arXiv subjects

Stéphane Chrétien

Publications and source records attributed to Stéphane Chrétien.

At least 19 recordsLinked to original sources

arXiv2026

MultiSigBERT: Beyond Survival Analysis through Multimodal and Sequential Modeling in Oncology

Machine learning has become an essential component of modern healthcare, where the integration of heterogeneous data sources offers unprecedented opportunities to improve clinical decision-making. Electronic Health Records (EHR) contain complementary information -- including narrative clinical reports, numerical measurements, and structured variables -- yet most survival models remain limited to a single modality or fail to exploit the temporal nature of patient trajectories. We propose MultiSigBERT, a unified framework for multimodal sequential survival modeling in oncology based on path signature representations. Here, narrative medical reports (free-text) are converted into sentence embeddings by extracting and averaging contextual word embeddings. These representations are then compressed via modality-specific PCA and concatenated with structured covariates to form joint temporal trajectories which are then encoded using the Signature transform, a tool from Rough Paths theory that efficiently captures higher-order temporal interactions across modalities without supervision needed. The computed Signature features are finally incorporated as high dimensional features into a LASSO-regularized Cox model to estimate individualized risk scores. The performance of our novel MultiSigBERT pipeline is illustrated on the analysis of a real-world oncology cohort from the Léon Bérard Center, comprising over 120,000 medical reports and structured records from more than 2,500 patients. The model achieves a concordance index of 0.743 (sd 0.029) on an independent test set, demonstrating the benefit of jointly modeling multimodal temporal dynamics together with patient-level geometric structure for survival prediction.

cs.LG↗

arXiv2026

Distribution of hitting times for dissipative random dynamical systems on $\mathbb{R}^d$, with application to stochastic gradient descent

Machine Learning and more specifically Deep Learning involves solving large scale nonconvex optimization problems. Several algorithms have been proposed in the literature, that seem to achieve satisfactory practical efficiency for difficult instances, the Stochastic Gradient Method being the most rudimentary, while still outperforming more recent algorithms at a number of learning tasks. A major open question about the current methods used in deep learning is to understand their convergence properties. Following a line of previous works about the long time behavior of gradient-type algorithms, %and in particular the recent contributions from Azizian et al., we present a new approach for studying the asymptotic properties of a wide family of methods from an ergodic theoretical viewpoint. Our main results include a study of the expected time for a stochastic optimisation algorithm to reach a certain small neighborhood of a minimizer and show that this reaching time distributes exponentially around its average, which is given by the inverse of the stationary measure of the target. The assumptions on the Stochastic Gradient noise include the Gaussian and the Sub-Exponential assumptions.

stat.ML↗

arXiv2026

The dual approach to non-negative super-resolution: perturbation analysis and $\ell_1$ data fidelity

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from (potentially noisy) samples of their convolution with a Gaussian kernel. Previous work has shown that exact recovery is possible by minimising the total variation norm of the measure, and a practical way to achieve this is by solving the dual problem. In this paper, we study the stability of the solution with respect to the solution of the dual problem, both in the case of exact measurements and in the case of measurements with additive noise. In particular, we establish a relationship between perturbations in the dual variable and perturbations in the primal variable around the true solution and, in the case of inexact measurements, we derive a similar relationship between the additive noise and perturbations in the dual variable using an $\ell_1$ data fidelity whose dual is box constrained. Our analysis is based on a quantitative version of the implicit function theorem.

math.OC↗

arXiv2026

Conformal Online Learning of Deep Koopman Linear Embeddings

We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multistep prediction consistency in the lifted space, where the dynamics evolve linearly. To prevent overfitting, COLoKe employs a conformal-style mechanism that shifts the focus from evaluating the conformity of new states to assessing the consistency of the current Koopman model. Updates are triggered only when the current model's prediction error exceeds a dynamically calibrated threshold, allowing selective refinement of the Koopman operator and embedding. Empirical results on benchmark dynamical systems demonstrate the effectiveness of COLoKe in maintaining long-term predictive accuracy while significantly reducing unnecessary updates and avoiding overfitting.

