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. ... Read more

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. ... Read more

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. ... Read more

Multivariate time series arise in a wide range of domains, such as weather forecasting and financial modeling, where multiple interdependent variables evolve simultaneously over time. For instance, temperature readings at one location may have a delayed influence on nearby regions, while currency exchange rates exhibit complex, lagged interactions across global financial markets Effectively modeling these spatiotemporal interactions, particularly in streaming and non-stationary settings, remains a fundamental challenge. Traditional approaches such as Temporal PCA operate on sample covariance matrices but often suffer from stability issues in the estimated eigenvectors, especially in low-data regimes or when the corresponding eigenvalues are close. These covariance estimation errors can propagate into the learned representation and degrade performance in downstream tasks. Recent graph-based learning methods address this limitation by constructing graphs from the sample covariance matrix and learning from its structure. However, these approaches typically consider only lag-zero correlations, thereby limiting their ability to model cross-temporal dependencies and fully capture the spatiotemporal structure inherent in multivariate time series. To overcome this, this thesis proposes the Lagged spatiotemporal coVariance Neural Network (LVNN), a neural network architecture that leverages lagged covariance information to learn representations from multivariate time series in a streaming setting. LVNN constructs a spatiotemporal graph by concatenating consecutive temporal samples, computing their extended sample covariance matrix, and using it as a structural prior for graph convolutions. This design enables the model to capture variable interactions not only within time steps but also across temporal lags. However, the use of a larger spatiotemporal covariance matrix introduces additional computational overhead and spurious correlations. To address this, we introduce two structural modifications to our proposed model. First, we retain only spatial and backward temporal connections, corresponding to the block upper triangular part of the extended covariance matrix. Second, we apply thresholding-based sparsification techniques to prune weak correlations and improve scalability. We begin by proving that LVNN is robust to perturbations in the online estimation of the extended covariance matrix in stationary settings, improving over the stability issues of temporal PCA-based methods. These findings are empirically validated on synthetic stationary datasets. Then, to assess the effectiveness of the learned embeddings, we evaluate LVNN on single-step forecasting tasks using three real-world datasets across different forecasting horizons. The standard LVNN model performs comparably to our baselines, while the LVNN variant with the block upper triangular matrix demonstrates the most consistent performance. Furthermore, applying hard and soft thresholding sparsification techniques to the extended covariance matrix substantially reduces the computational overhead, with only a minor impact on forecasting performance. These results support our hypothesis that cross-temporal covariance terms are a valuable source of inductive bias for representation learning in multivariate time series. ... Read more

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. ... Read more

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. ... Read more