}. \end{aligned}$$

where the indicator function $\mathbb {1}(b)$ returns 1 if its argument b is True, 0 otherwise. $R_{i}$ is the ranking of the ground-truth item i. The HIT@N function returns the average number of times the ground-truth item is ranked in the Top-N items. We compute HIT@5, HIT@10, HIT@25.

Normalized Discounted Cumulative Gain at position N(nDCG@N):

$$\begin{aligned} nDCG@N = \frac{1}{|U|\times N} \sum _{u \in U} \sum _{i_t\in GT^u}\frac{\mathbb {1}(R_{i_t} \le N)}{log_{2}(\max (R_{i_t}+2-t),2)}, \end{aligned}$$

The NDCG@k is a position-aware metric which assigns larger weights to higher positions. We compute NDCG@5, NDCG@10, NDCG@25 and NDCG@50.

Area Under Curve (AUC):

$$\begin{aligned} AUC = \frac{1}{|U|}\sum _{u\in U}\frac{1}{|GT^u|}\sum _{i_{t}\in GT^u} \frac{|I|-R_{i_{t}} -t}{|I|}. \end{aligned}$$

This measure calculates how high the ground-truth items of each user has been ranked in average.

Precision at N (Precision@N):

$$\begin{aligned} Precision@N = \frac{1}{U}\sum _{u\in U}\frac{ TN^u \cap GT^u}{N} \end{aligned}$$

Recall at N (Recall@N):

$$\begin{aligned} Recall@N = \frac{1}{U}\sum _{u\in U}\frac{ TN^u \cap GT^u}{|GT^u|} \end{aligned}$$

Mean Average Precision (MAP):

$$\begin{aligned} MAP = \frac{1}{|U|}\sum _{u\in U}\frac{\sum _{k=1}^{N} Precision@k \times rel(k)}{N} \end{aligned}$$

where $rel(k) = 1$ if the kth item in TN belongs to GT, the ground Truth items of the user.