cs.LG↗

arXiv2026

A Langevin sampler for quantum tomography

Quantum tomography involves obtaining a full classical description of a prepared quantum state from experimental results. We propose a Langevin sampler for quantum tomography, that relies on a new formulation of Bayesian quantum tomography exploiting the Burer-Monteiro factorization of Hermitian positive-semidefinite matrices. If the rank of the target density matrix is known, this formulation allows us to define a posterior distribution that is only supported on matrices whose rank is upper-bounded by the rank of the target density matrix. Conversely, if the target rank is unknown, any upper bound on the rank can be used by our algorithm, and the rank of the resulting posterior mean estimator is further reduced by the use of a low-rank promoting prior density. This prior density is a complex extension of the one proposed in (Annales de l'Institut Henri Poincare Probability and Statistics, 56(2):1465-1483, 2020). We derive a PAC-Bayesian bound on our proposed estimator that matches the best bounds available in the literature, and we show numerically that it leads to strong scalability improvements compared to existing techniques when the rank of the density matrix is known to be small.

math.ST↗

arXiv2025

SigBERT: Combining Narrative Medical Reports and Rough Path Signature Theory for Survival Risk Estimation in Oncology

Electronic medical reports (EHR) contain a vast amount of information that can be leveraged for machine learning applications in healthcare. However, existing survival analysis methods often struggle to effectively handle the complexity of textual data, particularly in its sequential form. Here, we propose SigBERT, an innovative temporal survival analysis framework designed to efficiently process a large number of clinical reports per patient. SigBERT processes timestamped medical reports by extracting and averaging word embeddings into sentence embeddings. To capture temporal dynamics from the time series of sentence embedding coordinates, we apply signature extraction from rough path theory to derive geometric features for each patient, which significantly enhance survival model performance by capturing complex temporal dynamics. These features are then integrated into a LASSO-penalized Cox model to estimate patient-specific risk scores. The model was trained and evaluated on a real-world oncology dataset from the Léon Bérard Center corpus, with a C-index score of 0.75 (sd 0.014) on the independent test cohort. SigBERT integrates sequential medical data to enhance risk estimation, advancing narrative-based survival analysis.

cs.CL↗

arXiv2025

Detecting malignant dynamics on very few blood sample using signature coefficients

Recent discoveries have suggested that the promising avenue of using circulating tumor DNA (ctDNA) levels in blood samples provides reasonable accuracy for cancer monitoring, with extremely low burden on the patient's side. It is known that the presence of ctDNA can result from various mechanisms leading to DNA release from cells, such as apoptosis, necrosis or active secretion. One key idea in recent cancer monitoring studies is that monitoring the dynamics of ctDNA levels might be sufficient for early multi-cancer detection. This interesting idea has been turned into commercial products, e.g. in the company named GRAIL. In the present work, we propose to explore the use of Signature theory for detecting aggressive cancer tumors based on the analysis of blood samples. Our approach combines tools from continuous time Markov modelling for the dynamics of ctDNA levels in the blood, with Signature theory for building efficient testing procedures. Signature theory is a topic of growing interest in the Machine Learning community (see Chevyrev2016 and Fermanian2021), which is now recognised as a powerful feature extraction tool for irregularly sampled signals. The method proposed in the present paper is shown to correctly address the challenging problem of overcoming the inherent data scarsity due to the extremely small number of blood samples per patient. The relevance of our approach is illustrated with extensive numerical experiments that confirm the efficiency of the proposed pipeline.

q-bio.QM↗

arXiv2024

Time topological analysis of EEG using signature theory

Anomaly detection in multivariate signals is a task of paramount importance in many disciplines (epidemiology, finance, cognitive sciences and neurosciences, oncology, etc.). In this perspective, Topological Data Analysis (TDA) offers a battery of "shape" invariants that can be exploited for the implementation of an effective detection scheme. Our contribution consists of extending the constructions presented in \cite{chretienleveraging} on the construction of simplicial complexes from the Signatures of signals and their predictive capacities, rather than the use of a generic distance as in \cite{petri2014homological}. Signature theory is a new theme in Machine Learning arXiv:1603.03788 stemming from recent work on the notions of Rough Paths developed by Terry Lyons and his team \cite{lyons2002system} based on the formalism introduced by Chen \cite{chen1957integration}. We explore in particular the detection of changes in topology, based on tracking the evolution of homological persistence and the Betti numbers associated with the complex introduced in \cite{chretienleveraging}. We apply our tools for the analysis of brain signals such as EEG to detect precursor phenomena to epileptic seizures.

