Accuracy‐driven recommender systems risk confining users to "filter‐bubbles'' of familiar content. Recent work on coVariance Neural Networks (VNNs) provides a scalable alternative to Principal Component Analysis (PCA) for modelling high-order correlations, but their impact on beyond-accuracy metrics (BAMs), such as Novelty and Diversity, remains unexplored.
We use the user–user covariance (or its inverse, the precision matrix) as a graph shift operator (GSO) and train SelectionGNN-based VNNs on the MovieLens-100K dataset.
Two training regimes are evaluated: (i) RMSE-only (No-BAM-SVNN) and (ii) a compound loss that also includes novelty and diversity terms (BAM-SVNN).
For each regime we sweep six graph configurations: covariance/precision crossed with {dense, hard-threshold, soft-threshold} sparsification, under five random seeds, yielding 30 runs per regime.
Baseline comparisons include PCA, a naive mean–std model, and a random predictor.

The best SVNN configuration increases recommendation Novelty by 2.8 percentage points and matches PCA’s Diversity while incurring only a 0.03 RMSE penalty.
Hard-thresholded precision graphs provide the lowest SVNN RMSE (0.952), whereas dense covariance graphs maximise diversity (0.868).
Integrating novelty/diversity directly into the loss offers no additional benefit yet multiplies runtime by x33.
One-way ANOVA indicates that model family explains 97.6% of RMSE variance (\(\eta^2=0.976\)) and 77.8% of novelty variance.

This work is the first to benchmark (sparsified) VNNs on beyond-accuracy metrics, demonstrating a favourable accuracy–novelty trade-off and clarifying when sparsification and BAM-weighted training pay off.
All code, data splits and statistical notebooks are released for full reproducibility.

Recommender systems help users navigate vast catalogs of content through recommendations, of which rating prediction remains an important task. Traditional methods such as collaborative filtering often struggle to model higher-order relationships between users and items, as well as suffer from the cold start problem when the number of users and items is still low. Graph Neural Networks (GNNs) have shown promise in this area, although they are often limited by their focus on local graph structures. This study explores the application of Covariance Neural Networks (VNNs) for rating prediction, leveraging covariance matrices to leverage global statistical dependencies and model higher-order relationships. Using the MovieLens-100k dataset, we evaluate the performance of VNNs against baselines and other models, using RMSE as the metric of evaluation. Our results demonstrate that VNNs outperform simple matrix completion techniques, but are limited by their susceptibility to oversmoothing. This work highlights the potential of VNNs for recommender systems while underscoring the need for careful architectural design to balance performance and stability.

This research investigates the application of Graph Neural Networks (GNNs) for rating prediction in recommender systems, utilizing precision matrices as graph filters. The focus is on movie recommendation, where graph-based structures are especially relevant due to the importance of user and item relationships. A leave-one-out masking strategy is employed during training to ensure the model learns from all available training data. The proposed model achieves a test root mean squared error (RMSE) of approximately 0.95 on the MovieLens-100k dataset, performing reasonably well compared to existing graph-based and matrix factorization methods. While the model accurately predicts average ratings, it tends to overestimate lower ratings. These results demonstrate the potential of precision-based graph filters in GNNs but also reveal significant room for improvement before reaching state-of-the-art performance. Future work may include output calibration and sparsification of the precision matrix to enhance both efficiency and predictive accuracy.

Covariance Neural Networks (VNNs) leverage the covariance matrix of user-item rating data to construct graph structures that enable effective graph convolutions for collaborative filtering. However, empirical covariance estimates often contain noisy correlations arising from limited or sparse data, which can degrade the stability and predictive accuracy of VNNs. This paper investigates how sparsification techniques applied to the covariance matrix can mitigate noise and improve model efficiency. We propose a flexible framework that performs thresholding, which removes edges with weights below a fixed cutoff, and stochastic sparsification, which randomly retains edges based on their strength, thereby adapting to both sparse and dense covariance patterns.

Graph Neural Networks (GNNs) are an effective architecture for implementing collaborative filtering-based recommender systems. This paper evaluates the performance and computational complexity of precision matrix-based VNNs as a collaborative filter on the MovieLens-100K dataset. Results show the estimated precision matrix contains a high amount of noise when calculated from sparse data, which impacts the performance of the model. After sparsifying the precision matrix, the performance and computational complexity improved significantly.