As recommender systems become widely deployed in different domains, they increasingly influence their users' beliefs and preferences. Auditing recommender systems is crucial as it not only ensures the continuous improvement of recommendation algorithms but also safeguards against potential issues like biases and ethical concerns. In this paper, we view recommender system auditing from a causal lens and provide a general recipe for defining auditing metrics. Under this general causal auditing framework, we categorize existing auditing metrics and identify gaps in them -- notably, the lack of metrics for auditing user agency while accounting for the multi-step dynamics of the recommendation process. We leverage our framework and propose two classes of such metrics:future- and past-reacheability and stability, that measure the ability of a user to influence their own and other users' recommendations, respectively. We provide both a gradient-based and a black-box approach for computing these metrics, allowing the auditor to compute them under different levels of access to the recommender system. In our experiments, we demonstrate the efficacy of methods for computing the proposed metrics and inspect the design of recommender systems through these proposed metrics.

To reduce the communication overhead caused by parallel training of multiple clients, various federated learning (FL) techniques use random client sampling. Nonetheless, ensuring the efficacy of random sampling and determining the optimal number of clients to sample in federated recommender systems (FRSs) remains challenging due to the isolated nature of each user as a separate client. This challenge is exacerbated in models where public and private features can be separated, and FL allows communication of only public features (item gradients). In this study, we establish sample complexity bounds that dictate the ideal number of clients required for improved communication efficiency and retained accuracy in such models. In line with our theoretical findings, we empirically demonstrate that RS-FairFRS reduces communication cost (~47%). Second, we demonstrate the presence of class imbalance among clients that raises a substantial equity concern for FRSs. Unlike centralized machine learning, clients in FRS can not share raw data, including sensitive attributes. For this, we introduce RS-FairFRS, first fairness under unawareness FRS built upon random sampling based FRS. While random sampling improves communication efficiency, we propose a novel two-phase dual-fair update technique to achieve fairness without revealing protected attributes of active clients participating in training. Our results on real-world datasets and different sensitive features illustrate a significant reduction in demographic bias (~approx40\%), offering a promising path to achieving fairness and communication efficiency in FRSs without compromising the overall accuracy of FRS.

This paper investigates a new yet challenging problem called Reverse $k$-Maximum Inner Product Search (R$k$MIPS). Given a query (item) vector, a set of item vectors, and a set of user vectors, the problem of R$k$MIPS aims to find a set of user vectors whose inner products with the query vector are one of the $k$ largest among the query and item vectors. We propose the first subquadratic-time algorithm, i.e., Shifting-aware Asymmetric Hashing (SAH), to tackle the R$k$MIPS problem. To speed up the Maximum Inner Product Search (MIPS) on item vectors, we design a shifting-invariant asymmetric transformation and develop a novel sublinear-time Shifting-Aware Asymmetric Locality Sensitive Hashing (SA-ALSH) scheme. Furthermore, we devise a new blocking strategy based on the Cone-Tree to effectively prune user vectors (in a batch). We prove that SAH achieves a theoretical guarantee for solving the RMIPS problem. Experimental results on five real-world datasets show that SAH runs 4$\sim$8$\times$ faster than the state-of-the-art methods for R$k$MIPS while achieving F1-scores of over 90\%. The code is available at \url{https://github.com/HuangQiang/SAH}.

Top-k recommendation seeks to deliver a personalized list of k items to each individual user. An established methodology in the literature based on matrix factorization (MF), which usually represents users and items as vectors in low-dimensional space, is an effective approach to recommender systems, thanks to its superior performance in terms of recommendation quality and scalability. A typical matrix factorization recommender system has two main phases: preference elicitation and recommendation retrieval. The former analyzes user-generated data to learn user preferences and item characteristics in the form of latent feature vectors, whereas the latter ranks the candidate items based on the learnt vectors and returns the top-k items from the ranked list. For preference elicitation, there have been numerous works to build accurate MF-based recommendation algorithms that can learn from large datasets. However, for the recommendation retrieval phase, naively scanning a large number of items to identify the few most relevant ones may inhibit truly real-time applications. In this work, we survey recent advances and state-of-the-art approaches in the literature that enable fast and accurate retrieval for MF-based personalized recommendations. Also, we include analytical discussions of approaches along different dimensions to provide the readers with a more comprehensive understanding of the surveyed works.

The Maximum Inner Product Search (MIPS) problem, prevalent in matrix factorization-based recommender systems, scales linearly with the number of objects to score. Recent work has shown that clever post-processing steps can turn the MIPS problem into a nearest neighbour one, allowing sublinear retrieval time either through Locality Sensitive Hashing or various tree structures that partition the Euclidian space. This work shows that instead of employing post-processing steps, substantially faster retrieval times can be achieved for the same accuracy when inference is not decoupled from the indexing process. By framing matrix factorization to be natively indexable, so that any solution is immediately sublinearly searchable, we use the machinery of Machine Learning to best learn such a solution. We introduce Indexable Probabilistic Matrix Factorization (IPMF) to shift the traditional post-processing complexity into the training phase of the model. Its inference procedure is based on Geodesic Monte Carlo, and adds minimal additional computational cost to standard Monte Carlo methods for matrix factorization. By coupling inference and indexing in this way, we achieve more than a 50% improvement in retrieval time against two state of the art methods, for a given level of accuracy in the recommendations of two large-scale recommender systems.