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Learning-based and data-driven techniques have recently become a subject of primary interest in the field of reconstruction and regularization of inverse problems. Besides the development of novel methods, yielding excellent results in…
It is impossible today to pretend that the practice of machine learning is always compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how…
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…
{\em Multi-objective samples} are powerful and versatile summaries of large data sets. For a set of keys $x\in X$ and associated values $f_x \geq 0$, a weighted sample taken with respect to $f$ allows us to approximate {\em segment-sum…
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional data observed under a fixed synchronous design over H\"older…
We initiate a study of supervised learning from many independent sequences ("trajectories") of non-independent covariates, reflecting tasks in sequence modeling, control, and reinforcement learning. Conceptually, our multi-trajectory setup…
Given a sample of size $N$, it is often useful to select a subsample of smaller size $n<N$ to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the…
A crucial aspect in reliable machine learning is to design a deployable system in generalizing new related but unobserved environments. Domain generalization aims to alleviate such a prediction gap between the observed and unseen…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Data selection is essential for training deep learning models. An effective data sampler assigns proper sampling probability for training data and helps the model converge to a good local minimum with high performance. Previous studies in…
There is a growing interest in societal concerns in machine learning systems, especially in fairness. Multicalibration gives a comprehensive methodology to address group fairness. In this work, we address the multicalibration error and…
This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the…
Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
Many signal and image processing applications have benefited remarkably from the fact that the underlying signals reside in a low dimensional subspace. One of the main models for such a low dimensionality is the sparsity one. Within this…
Neural scaling laws establish a predictable relationship between model performance and data or compute, offering crucial guidance for resource allocation in new domains and tasks. Yet such laws are most needed precisely where they are…
The problem of statistical learning is to construct a predictor of a random variable $Y$ as a function of a related random variable $X$ on the basis of an i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable predictors…
Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…