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Laurent Oudre

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

6 papers

2 author rows

ICML Conference 2025 Conference Paper

Time Series Representations with Hard-Coded Invariances

Thibaut Germain
Chrysoula Kosma
Laurent Oudre

Automatically extracting robust representations from large and complex time series data is becoming imperative for several real-world applications. Unfortunately, the potential of common neural network architectures in capturing invariant properties of time series remains relatively underexplored. For instance, convolutional layers often fail to capture underlying patterns in time series inputs that encompass strong deformations, such as trends. Indeed, invariances to some deformations may be critical for solving complex time series tasks, such as classification, while guaranteeing good generalization performance. To address these challenges, we mathematically formulate and technically design efficient and hard-coded invariant convolutions for specific group actions applicable to the case of time series. We construct these convolutions by considering specific sets of deformations commonly observed in time series, including scaling, offset shift, and trend. We further combine the proposed invariant convolutions with standard convolutions in single embedding layers, and we showcase the layer capacity to capture complex invariant time series properties in several scenarios.

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TMLR Journal 2024 Journal Article

A persistent homology-based algorithm for unsupervised anomaly detection in time series

Alexandre Bois
Brian Tervil
Laurent Oudre

In this article, we propose a new algorithm for unsupervised anomaly detection in univariate time series, based on topological data analysis. It relies on delay embeddings and on the extraction of persistent cycles from the 1-dimensional persistent homology constructed from the distance to measure Rips filtration. This filtration makes it possible to identify 1-cycles (i.e. loops) corresponding to recurrent patterns by leveraging density information. Points in those cycles are considered as normal, and the algorithm can then assign an anomaly score to any point which is its distance to the normal set. In this paper, we describe the algorithm, make a theoretical study, and test it on several real-world and synthetic datasets, showing that it is competitive with state-of-the-art anomaly detection methods.

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TMLR Journal 2024 Journal Article

Learning Network Granger causality using Graph Prior Knowledge

Lucas Zoroddu
Pierre Humbert
Laurent Oudre

Understanding the relationships among multiple entities through Granger causality graphs within multivariate time series data is crucial across various domains, including economics, finance, neurosciences, and genetics. Despite its broad utility, accurately estimating Granger causality graphs in high-dimensional scenarios with few samples remains a persistent chal- lenge. In response, this study introduces a novel model that leverages prior knowledge in the form of a noisy undirected graph to facilitate the learning of Granger causality graphs, while assuming sparsity. In this study we introduce an optimization problem, we propose to solve it with an alternative minimization approach and we proved the convergence of our fitting algorithm, highlighting its effectiveness. Furthermore, we present experimental results derived from both synthetic and real-world datasets. These results clearly illustrate the advantages of our proposed method over existing alternatives, particularly in situations where few samples are available. By incorporating prior knowledge and emphasizing spar- sity, our approach offers a promising solution to the complex problem of estimating Granger causality graphs in high-dimensional, data-scarce environments.

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NeurIPS Conference 2024 Conference Paper

Shape analysis for time series

Thibaut Germain
Samuel Gruffaz
Charles Truong
Laurent Oudre
Alain Durmus

Analyzing inter-individual variability of physiological functions is particularly appealing in medical and biological contexts to describe or quantify health conditions. Such analysis can be done by comparing individuals to a reference one with time series as biomedical data. This paper introduces an unsupervised representation learning (URL) algorithm for time series tailored to inter-individual studies. The idea is to represent time series as deformations of a reference time series. The deformations are diffeomorphisms parameterized and learned by our method called TS-LDDMM. Once the deformations and the reference time series are learned, the vector representations of individual time series are given by the parametrization of their corresponding deformation. At the crossroads between URL for time series and shape analysis, the proposed algorithm handles irregularly sampled multivariate time series of variable lengths and provides shape-based representations of temporal data. In this work, we establish a representation theorem for the graph of a time series and derive its consequences on the LDDMM framework. We showcase the advantages of our representation compared to existing methods using synthetic data and real-world examples motivated by biomedical applications.

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JMLR Journal 2021 Journal Article

Learning Laplacian Matrix from Graph Signals with Sparse Spectral Representation

Pierre Humbert
Batiste Le Bars
Laurent Oudre
Argyris Kalogeratos
Nicolas Vayatis

In this paper, we consider the problem of learning a graph structure from multivariate signals, known as graph signals. Such signals are multivariate observations carrying measurements corresponding to the nodes of an unknown graph, which we desire to infer. They are assumed to enjoy a sparse representation in the graph spectral domain, a feature which is known to carry information related to the cluster structure of a graph. The signals are also assumed to behave smoothly with respect to the underlying graph structure. For the graph learning problem, we propose a new optimization program to learn the Laplacian of this graph and provide two algorithms to solve it, called IGL-3SR and FGL-3SR. Based on a 3-step alternating procedure, both algorithms rely on standard minimization methods --such as manifold gradient descent or linear programming-- and have lower complexity compared to state-of-the-art algorithms. While IGL-3SR ensures convergence, FGL-3SR acts as a relaxation and is significantly faster since its alternating process relies on multiple closed-form solutions. Both algorithms are evaluated on synthetic and real data. They are shown to perform as good or better than their competitors in terms of both numerical performance and scalability. Finally, we present a probabilistic interpretation of the proposed optimization program as a Factor Analysis Model. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

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ICML Conference 2018 Conference Paper

DICOD: Distributed Convolutional Coordinate Descent for Convolutional Sparse Coding

Thomas Moreau 0001
Laurent Oudre
Nicolas Vayatis

In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it communication efficient. It is based on coordinate descent and uses locally greedy updates which accelerate the resolution compared to greedy coordinate selection. We prove the convergence of this algorithm and highlight its computational speed-up which is super-linear in the number of cores used. We also provide empirical evidence for the acceleration properties of our algorithm compared to state-of-the-art methods.

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