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Thomas Markovich

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7 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Uncertainty Estimation on Graphs with Structure Informed Stochastic Partial Differential Equations

Fred Xu
Thomas Markovich

Graph Neural Networks (GNNs) have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult—especially under distributional shifts. Unlike traditional uncertainty estimation, graph-based uncertainty must account for randomness arising from both the graph’s structure and its label distribution, which adds complexity. In this paper, making an analogy between the evolution of a stochastic partial differential equation (SPDE) driven by Mat\'ern Gaussian Process and message passing using GNN layers, we present a principled way to design a novel message passing scheme that incorporates spatial-temporal noises motivated by the Gaussian Process approach to SPDE. Our method simultaneously captures uncertainty across space and time and allows explicit control over the covariance kernel’s smoothness, thereby enhancing uncertainty estimates on graphs with both low and high label informativeness. Our extensive experiments on Out-of-Distribution (OOD) detection on graph datasets with varying label informativeness demonstrate the soundness and superiority of our model to existing approaches.

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ICML Conference 2025 Conference Paper

When to retrain a machine learning model

Florence Regol
Leo Schwinn
Kyle Sprague
Mark Coates
Thomas Markovich

A significant challenge in maintaining real-world machine learning models is responding to the continuous and unpredictable evolution of data. Most practitioners are faced with the difficult question: when should I retrain or update my machine learning model? This seemingly straightforward problem is particularly challenging for three reasons: 1) decisions must be made based on very limited information - we usually have access to only a few examples, 2) the nature, extent, and impact of the distribution shift are unknown, and 3) it involves specifying a cost ratio between retraining and poor performance, which can be hard to characterize. Existing works address certain aspects of this problem, but none offer a comprehensive solution. Distribution shift detection falls short as it cannot account for the cost trade-off; the scarcity of the data, paired with its unusual structure, makes it a poor fit for existing offline reinforcement learning methods, and the online learning formulation overlooks key practical considerations. To address this, we present a principled formulation of the retraining problem and propose an uncertainty-based method that makes decisions by continually forecasting the evolution of model performance evaluated with a bounded metric. Our experiments, addressing classification tasks, show that the method consistently outperforms existing baselines on 7 datasets. We thoroughly assess its robustness to varying cost trade-off values and mis-specified cost trade-offs.

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TMLR Journal 2024 Journal Article

QDC: Quantum Diffusion Convolution Kernels on Graphs

Thomas Markovich

Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and significant work has been dedicated to improving predictive accuracy by altering the ways of message passing. In this work, we propose a new convolution kernel that effectively rewires the graph according to the occupation correlations of the vertices by trading on the generalized diffusion paradigm for the propagation of a quantum particle over the graph. We term this new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In addition, we introduce a multiscale variant that combines messages from the QDC operator and the traditional combinatorial Laplacian. To understand our method, we explore the spectral dependence of homophily and the importance of quantum dynamics in the construction of a bandpass filter. Through these studies, as well as experiments on a range of datasets, we observe that QDC improves predictive performance on the widely used benchmark datasets when compared to similar methods.

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TMLR Journal 2024 Journal Article

Recent Link Classification on Temporal Graphs Using Graph Profiler

Muberra Ozmen
Thomas Markovich

The performance of Temporal Graph Learning (TGL) methods are typically evaluated on the future link prediction task, i.e., whether two nodes will get connected and dynamic node classification task, i.e., whether a node's class will change. Comparatively, recent link classification, i.e., to what class an emerging edge belongs to, is investigated much less even though it exists in many industrial settings. In this work, we first formalize recent link classification on temporal graphs as a benchmark downstream task and introduce corresponding benchmark datasets. Secondly, we evaluate the performance of state-of-the-art methods with a statistically meaningful metric Matthews Correlation Coefficient, which is more robust to imbalanced datasets, in addition to the commonly used average precision and area under the curve. We propose several design principles for tailoring models to specific requirements of the task and the dataset including modifications on message aggregation schema, readout layer and time encoding strategy which obtain significant improvement on benchmark datasets. Finally, we propose an architecture that we call Graph Profiler, which is capable of encoding previous events' class information on source and destination nodes. The experiments show that our proposed model achieves an improved Matthews Correlation Coefficient on most cases under interest. We believe the introduction of recent link classification as a benchmark task for temporal graph learning will be useful for the evaluation of prospective methods within the field.

