Linus Bleistein

Linus Bleistein, Adeline Fermanian, Anne-Sophie Jannot et al.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Linus Bleistein, Mathieu Dagréou, Francisco Andrade et al.

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose \texttt{FairSinkhorn}, a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalised OT problem, for which we derive novel finite-sample complexity guarantees. This result is of independent interest as it can be generalized to arbitrary convex penalties. Our second strategy leverages bilevel optimization to learn a ground cost that induces a fair OT solution, and we establish a bound guaranteeing that the learned cost yields fair matchings on unseen data. Finally, we present empirical results that illustrate the trade-offs between fairness and performance.

Tudor Cebere, Mathieu Even, Linus Bleistein et al.

Privacy auditing provides empirical lower bounds on the differential privacy parameters of learning algorithms. Existing methods, however, require interventional access to the training pipeline, either to retrain multiple times or to randomize data inclusion. This is often infeasible for large deployed systems such as foundation models. We introduce Zero-Run privacy auditing, a post-hoc framework for auditing models using two fixed datasets: examples known to be training-set members and examples known to be non-members. In this observational regime, membership is no longer randomized; instead, member and non-member data often differ in distribution, so membership inference scores may reflect a distribution shift rather than algorithmic leakage. Drawing on ideas from causal inference, we formalize this confounding effect and propose two complementary corrections that yield valid privacy audits. Our first approach models the combined effect of distribution shift and algorithmic leakage as an adaptive composition, producing conservative global corrections. Our second approach conditions on observed data and adjusts pointwise membership guesses, yielding sharper instance-dependent bounds. Experiments on synthetic data and large-scale models show that Zero-Run auditing enables practical privacy evaluation when retraining or controlled data insertion is infeasible.

Linus Bleistein, Van-Tuan Nguyen, Adeline Fermanian et al.

We consider the task of learning individual-specific intensities of counting processes from a set of static variables and irregularly sampled time series. We introduce a novel modelization approach in which the intensity is the solution to a controlled differential equation. We first design a neural estimator by building on neural controlled differential equations. In a second time, we show that our model can be linearized in the signature space under sufficient regularity conditions, yielding a signature-based estimator which we call CoxSig. We provide theoretical learning guarantees for both estimators, before showcasing the performance of our models on a vast array of simulated and real-world datasets from finance, predictive maintenance and food supply chain management.

Linus Bleistein, Aurélien Bellet, Julie Josse

We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous missingness probabilities across features and across the two distributions. As a first contribution, we show that the Wasserstein distance between empirical Gaussian distributions and linear Monge maps between arbitrary distributions can be debiased without significantly affecting the sample complexity. Secondly, we show that entropic regularized optimal transport can be estimated efficiently and consistently using iterative singular value thresholding (ISVT). We propose a validation set-free hyperparameter selection strategy for ISVT that leverages our estimator of the Bures-Wasserstein distance, which could be of independent interest in general matrix completion problems. Finally, we validate our findings on a wide range of numerical applications.

Barbara Bodinier, Gaetan Dissez, Lucile Ter-Minassian et al.

High-throughput preclinical perturbation screens, where the effects of genetic, chemical, or environmental perturbations are systematically tested on disease models, hold significant promise for machine learning-enhanced drug discovery due to their scale and causal nature. Predictive models trained on such datasets can be used to (i) infer perturbation response for previously untested disease models, and (ii) characterise the biological context that affects perturbation response. Existing predictive models suffer from limited reproducibility, generalisability and interpretability. To address these issues, we introduce a framework of Layered Ensemble of Autoencoders and Predictors (LEAP), a general and flexible ensemble strategy to aggregate predictions from multiple regressors trained using diverse gene expression representation models. LEAP consistently improves prediction performances in unscreened cell lines across modelling strategies. In particular, LEAP applied to perturbation-specific LASSO regressors (PS-LASSO) provides a favorable balance between near state-of-the-art performance and low computation time. We also propose an interpretability approach combining model distillation and stability selection to identify important biological pathways for perturbation response prediction in LEAP. Our models have the potential to accelerate the drug discovery pipeline by guiding the prioritisation of preclinical experiments and providing insights into the biological mechanisms involved in perturbation response. The code and datasets used in this work are publicly available.

Mathieu Even, Clément Berenfeld, Linus Bleistein et al.

Membership Inference Attacks (MIAs) are widely used to quantify training data memorization and assess privacy risks. Standard evaluation requires repeated retraining, which is computationally costly for large models. One-run methods (single training with randomized data inclusion) and zero-run methods (post hoc evaluation) are often used instead, though their statistical validity remains unclear. To address this gap, we frame MIA evaluation as a causal inference problem, defining memorization as the causal effect of including a data point in the training set. This novel formulation reveals and formalizes key sources of bias in existing protocols: one-run methods suffer from interference between jointly included points, while zero-run evaluations popular for LLMs are confounded by non-random membership assignment. We derive causal analogues of standard MIA metrics and propose practical estimators for multi-run, one-run, and zero-run regimes with non-asymptotic consistency guarantees. Experiments on real-world data show that our approach enables reliable memorization measurement even when retraining is impractical and under distribution shift, providing a principled foundation for privacy evaluation in modern AI systems.

Linus Bleistein, Agathe Guilloux

Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it remains unclear in particular how the irregularity of the time series affects their predictions. By merging the rich theory of controlled differential equations (CDE) and Lipschitz-based measures of the complexity of deep neural nets, we take a first step towards the theoretical understanding of NCDE. Our first result is a generalization bound for this class of predictors that depends on the regularity of the time series data. In a second time, we leverage the continuity of the flow of CDEs to provide a detailed analysis of both the sampling-induced bias and the approximation bias. Regarding this last result, we show how classical approximation results on neural nets may transfer to NCDEs. Our theoretical results are validated through a series of experiments.