15 accepted papers
Concept Activation Vectors (CAVs) are a tool from explainable AI, offering a promising approach for understanding how human-understandable concepts are encoded in a model's latent spaces. They are computed from hidden-layer activations of inputs belonging either to a concept class or to non-concept…
We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min–Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min–max characterization of key statistics, enabling approximation of th…
Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum a posteriori (MAP) regression with Gaussian priors centered…
While foundation models have revolutionized various domains, their application to time series classification remains rather under-explored, with existing literature predominantly focused on forecasting. To bridge this gap, we introduce \textbf{Mantis}, a transformer-based foundation model pre-traine…
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enab…
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks.…
Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter…
Catastrophic forgetting and the stability-plasticity dilemma are two major obstacles to continual learning. In this paper we first propose a theoretical analysis of a SPCA-based continual learning algorithm using high dimensional statistics. Second, we design OSCL (Optimized Spca-based Continual Le…
The article proposes and theoretically analyses a *computationally efficient* multi-task learning (MTL) extension of popular principal component analysis (PCA)-based supervised learning schemes. The analysis reveals that (i) by default, learning may dramatically fail by suffering from *negative tran…
We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density separation assumption is implemented via quadratic margin maxi…
This paper proposes a theoretical analysis of a Lasso-based classification algorithm. Leveraging on a realistic regime where the dimension of the data $p$ and their number $n$ are of the same order of magnitude, the theoretical classification error is derived as a function of the data statistics. As…
This article provides theoretical insights into the inner workings of multi-task and transfer learning methods, by studying the tractable least-square support vector machine multi-task learning (LS-SVM MTL) method, in the limit of large ($p$) and numerous ($n$) data. By a random matrix analysis appl…
Inspired by human learning, which transfers knowledge from learned tasks to solve new tasks, multitask learning aims at simultaneously solving multiple tasks by a smart exploitation of their similarities. How to relate the tasks so to optimize their performances is however a largely open problem.Bas…
A wide range of machine learning and signal processing applications involve data discrimination through covariance matrices. A broad family of metrics, among which the Frobe-nius, Fisher, Bhattacharyya distances, as well as the Kullback-Leibler or Rényi divergences, are regularly exploited. Not bein…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and t…