Multivariate time series modeling requires capturing complex dependencies both within individual time series and across different variables. Existing graph-based approaches are limited to pairwise interactions, while recent product cell complex methods assume homogeneous higher-order relationships. This thesis proposes the Simplicial Product Complex (SPC), a topological framework that constructs simplicial complexes in the product space to capture heterogeneous higher-order interactions across space and time. The key innovation is the ability to distinguish between different relationship types and learn their relative importance from data. We develop the Simplicial Product Complex Convolutional Neural Network (SPCCNN) to perform data-adaptive learning over these structures. Experimental evaluation shows SPCCNN achieves competitive performance with state-of-the-art methods while offering enhanced flexibility through parameterized structures. The model adapts to dataset-specific patterns and maintains computational efficiency through sparsity regularization. Our findings demonstrate the effectiveness of higher-order simplicial modeling for capturing complex temporal dynamics in multivariate time series data.

Accurate residential property valuation is essential for mortgage lending, taxation, and urban planning, yet remains challenging due to complex spatial and temporal dynamics. Traditional econometric models are interpretable but rely on restrictive assumptions, while machine learning–based automated valuation models (AVMs) improve predictive accuracy but treat transactions as independent, overlooking spatial spillovers and evolving trends. Recent graph-based approaches partially address spatial autocorrelation, but often rely on static or unidirectional structures that limit their expressiveness.

We introduce a Multi-Scale Bidirectional Spatio-Temporal Graph Neural Network (MBSTGNN) that models transactions and neighbourhoods as dynamic graphs linked through bidirectional message passing. A temporal memory mechanism maintains consistency across time, enabling the model to capture evolving market conditions. Evaluated on Rotterdam housing transactions, MBSTGNN outperforms strong baselines, particularly in sparse-data settings, and produces embeddings that reveal domain-consistent socio-spatial and temporal patterns. These results demonstrate its potential for advancing automated valuation and related spatio-temporal prediction tasks.

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.

Estimating bike trip times is becoming more and more important in many different areas such as urban mobility and route planning. However, especially in real-world, the GPS data used to generate these estimations is frequently noisy, irregularly sampled, or incomplete. With an emphasis on how these strategies interact with trip length and speed variance, this study intends to examine the effects of various data resampling techniques on the precision of bicycle travel time estimations. To analyze the impact of different preprocessing methods, we apply and assess a graph neural network model using various resampling techniques. Instinctively, the assumption that we expect to be concluded from this research is that there is no single resampling technique works well for every kind of trip. Rather, trip parameters like duration and speed fluctuation have a significant impact on accuracy.

This research investigates the effectiveness of graph-based data augmentation techniques in improving the performance of DG4b, a deep learning model designed to estimate bicycle travel times in urban environments. Given the limitations of real-world cycling datasets, particularly data scarcity and trip-length imbalance, we propose two augmentation methods: Graph Stitching (GS), which combines segments of existing trips to form new trajectories, and Graphon-Inspired Trip Generation (GITG), which uses an empirically estimated transition kernel to simulate realistic trip patterns through probabilistic sampling.
Despite limited improvements, this study establishes a foundation for future research in graph-based trajectory augmentation. Integrating richer trip-level features, such as dynamic environmental conditions or behavioral data, with structural augmentation could lead to more effective training data and improved model generalization.

Aligning diffusion model outputs with downstream objectives is essential for improving task-specific performance. Broadly, inference-time training-free approaches for aligning diffusion models can be categorized into two main strategies: sampling-based methods, which explore multiple candidate outputs and select those with higher reward signals, and gradient-guided methods, which use differentiable reward approximations to directly steer the generation process. In this work, we propose a universal algorithm, CoDeX, which brings together the strengths of blockwise sampling and gradient-based guidance into a unified framework. Building on the blockwise sampling paradigm of CoDe, CoDeX integrates local gradient signals during sampling, thereby addressing the sampling inefficiency inherent in complex reward-based sampling approaches like CoDe. At the same time, it overcomes the limited applicability of traditional gradient-guided methods, which often struggle with non-differentiable rewards. By cohesively combining these two paradigms, CoDeX enables more efficient sampling while offering better trade-offs between reward alignment and divergence from the diffusion unconditional prior. Empirical results demonstrate that CoDeX consistently outperforms CoDe and remains competitive with state-of-the-art baselines across a range of tasks.

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.

Accurate prediction of bicycle travel time is critical for efficient urban mobility and sustainable transport planning. However, real-world datasets are noisy, imbalanced and lack rich contextual features. This limits the effectiveness of current graph-based neural network models. This research aims to explore how feature engineering and model enhancements can improve the performance of a Graph Convolutional Neural Network (GCNN) in the context of travel time prediction. Building on a currently existing DG4b architecture, the input data is enriched with temporal, spatial and traffic-related features. Architectural enhancements are integrated by employing techniques such as graph data augmentation, and multi-scale graph learning. Using a dataset from Berlin, the improvements are evaluated primarily in terms of prediction accuracy across varying trip lengths, which implicitly reflect speed variability and route diversity. The goal is to explore how targeted feature engineering and graph-based modeling techniques influence the accuracy of bicycle travel time estimation, especially across different trip durations that reflect real-world cycling variability. The results show that optimal feature engineering improved the model up to 6% and a combination of the model enhancement techniques improved the model up to 2%.

