Related papers: Learning the Hypotheses Space from data Part II: C…

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…

We introduce a number of tools for finding and studying \emph{hierarchically hyperbolic spaces (HHS)}, a rich class of spaces including mapping class groups of surfaces, Teichm\"{u}ller space with either the Teichm\"{u}ller or…

In high-dimensional prediction settings, it remains challenging to reliably estimate the test performance. To address this challenge, a novel performance estimation framework is presented. This framework, called Learn2Evaluate, is based on…

Given the ever increasing bandwidth of the visual information available to many intelligent systems, it is becoming essential to endow them with a sense of what is worthwhile their attention and what can be safely disregarded. This article…

Standard practice in Hidden Markov Model (HMM) selection favors the candidate with the highest full-sequence likelihood, although this is equivalent to making a decision based on a single realization. We introduce a \emph{fragment-based}…

Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical…

We propose using neural networks to detect data departures from a given reference model, with no prior bias on the nature of the new physics responsible for the discrepancy. The virtues of neural networks as unbiased function approximants…

We study non-convex empirical risk minimization for learning halfspaces and neural networks. For loss functions that are $L$-Lipschitz continuous, we present algorithms to learn halfspaces and multi-layer neural networks that achieve…

This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to…

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…

Data selection plays a crucial role in data-driven decision-making, including in large language models (LLMs), and is typically task-dependent. Properties such as data quality and diversity have been extensively studied and are known to…

High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…

Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we…

We introduce a novel ensemble approach for feature selection based on hierarchical stacking for non-stationarity and/or a limited number of samples with a large number of features. Our approach exploits the co-dependency between features…

Latent space models assume that network ties are more likely between nodes that are closer together in an underlying latent space. Euclidean space is a popular choice for the underlying geometry, but hyperbolic geometry can mimic more…

Machine learning (ML) has become a commodity in our every-day lives. We routinely ask ML empowered smartphones to suggest lovely food places or to guide us through a strange place. ML methods have also become standard tools in many fields…

We investigate sample-based learning of conditional distributions on multi-dimensional unit boxes, allowing for different dimensions of the feature and target spaces. Our approach involves clustering data near varying query points in the…

The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…