The task of reconstructing a matrix given a sample of observed entries is known as the matrix completion problem . It arises in a wide range of problems, including recommender systems, collaborative filtering, dimensionality reduction, image processing, quantum physics or multi-class classification to name a few. Most works have focused on recovering an unknown real-valued low-rank matrix from randomly sub-sampling its entries. Here, we investigate the case where the observations take a finite number of values, corresponding for examples to ratings in recommender systems or labels in multi-class classification. We also consider a general sampling scheme (not necessarily uniform) over the matrix entries. The performance of a nuclear-norm penalized estimator is analyzed theoretically. More precisely, we derive bounds for the Kullback-Leibler divergence between the true and estimated distributions. In practice, we have also proposed an efficient algorithm based on lifted coordinate gradient descent in order to tackle potentially high dimensional settings.

A case in point occurs in personalized recommendation systems where users' preferences are judged

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As a result, these and other large conferences must rely on automated systems to decide what members of the impaneled reviewer pool will review each paper.

In recommender systems, the collected data used for training is always subject to selection bias, which poses a great challenge for unbiased learning.

Machine learning (ML) is pervasively deployed.

Federated Learning (FL) is gaining prominence in machine learning as privacy concerns grow. This paradigm allows each client (e.g., an individual online store) to train a recommendation model locally while sharing only model updates, without exposing the raw interaction logs to a central server, thereby preserving privacy in a decentralized environment. Nonetheless, most existing FL-based recommender systems still rely solely on each client's private data, despite the abundance of publicly available datasets that could be leveraged to enrich local training; this potential remains largely underexplored. To this end, we consider a realistic scenario wherein a large shopping platform collaborates with multiple small online stores to build a global recommender system. The platform possesses global data, such as shareable user and item lists, while each store holds a portion of interaction data privately (or locally). Although integrating global data can help mitigate the limitations of sparse and biased clients' local data, it also introduces additional challenges: simply combining all global interactions can amplify noise and irrelevant patterns, worsening personalization and increasing computational costs. To address these challenges, we propose FedGDVE, which selectively augments each client's local graph with semantically aligned samples from the global dataset. FedGDVE employs: (i) a pre-trained graph encoder to extract global structural features, (ii) a local valid predictor to assess client-specific relevance, (iii) a reinforcement-learning-based probability estimator to filter and sample only the most pertinent global interactions. FedGDVE improves performance by up to 34.86% on recognized benchmarks in FL environments.