机器学习

The nonconvex formulation of the matrix completion problem has received significant attention in recent years due to its affordable complexity compared to the convex formulation. Gradient Descent (GD) is a simple yet efficient baseline…

Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such…

In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear…

Stability for dynamic network embeddings ensures that nodes behaving the same at different times receive the same embedding, allowing comparison of nodes in the network across time. We present attributed unfolded adjacency spectral…

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in…

Adaptive Conformal Inference (ACI) provides finite-sample coverage guarantees, enhancing the prediction reliability under non-exchangeability. This study demonstrates that these desirable properties of ACI do not require the use of…

The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…

We propose a novel test for assessing partial effects in Frechet regression on Bures Wasserstein manifolds. Our approach employs a sample splitting strategy: the first subsample is used to fit the Frechet regression model, yielding…

Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Cancer is a genetic disorder whose clonal evolution can be monitored by tracking noisy genome-wide copy number variants. We introduce the Copy Number Stochastic Block Model (CN-SBM), a probabilistic framework that jointly clusters samples…

Detecting a minor average treatment effect is a major challenge in large-scale applications, where even minimal improvements can have a significant economic impact. Traditional methods, reliant on normal distribution-based or expanded…

Domain generalization (DG) aims to learn models that perform well on unseen target domains by training on multiple source domains. Sharpness-Aware Minimization (SAM), known for finding flat minima that improve generalization, has therefore…

We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging…

Existing contextual multi-armed bandit (MAB) algorithms fail to effectively capture both long-term trends and local patterns across all arms, leading to suboptimal performance in environments with rapidly changing reward structures. They…

We derive a fundamental trade-off between standard and adversarial risk in a rather general situation that formalizes the following simple intuition: "If no (nearly) optimal predictor is smooth, adversarial robustness comes at the cost of…

Motivated by the concept of satisficing in decision-making, we consider the problem of satisficing regret minimization in bandit optimization. In this setting, the learner aims at selecting satisficing arms (arms with mean reward exceeding…

Text watermarks in large language models (LLMs) are an increasingly important tool for detecting synthetic text and distinguishing human-written content from LLM-generated text. While most existing studies focus on determining whether…

Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions. Many biological processes unfold along continuous trajectories, yet it remains challenging to extract smooth, low-dimensional…