eess.SP↗

arXiv2024

Registration of algebraic varieties using Riemannian optimization

We consider the point cloud registration problem, the task of finding a transformation between two point clouds that represent the same object but are expressed in different coordinate systems. Our approach is not based on a point-to-point correspondence, matching every point in the source point cloud to a point in the target point cloud. Instead, we assume and leverage a low-dimensional nonlinear geometric structure of the data. Firstly, we approximate each point cloud by an algebraic variety (a set defined by finitely many polynomial equations). This is done by solving an optimization problem on the Grassmann manifold, using a connection between algebraic varieties and polynomial bases. Secondly, we solve an optimization problem on the orthogonal group to find the transformation (rotation $+$ translation) which makes the two algebraic varieties overlap. We use second-order Riemannian optimization methods for the solution of both steps. Numerical experiments on real and synthetic data are provided, with encouraging results. Our approach is particularly useful when the two point clouds describe different parts of an objects (which may not even be overlapping), on the condition that the surface of the object may be well approximated by a set of polynomial equations. The first procedure -- the approximation -- is of independent interest, as it can be used for denoising data that belongs to an algebraic variety. We provide statistical guarantees for the estimation error of the denoising using Stein's unbiased estimator.

math.OC↗

arXiv2023

Mixture model for designs in high dimensional regression and the LASSO

The LASSO is a recent technique for variable selection in the regression model \bean y & = & Xβ+ z, \eean where $X\in \R^{n\times p}$ and $z$ is a centered gaussian i.i.d. noise vector $\mathcal N(0,σ^2I)$. The LASSO has been proved to achieve remarkable properties such as exact support recovery of sparse vectors when the columns are sufficently incoherent and low prediction error under even less stringent conditions. However, many matrices do not satisfy small coherence in practical applications and the LASSO estimator may thus suffer from what is known as the slow rate regime. The goal of the present paper is to study the LASSO from a slightly different perspective by proposing a mixture model for the design matrix which is able to capture in a natural way the potentially clustered nature of the columns in many practical situations. In this model, the columns of the design matrix are drawn from a Gaussian mixture model. Instead of requiring incoherence for the design matrix $X$, we only require incoherence of the much smaller matrix of the mixture's centers. Our main result states that $Xβ$ can be estimated with the same precision as for incoherent designs except for a correction term depending on the maximal variance in the mixture model.

math.ST↗

arXiv2023

Convergence and scaling of Boolean-weight optimization for hardware reservoirs

Hardware implementation of neural network are an essential step to implement next generation efficient and powerful artificial intelligence solutions. Besides the realization of a parallel, efficient and scalable hardware architecture, the optimization of the system's extremely large parameter space with sampling-efficient approaches is essential. Here, we analytically derive the scaling laws for highly efficient Coordinate Descent applied to optimizing the readout layer of a random recurrently connection neural network, a reservoir. We demonstrate that the convergence is exponential and scales linear with the network's number of neurons. Our results perfectly reproduce the convergence and scaling of a large-scale photonic reservoir implemented in a proof-of-concept experiment. Our work therefore provides a solid foundation for such optimization in hardware networks, and identifies future directions that are promising for optimizing convergence speed during learning leveraging measures of a neural network's amplitude statistics and the weight update rule.

stat.ML↗

arXiv2021

An SDP dual relaxation for the Robust Shortest Path Problem with ellipsoidal uncertainty: Pierra's decomposition method and a new primal Frank-Wolfe-type heuristics for duality gap evaluation

This work addresses the Robust counterpart of the Shortest Path Problem (RSPP) with a correlated uncertainty set. Since this problem is hard, a heuristic approach, based on Frank-Wolfe's algorithm named Discrete Frank-Wolf (DFW), has recently been proposed. The aim of this paper is to propose a semi-definite programming relaxation for the RSPP that provides a lower bound to validate approaches such as DFW Algorithm. The relaxed problem results from a bidualization that is done {through} a reformulation of the RSPP into a quadratic problem. Then the relaxed problem is solved using a sparse version of Pierra's decomposition in a product space method. This validation method is suitable for large size problems. The numerical experiments show that the gap between the solutions obtained with the relaxed and the heuristic approaches is relatively small.

math.OC↗

arXiv2021

Boolean learning under noise-perturbations in hardware neural networks

A high efficiency hardware integration of neural networks benefits from realizing nonlinearity, network connectivity and learning fully in a physical substrate. Multiple systems have recently implemented some or all of these operations, yet the focus was placed on addressing technological challenges. Fundamental questions regarding learning in hardware neural networks remain largely unexplored. Noise in particular is unavoidable in such architectures, and here we investigate its interaction with a learning algorithm using an opto-electronic recurrent neural network. We find that noise strongly modifies the system's path during convergence, and surprisingly fully decorrelates the final readout weight matrices. This highlights the importance of understanding architecture, noise and learning algorithm as interacting players, and therefore identifies the need for mathematical tools for noisy, analogue system optimization.

