arXiv subjects

Deborah Sulem

Publications and source records attributed to Deborah Sulem.

7 recordsLinked to original sources

arXiv2026

Posterior concentration in spatio-temporal Hawkes processes

We develop a Bayesian nonparametric framework for inference in spatio-temporal Hawkes processes, extending existing theoretical results beyond the purely temporal setting. Our framework encompasses modelling both the background and triggering components of the Hawkes process through Gaussian Processes priors. Under appropriate smoothness and regularity assumptions on the true parameter and the nonparametric prior family, we derive explicit posterior contraction rates for the conditional intensity function and the model's parameter, in the asymptotic regime of repeatedly observed and independent sequences. Our analysis generalizes known contraction results for purely temporal Hawkes processes to the spatio-temporal setting, which allows to jointly model self-excitation across time and space in event data. These results provide, to our knowledge, the first theoretical guarantees for Bayesian nonparametric methods in spatio-temporal point data.

math.ST↗

arXiv2025

Bayesian computation for high-dimensional Gaussian Graphical Models with spike-and-slab priors

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the data, and parameter estimates. However, computational demands have limited their application when the number of variables is large, which prompted the use of pseudo-Bayesian approaches. We propose fully Bayesian algorithms that provably scale to high dimensions when the data-generating precision matrix is sparse, at a similar cost to the best pseudo-Bayesian methods. First, a Metropolis-Hastings-within-Block-Gibbs algorithm that allows row-wise updates of the precision matrix, using local moves. Second, a global proposal that enables adding or removing multiple edges within a row, which can help explore multi-modal posteriors. We obtain mixing bounds for both samplers relative to an ideal Gibbs sampler that are dimension-free under suitable settings, and prove that this ideal Gibbs sampler is geometrically ergodic. We also provide worst-case polynomial bounds on per-iteration costs, though in practice the cost is lower by using sparse linear algebra. Our examples show that the methods extend the applicability of exact Bayesian inference from roughly 100 to roughly 1000 variables (equivalently, from 5,000 edges to 500,000 edges).

stat.ME↗

arXiv2023

An Empirical Study of Self-supervised Learning with Wasserstein Distance

In this study, we delve into the problem of self-supervised learning (SSL) utilizing the 1-Wasserstein distance on a tree structure (a.k.a., Tree-Wasserstein distance (TWD)), where TWD is defined as the L1 distance between two tree-embedded vectors. In SSL methods, the cosine similarity is often utilized as an objective function; however, it has not been well studied when utilizing the Wasserstein distance. Training the Wasserstein distance is numerically challenging. Thus, this study empirically investigates a strategy for optimizing the SSL with the Wasserstein distance and finds a stable training procedure. More specifically, we evaluate the combination of two types of TWD (total variation and ClusterTree) and several probability models, including the softmax function, the ArcFace probability model, and simplicial embedding. We propose a simple yet effective Jeffrey divergence-based regularization method to stabilize optimization. Through empirical experiments on STL10, CIFAR10, CIFAR100, and SVHN, we find that a simple combination of the softmax function and TWD can obtain significantly lower results than the standard SimCLR. Moreover, a simple combination of TWD and SimSiam fails to train the model. We find that the model performance depends on the combination of TWD and probability model, and that the Jeffrey divergence regularization helps in model training. Finally, we show that the appropriate combination of the TWD and probability model outperforms cosine similarity-based representation learning.

stat.ML↗

arXiv2022

Scalable and adaptive variational Bayes methods for Hawkes processes

Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. In particular, for generalised nonlinear Hawkes processes, Monte-Carlo Markov Chain methods applied to compute the doubly intractable posterior distribution are not scalable to high-dimensional processes in practice. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed. In this work, we first unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model. Secondly, we propose a novel sparsity-inducing procedure, and derive an adaptive mean-field variational algorithm for the popular sigmoid Hawkes processes. Our algorithm is parallelisable and therefore computationally efficient in high-dimensional setting. Through an extensive set of numerical simulations, we also demonstrate that our procedure is able to adapt to the dimensionality of the parameter of the Hawkes process, and is partially robust to some type of model mis-specification.

math.ST↗

arXiv2022

Graph similarity learning for change-point detection in dynamic networks

Dynamic networks are ubiquitous for modelling sequential graph-structured data, e.g., brain connectome, population flows and messages exchanges. In this work, we consider dynamic networks that are temporal sequences of graph snapshots, and aim at detecting abrupt changes in their structure. This task is often termed network change-point detection and has numerous applications, such as fraud detection or physical motion monitoring. Leveraging a graph neural network model, we design a method to perform online network change-point detection that can adapt to the specific network domain and localise changes with no delay. The main novelty of our method is to use a siamese graph neural network architecture for learning a data-driven graph similarity function, which allows to effectively compare the current graph and its recent history. Importantly, our method does not require prior knowledge on the network generative distribution and is agnostic to the type of change-points; moreover, it can be applied to a large variety of networks, that include for instance edge weights and node attributes. We show on synthetic and real data that our method enjoys a number of benefits: it is able to learn an adequate graph similarity function for performing online network change-point detection in diverse types of change-point settings, and requires a shorter data history to detect changes than most existing state-of-the-art baselines.

stat.ML↗

arXiv2022

Diverse Counterfactual Explanations for Anomaly Detection in Time Series

Data-driven methods that detect anomalies in times series data are ubiquitous in practice, but they are in general unable to provide helpful explanations for the predictions they make. In this work we propose a model-agnostic algorithm that generates counterfactual ensemble explanations for time series anomaly detection models. Our method generates a set of diverse counterfactual examples, i.e, multiple perturbed versions of the original time series that are not considered anomalous by the detection model. Since the magnitude of the perturbations is limited, these counterfactuals represent an ensemble of inputs similar to the original time series that the model would deem normal. Our algorithm is applicable to any differentiable anomaly detection model. We investigate the value of our method on univariate and multivariate real-world datasets and two deep-learning-based anomaly detection models, under several explainability criteria previously proposed in other data domains such as Validity, Plausibility, Closeness and Diversity. We show that our algorithm can produce ensembles of counterfactual examples that satisfy these criteria and thanks to a novel type of visualisation, can convey a richer interpretation of a model's internal mechanism than existing methods. Moreover, we design a sparse variant of our method to improve the interpretability of counterfactual explanations for high-dimensional time series anomalies. In this setting, our explanation is localised on only a few dimensions and can therefore be communicated more efficiently to the model's user.

cs.LG↗

arXiv2021

Bayesian estimation of nonlinear Hawkes process

Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of occurrences of new events depend on the past of the process is the Hawkes process. In this work we consider the nonlinear Hawkes process, which notably models excitation and inhibition phenomena between dimensions of the process. In a nonparametric Bayesian estimation framework, we obtain concentration rates of the posterior distribution on the parameters, under mild assumptions on the prior distribution and the model. These results also lead to convergence rates of Bayesian estimators. Another object of interest in event-data modelling is to recover the graph of interaction - or Granger connectivity graph - of the phenomenon. We provide consistency guarantees on Bayesian methods for estimating this quantity; in particular, we prove that the posterior distribution is consistent on the graph adjacency matrix of the process, as well as a Bayesian estimator based on an adequate loss function.

math.ST↗