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.

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.

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.

Extending the concepts of classical signal processing to graphs, a wide array of methods have come to the fore, including filtering, reconstruction, classification, and sampling. Existing approaches in graph signal processing consider a known and static topology, i.e., fixed number of nodes and a fixed edge support. Two types of tasks stand out, namely, topology inference, where the edge support along with their weights are estimated from signals; and data processing, where existing data and the known topology are used to perform different tasks. However, such tasks become quite challenging when the network size and support changes over time. Particularly, these challenges involve adapting to the changing topology, data distributions and dealing with unknown topological information. The latter manifests for example, when new nodes are available to attach to the graph but their connectivity is uncertain as is the case in cold start graph-based recommender systems.
The key contribution of this dissertation is proposing methodologies for signal processing over dynamic networks which are aimed at the two aforementioned tasks. For dynamic networks with incoming nodes, we process signals by introducing a parametric stochastic attachment model. In this model, the incoming nodes connect with probability to existing nodes with certain weights. This uncertainty allows us to model input output relations and allows us to cast them in the context of different graph signal processing tasks. We learn the model attachment parameters in a task-aware setting, allowing us to interpret topology identification in task-aware settings. Separately, we also propose filter design strategies for processing signals both at the incoming and existing nodes using stochastic attachment models.
Another contribution of this dissertation is to extend graph signal processing with graph filters to the scenario where the graph keeps growing in size with streaming data. We propose online graph filter design which updates the filter online, based on incoming nodes. We design this both for scenarios where the incoming node connectivity is known and unknown. In the unknown connectivity case, we study the performance difference between knowing and not knowing the topology and how the stochastic attachment influences it. We also show that by adapting the stochastic attachment, we can learn faster from the data stream.
Finally,we consider the task of topology decomposition and identification for dynamic networks with fixed nodes but changing edge support. We build a tensor of partially observed adjacency matrices corresponding to such a dynamic topology and express this in terms of underlying latent graphs and their temporal signatures. Furthermore, we account for the time-varying graph signals as a prior to aid identifying these latent graphs and missing components of the topology. These latent graphs are individually and collectively expressive and provide interpretable decompositions along with outperforming traditional structure agnostic low-rank decompositions.

Machine learning has been growing beyond data living on Euclidean spaces (e.g., texts, audios, images). Graph machine learning models, e.g., graph neural networks (GNNs), succeed in learning from graph-structured data using the graph topological information. In this thesis, we focus on a new domain, simplicial complexes. Not only are they a popular higher-order network model that generalizes graph models encoding pairwise relations between nodes, but they also allow us to support signals on various network objects (nodes, edges, and faces). For example, edge flows defined on a simplicial complex can be studied in terms of both divergent and rotational properties, providing a better model for real-world flows like traffic flows, water flows, money flows, etc.
The main theme of the thesis is to develop principled machine learning models for signals on simplicial complexes. By principled, we mean that the models leverage the intrinsic priors of the domain and the signals, namely, the topological structure of simplicial compelxes and the Hodge decomposition of simplicial signals. The latter states that, for example, edge flows can be decomposed into a divergence-free part and a curl-free part, each modeling the distinct properties of real-world flows — the conservation of flows (e.g., water flows) and the rotational properties of flows (e.g., electric currents)....

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in various applications due to their ability to capture complex structural relationships within graph data. However, their inherent black-box nature poses significant challenges to model interpretability, particularly in the context of link prediction tasks. This thesis investigates the explainability of GNNs for link prediction, a critical task in domains such as social network analysis and recommendation systems. We propose an efficient extension of the Zorro explainer, originally designed for node classification, to address the unique challenges of explaining link predictions. Our method leverages top similar nodes for initialization and incorporates techniques to accelerate the greedy search process, ultimately producing binary node and feature masks as explanations. Additionally, we introduce a novel Edge-level RDT-Fidelity metric to better evaluate explainers that generate edge masks, complementing existing metrics like RDT-Fidelity and Sparsity. Experimental results on the Cora and PubMed datasets demonstrate the superior performance and efficiency of our Zorro extension. This work contributes to the growing field of GNN interpretability by providing new methodologies and evaluation frameworks specifically tailored for link prediction.

