We present the Temporal Graph Benchmark (TGB), a collection of challenging and diverse benchmark datasets for realistic, reproducible, and robust evaluation of machine learning models on temporal graphs. TGB datasets are of large scale, spanning years in duration, incorporate both node and edge-level prediction tasks and cover a diverse set of domains including social, trade, transaction, and transportation networks. For both tasks, we design evaluation protocols based on realistic use-cases. We extensively benchmark each dataset and find that the performance of common models can vary drastically across datasets. In addition, on dynamic node property prediction tasks, we show that simple methods often achieve superior performance compared to existing temporal graph models. We believe that these findings open up opportunities for future research on temporal graphs. Finally, TGB provides an automated machine learning pipeline for reproducible and accessible temporal graph research, including data loading, experiment setup and performance evaluation. TGB will be maintained and updated on a regular basis and welcomes community feedback. TGB datasets, data loaders, example codes, evaluation setup, and leaderboards are publicly available at https://tgb.complexdatalab.com/.

How can we detect traffic disturbances from international flight transportation logs or changes to collaboration dynamics in academic networks? These problems can be formulated as detecting anomalous change points in a dynamic graph. Current solutions do not scale well to large real-world graphs, lack robustness to large amounts of node additions/deletions, and overlook changes in node attributes. To address these limitations, we propose a novel spectral method: Scalable Change Point Detection (SCPD). SCPD generates an embedding for each graph snapshot by efficiently approximating the distribution of the Laplacian spectrum at each step. SCPD can also capture shifts in node attributes by tracking correlations between attributes and eigenvectors. Through extensive experiments using synthetic and real-world data, we show that SCPD (a) achieves state-of-the art performance, (b) is significantly faster than the state-of-the-art methods and can easily process millions of edges in a few CPU minutes, (c) can effectively tackle a large quantity of node attributes, additions or deletions and (d) discovers interesting events in large real-world graphs. The code is publicly available at https://github.com/shenyangHuang/SCPD.git

Dynamic graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion identification in network systems, detection of ecosystem disturbances and detection of epidemic outbreaks. In this paper, we focus on change point detection in dynamic graphs and address three main challenges associated with this problem: i). how to compare graph snapshots across time, ii). how to capture temporal dependencies, and iii). how to combine different views of a temporal graph. To solve the above challenges, we first propose Laplacian Anomaly Detection (LAD) which uses the spectrum of graph Laplacian as the low dimensional embedding of the graph structure at each snapshot. LAD explicitly models short term and long term dependencies by applying two sliding windows. Next, we propose MultiLAD, a simple and effective generalization of LAD to multi-view graphs. MultiLAD provides the first change point detection method for multi-view dynamic graphs. It aggregates the singular values of the normalized graph Laplacian from different views through the scalar power mean operation. Through extensive synthetic experiments, we show that i). LAD and MultiLAD are accurate and outperforms state-of-the-art baselines and their multi-view extensions by a large margin, ii). MultiLAD's advantage over contenders significantly increases when additional views are available, and iii). MultiLAD is highly robust to noise from individual views. In five real world dynamic graphs, we demonstrate that LAD and MultiLAD identify significant events as top anomalies such as the implementation of government COVID-19 interventions which impacted the population mobility in multi-view traffic networks.

Weighted finite automata (WFAs) have been widely applied in many fields. One of the classic problems for WFAs is probability distribution estimation over sequences of discrete symbols. Although WFAs have been extended to deal with continuous input data, namely continuous WFAs (CWFAs), it is still unclear how to approximate density functions over sequences of continuous random variables using WFA-based models, due to the limitation on the expressiveness of the model as well as the tractability of approximating density functions via CWFAs. In this paper, we propose a nonlinear extension to the CWFA model to first improve its expressiveness, we refer to it as the nonlinear continuous WFAs (NCWFAs). Then we leverage the so-called RNADE method, which is a well-known density estimator based on neural networks, and propose the RNADE-NCWFA model. The RNADE-NCWFA model computes a density function by design. We show that this model is strictly more expressive than the Gaussian HMM model, which CWFA cannot approximate. Empirically, we conduct a synthetic experiment using Gaussian HMM generated data. We focus on evaluating the model's ability to estimate densities for sequences of varying lengths (longer length than the training data). We observe that our model performs the best among the compared baseline methods.