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TMLR Journal 2023 Journal Article

Causally-guided Regularization of Graph Attention Improves Generalizability

Alexander P Wu
Thomas Markovich
Bonnie Berger
Nils Yannick Hammerla
Rohit Singh

Graph attention networks estimate the relational importance of node neighbors to aggregate relevant information over local neighborhoods for a prediction task. However, the inferred attentions are vulnerable to spurious correlations and connectivity in the training data, hampering the generalizability of models. We introduce CAR, a general-purpose regularization framework for graph attention networks. Embodying a causal inference approach based on invariance prediction, CAR aligns the attention mechanism with the causal effects of active interventions on graph connectivity in a scalable manner. CAR is compatible with a variety of graph attention architectures, and we show that it systematically improves generalizability on various node classification tasks. Our ablation studies indicate that CAR hones in on the aspects of graph structure most pertinent to the prediction (e.g., homophily), and does so more effectively than alternative approaches. Finally, we also show that \methodname enhances interpretability of attention coefficients by accentuating node-neighbor relations that point to causal hypotheses.

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ICLR Conference 2023 Conference Paper

Graph Neural Networks for Link Prediction with Subgraph Sketching

Ben Chamberlain 0001
Sergey Shirobokov
Emanuele Rossi 0001
Fabrizio Frasca
Thomas Markovich
Nils Hammerla
Michael M. Bronstein
Max Hansmire

Many Graph Neural Networks (GNNs) perform poorly compared to simple heuristics on Link Prediction (LP) tasks. This is due to limitations in expressive power such as the inability to count triangles (the backbone of most LP heuristics) and because they can not distinguish automorphic nodes (those having identical structural roles). Both expressiveness issues can be alleviated by learning link (rather than node) representations and incorporating structural features such as triangle counts. Since explicit link representations are often prohibitively expensive, recent works resorted to subgraph-based methods, which have achieved state-of-the-art performance for LP, but suffer from poor efficiency due to high levels of redundancy between subgraphs. We analyze the components of subgraph GNN (SGNN) methods for link prediction. Based on our analysis, we propose a novel full-graph GNN called ELPH (Efficient Link Prediction with Hashing) that passes subgraph sketches as messages to approximate the key components of SGNNs without explicit subgraph construction. ELPH is provably more expressive than Message Passing GNNs (MPNNs). It outperforms existing SGNN models on many standard LP benchmarks while being orders of magnitude faster. However, it shares the common GNN limitation that it is only efficient when the dataset fits in GPU memory. Accordingly, we develop a highly scalable model, called BUDDY, which uses feature precomputation to circumvent this limitation without sacrificing predictive performance. Our experiments show that BUDDY also outperforms SGNNs on standard LP benchmarks while being highly scalable and faster than ELPH.

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TMLR Journal 2023 Journal Article

Understanding convolution on graphs via energies

Francesco Di Giovanni
James Rowbottom
Benjamin Paul Chamberlain
Thomas Markovich
Michael M. Bronstein

Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed by a shared, linear transformation before being propagated over the edges. On node-classification tasks, graph convolutions have been shown to suffer from two limitations: poor performance on heterophilic graphs, and over-smoothing. It is common belief that both phenomena occur because such models behave as low-pass filters, meaning that the Dirichlet energy of the features decreases along the layers incurring a smoothing effect that ultimately makes features no longer distinguishable. In this work, we rigorously prove that simple graph-convolutional models can actually enhance high frequencies and even lead to an asymptotic behaviour we refer to as over-sharpening, opposite to over-smoothing. We do so by showing that linear graph convolutions with symmetric weights minimize a multi-particle energy that generalizes the Dirichlet energy; in this setting, the weight matrices induce edge-wise attraction (repulsion) through their positive (negative) eigenvalues, thereby controlling whether the features are being smoothed or sharpened. We also extend the analysis to non-linear GNNs, and demonstrate that some existing time-continuous GNNs are instead always dominated by the low frequencies. Finally, we validate our theoretical findings through ablations and real-world experiments.

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