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We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many…
This paper addresses the problem of matching $N$ weighted graphs referring to an identical object or category. More specifically, matching the common node correspondences among graphs. This multi-graph matching problem involves two…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
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…
The primary goal of a recommender system is often known as "helping users find relevant items", and a lot of recommendation algorithms are proposed accordingly. However, these accuracy-oriented methods usually suffer the problem of…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…
Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing…
We introduce a novel class of factor analysis methodologies for the joint analysis of multiple studies. The goal is to separately identify and estimate 1) common factors shared across multiple studies, and 2) study-specific factors. We…
Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet…
We propose a generic variance-reduced algorithm, which we call MUltiple RANdomized Algorithm (MURANA), for minimizing a sum of several smooth functions plus a regularizer, in a sequential or distributed manner. Our method is formulated with…
Data integration has become increasingly popular owing to the availability of multiple data sources. This study considered quantile regression estimation when a key covariate had multiple proxies across several datasets. In a unified…
Context: The importance of the feature modeling for the software product lines considering the modeling and management of the variability. Objective: Define a protocol to conduct a systematic mapping study to summarize and synthesize the…
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…
In the literature, there are a few researches to design some parameters in the Proximal Point Algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it more flexible and…
Multiple imputation is a straightforward method for handling missing data in a principled fashion. This paper presents an overview of multiple imputation, including important theoretical results and their practical implications for…
Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…