We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based methods allows us to derive strong theoretical guarantees on the expected return of the reconstructed policy. Such guarantees are typically lacking in black-box models, but are very desirable in tasks requiring stability and convergence guarantees. We conduct several experiments on classic RL domains. The results confirm that the policies can be robustly represented in a low-dimensional space while the embedded policy incurs almost no decrease in returns.

Random projection (RP) have recently emerged as popular techniques in themachine learning community for their ability in reducing the dimension of veryhigh-dimensional tensors. Following the work in [29], we consider a tensorizedrandom projection relying on Tensor Train (TT) decomposition where each elementof the core tensors is drawn from a Rademacher distribution. Our theoreticalresults reveal that the Gaussian low-rank tensor represented in compressed formin TT format in [29] can be replaced by a TT tensor with core elements drawnfrom a Rademacher distribution with the same embedding size. Experiments onsynthetic data demonstrate that tensorized Rademacher RP can outperform thetensorized Gaussian RP studied in [29]. In addition, we show both theoreticallyand experimentally, that the tensorized RP in the Matrix Product Operator (MPO)format proposed in [5] for performing SVD on large matrices is not a Johnson-Lindenstrauss transform (JLT) and therefore not a well-suited random projectionmap

Airlines have been making use of highly complex Revenue Management Systems to maximize revenue for decades. Estimating the impact of changing one component of those systems on an important outcome such as revenue is crucial, yet very challenging. It is indeed the difference between the generated value and the value that would have been generated keeping business as usual, which is not observable. We provide a comprehensive overview of counterfactual prediction models and use them in an extensive computational study based on data from Air Canada to estimate such impact. We focus on predicting the counterfactual revenue and compare it to the observed revenue subject to the impact. Our microeconomic application and small expected treatment impact stand out from the usual synthetic control applications. We present accurate linear and deep-learning counterfactual prediction models which achieve respectively 1.1% and 1% of error and allow to estimate a simulated effect quite accurately.

Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method reduces CF on classical CL datasets.

Tensor decomposition techniques have shown great successes in machine learning and data science by extending classical algorithms based on matrix factorization to multi-modal and multi-way data. However, there exist many tensor decomposition models (CP, Tucker, Tensor Train, etc.) and the rank of such a decomposition is typically a collection of integers rather than a unique number, making model and hyper-parameter selection a tedious and costly task. At the same time, tensor network methods are powerful tools developed in the physics community which have recently shown their potential for machine learning applications and offer a unifying view of the various tensor decomposition models. In this paper, we leverage the tensor network formalism to develop a generic and efficient adaptive algorithm for tensor learning. Our method is based on a simple greedy approach optimizing a differentiable loss function starting from a rank one tensor and successively identifying the most promising tensor network edges for small rank increments. Our algorithm can adaptively identify tensor network structures with small number of parameters that effectively optimize the objective function from data. The framework we introduce is very broad and encompasses many common tensor optimization problems. Experiments on tensor decomposition and tensor completion tasks with both synthetic and real world data demonstrate the effectiveness of the proposed algorithm.

Dynamic and temporal graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion identification in network systems, detection of ecosystem disturbances and detection of epidemic outbreaks. In this paper, we focus on change point detection in dynamic graphs and address two main challenges associated with this problem: I) how to compare graph snapshots across time, II) how to capture temporal dependencies. To solve the above challenges, we propose Laplacian Anomaly Detection (LAD) which uses the spectrum of the Laplacian matrix of the graph structure at each snapshot to obtain low dimensional embeddings. LAD explicitly models short term and long term dependencies by applying two sliding windows. In synthetic experiments, LAD outperforms the state-of-the-art method. We also evaluate our method on three real dynamic networks: UCI message network, US senate co-sponsorship network and Canadian bill voting network. In all three datasets, we demonstrate that our method can more effectively identify anomalous time points according to significant real world events.