cs.NE↗

arXiv2020

Revisiting clustering as matrix factorisation on the Stiefel manifold

This paper studies clustering for possibly high dimensional data (e.g. images, time series, gene expression data, and many other settings), and rephrase it as low rank matrix estimation in the PAC-Bayesian framework. Our approach leverages the well known Burer-Monteiro factorisation strategy from large scale optimisation, in the context of low rank estimation. Moreover, our Burer-Monteiro factors are shown to lie on a Stiefel manifold. We propose a new generalized Bayesian estimator for this problem and prove novel prediction bounds for clustering. We also devise a componentwise Langevin sampler on the Stiefel manifold to compute this estimator.

cs.LG↗

arXiv2020

Learning with Semi-Definite Programming: new statistical bounds based on fixed point analysis and excess risk curvature

Many statistical learning problems have recently been shown to be amenable to Semi-Definite Programming (SDP), with community detection and clustering in Gaussian mixture models as the most striking instances [javanmard et al., 2016]. Given the growing range of applications of SDP-based techniques to machine learning problems, and the rapid progress in the design of efficient algorithms for solving SDPs, an intriguing question is to understand how the recent advances from empirical process theory can be put to work in order to provide a precise statistical analysis of SDP estimators. In the present paper, we borrow cutting edge techniques and concepts from the learning theory literature, such as fixed point equations and excess risk curvature arguments, which yield general estimation and prediction results for a wide class of SDP estimators. From this perspective, we revisit some classical results in community detection from [guédon et al.,2016] and [chen et al., 2016], and we obtain statistical guarantees for SDP estimators used in signed clustering, group synchronization and MAXCUT.

math.ST↗

arXiv2020

Multi-kernel unmixing and super-resolution using the Modified Matrix Pencil method

Consider $L$ groups of point sources or spike trains, with the $l^{\text{th}}$ group represented by $x_l(t)$. For a function $g:\mathbb{R} \rightarrow \mathbb{R}$, let $g_l(t) = g(t/μ_l)$ denote a point spread function with scale $μ_l > 0$, and with $μ_1 < \cdots < μ_L$. With $y(t) = \sum_{l=1}^{L} (g_l \star x_l)(t)$, our goal is to recover the source parameters given samples of $y$, or given the Fourier samples of $y$. This problem is a generalization of the usual super-resolution setup wherein $L = 1$; we call this the multi-kernel unmixing super-resolution problem. Assuming access to Fourier samples of $y$, we derive an algorithm for this problem for estimating the source parameters of each group, along with precise non-asymptotic guarantees. Our approach involves estimating the group parameters sequentially in the order of increasing scale parameters, i.e., from group $1$ to $L$. In particular, the estimation process at stage $1 \leq l \leq L$ involves (i) carefully sampling the tail of the Fourier transform of $y$, (ii) a \emph{deflation} step wherein we subtract the contribution of the groups processed thus far from the obtained Fourier samples, and (iii) applying Moitra's modified Matrix Pencil method on a deconvolved version of the samples in (ii).

cs.IT↗

arXiv2018

Online shortest paths with confidence intervals for routing in a time varying random network

The increase in the world's population and rising standards of living is leading to an ever-increasing number of vehicles on the roads, and with it ever-increasing difficulties in traffic management. This traffic management in transport networks can be clearly optimized by using information and communication technologies referred as Intelligent Transport Systems (ITS). This management problem is usually reformulated as finding the shortest path in a time varying random graph. In this article, an online shortest path computation using stochastic gradient descent is proposed. This routing algorithm for ITS traffic management is based on the online Frank-Wolfe approach. Our improvement enables to find a confidence interval for the shortest path, by using the stochastic gradient algorithm for approximate Bayesian inference.

cs.DS↗

arXiv2017

Finding optimal finite biological sequences over finite alphabets: the OptiFin toolbox

In this paper, we present a toolbox for a specific optimization problem that frequently arises in bioinformatics or genomics. In this specific optimisation problem, the state space is a set of words of specified length over a finite alphabet. To each word is associated a score. The overall objective is to find the words which have the lowest possible score. This type of general optimization problem is encountered in e.g 3D conformation optimisation for protein structure prediction, or largest core genes subset discovery based on best supported phylogenetic tree for a set of species. In order to solve this problem, we propose a toolbox that can be easily launched using MPI and embeds 3 well-known metaheuristics. The toolbox is fully parametrized and well documented. It has been specifically designed to be easy modified and possibly improved by the user depending on the application, and does not require to be a computer scientist. We show that the toolbox performs very well on two difficult practical problems.

cs.AI↗