Analyzing and forecasting multivariate time series using networks is interesting in traffic, energy consumption, or financial forecasting applications. The main challenge is to capture both spatial and temporal dependencies in the data alongside the dynamics of the network itself. Graph Neural Networks (GNNs) have shown reliable performance in network-based data by modeling the connections as a graph. GNNs, using temporal and recurrent structures, are further developed as a prominent tool for processing multivariate time series. However, the dynamics of the network, the evolution of the network over time, and its effect on the data should be studied more. Recent works augment temporal GNNs with graph learning modules to account for the changes in the network; however, often, these methods do not consider the dynamics directly, and all of them stop the graph changing after the training phase. This thesis focuses on an online graph adapting approach to deal with the dynamic data over networks. The proposed method is a hybrid model consisting of a temporal GNN inspired by the physics of dynamic networks, trains its parameters during the training phase, and adapts the graph with the stream of temporal data online. The experiments study the graph adaptation module's role on various benchmark datasets in forecasting tasks, such as traffic, windmill energy, and financial forecasting.

This thesis investigates the application of multi-agent reinforcement learning (MARL) to the optimization of radar waveforms. Radar technology is crucial in fields such as aviation, maritime navigation, and defense, but faces challenges such as interference, clutter, and the need for high resolution and accuracy. Cognitive radar, which adapts to environmental changes in real-time, offers a promising solution. This research aims to explore the potential of MARL in optimizing radar waveforms and examines whether incorporating domain knowledge can enhance performance.

The radar waveform optimization problem is framed within the Decentralized Partially Observable Markov Decision Process (Dec-POMDP) framework, defining the radar environment, agents' observations and actions, and reward functions. The study experiments with different architectures, including decentralized actors with a centralized critic. The centralized critic, having access to global state information, helps stabilize the learning process and mitigate non-stationarity and credit assignment problems. The use of GNNs as a centralized critic is proposed to leverage graph data sparsity, enhancing scalability.

The proposed models are trained and tested in a radar-tracking scenario, evaluated in terms of Pareto optimality and optimization times. The results show that both Independent Actor-Critic (IAC) and Independent Actor with Centralized Critic (IACC) models outperform traditional methods in terms of probability of detection, waveform duration, and optimization speed. The findings highlight the effectiveness of MARL approaches in optimizing radar waveforms, emphasizing the benefits of centralized critics for robustness and coordination. However, the choice of architecture significantly impacts performance, and while GNNs offer potential scalability advantages, their integration of domain knowledge did not yield significant improvements in this study. This research lays a foundation for future exploration of MARL and GNNs in radar waveform optimization.

GNNs are a powerful tool for learning tasks on data with a graph structure. However, the topology of the graph in which GNNs are trained is often subject to change due to random, external perturbations. This research investigates the relationship between 5 topological properties of graphs (assortativity, density, edge connectivity, closeness centrality, diameter) and how stable GNNs trained on graphs with different topological properties are against different perturbations. The analysis is conducted by first synthetically generating graphs with different topological properties and training a GNN using the generated graphs. The synthetic graphs are then perturbed, and the relative change in the GNNs' output is measured. These results are further supported by conducting the same process on three popular GNN datasets: Cora, CiteSeer and PubMed citations. Finally, relationships between the graph properties under investigation and GNN stability are inferred using the results obtained from both synthetic and real-world datasets.

Graph Neural Networks are widely used as useful tools to investigate graphs because they can learn from the topological structure of graphs. In practical applications, the graph’s structure can change over time, have errors or be subject to adversarial attacks. These perturbations negatively impact the accuracy of the neural network. The theoretical stability of graph neural networks has been analysed already and in this paper, the stability of graph neural networks is investigated experimentally. The performance of different perturbation strategies is compared to see how different perturbations impact stability.

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning from relational data. The real-world graphs such models are trained on are susceptible to changes in their topology. A growing body of work in the field of GNNs' stability to topology perturbations is trying to characterise how models respond to those changes, providing valuable insights that have enhanced the robustness of GNNs to adversarial attacks. The past work in this field, however, has only approached stability analysis using spectral graph theory, which is not applicable to all kinds of GNN models. In this paper, we aim to extend the past work in GNN stability by proposing an algorithm for analysing the stability of GNNs with model-agnostic GNN explainability tools instead of the mathematical framework of spectral graph theory. We demonstrate that the outputs of explainability tools can encode useful insights into the stability of GNNs and present a case study on using those insights to analyse node removal, edge removal, and edge weight perturbations.

Graph Neural Network holds significant impor- tance in various applications. Pioneering research has demonstrated state-of-the-art performance in practical applications such as Fraud Detection, Recommender Systems, or Traffic Forecasting by utilizing various Graph Neural Networks (GNNs) architectures. For these applications, one of the most important properties that needs to hold is the stability of GNN under stochastic perturbation as real-life networks undergo changes in topology on a frequent basis. However, it remains unclear how different architectures preserve this property under different perturbations. In this research, we aim to shed light on if this stability property undergoes drastic changes in the graph underlying topology, and if it affects the overall performance of the GNN in Traffic Forecasting problems. We demonstrate that the architectures differ in the stability property measured by different metrics, while some archi- tectures retains their state-of-the-art performance, providing useful insight on the analysis of stability property on different graph neural network archi- tectures in Traffic Forecasting problem.