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We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…

Statistics Theory · Mathematics 2007-06-13 Anatoli Juditsky , Alexander Nazin , Alexandre Tsybakov , Nicolas Vayatis

We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via…

Probability · Mathematics 2024-10-15 Cathrine Aeckerle-Willems , Claudia Strauch , Lukas Trottner

In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead to generalized sequences of weights which depend on an…

Probability · Mathematics 2019-06-21 Marie Ernst , Gesine Reinert , Yvik Swan

Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss…

Statistics Theory · Mathematics 2021-10-28 A. G. Nogales

We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as…

Machine Learning · Computer Science 2018-11-21 Loucas Pillaud-Vivien , Alessandro Rudi , Francis Bach

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the…

Machine Learning · Computer Science 2021-12-13 Matias Vera , Leonardo Rey Vega , Pablo Piantanida

Adversarial robustness of machine learning models is critical to ensuring reliable performance under data perturbations. Recent progress has been on point estimators, and this paper considers distributional predictors. First, using the link…

Machine Learning · Computer Science 2025-02-21 Mahalakshmi Sabanayagam , Russell Tsuchida , Cheng Soon Ong , Debarghya Ghoshdastidar

We introduce a new recursive aggregation procedure called Bernstein Online Aggregation (BOA). The exponential weights include an accuracy term and a second order term that is a proxy of the quadratic variation as in Hazan and Kale (2010).…

Machine Learning · Statistics 2016-09-14 Olivier Wintenberger

Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…

Machine Learning · Computer Science 2025-07-14 Masahiro Fujisawa , Futoshi Futami

Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…

Machine Learning · Computer Science 2025-03-12 Siyao Wang , Miles E. Lopes

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense…

This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method…

Statistics Theory · Mathematics 2007-12-18 Denis Belomestny , Vladimir Spokoiny

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…

Machine Learning · Statistics 2012-08-21 Karim Lounici , Massimiliano Pontil , Alexandre B. Tsybakov , Sara van de Geer

Probabilistic Coalition Structure Generation (PCSG) is NP-hard and can be recast as an $l_0$-type sparse recovery problem by representing coalition structures as sparse coefficient vectors over a coalition-incidence design. A natural…

Computer Science and Game Theory · Computer Science 2026-01-12 Angshul Majumdar

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

Statistics Theory · Mathematics 2014-01-23 Mélanie Blazère , Jean-Michel Loubes , Fabrice Gamboa

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Optimization and Control · Mathematics 2022-11-23 Quentin Jacquet , Riadh Zorgati

While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on…

Machine Learning · Computer Science 2022-11-28 Sanae Lotfi , Marc Finzi , Sanyam Kapoor , Andres Potapczynski , Micah Goldblum , Andrew Gordon Wilson

Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance \cite{biau:16}), classification rules (see…

Statistics Theory · Mathematics 2018-12-24 Alejandro Cholaquidis , Ricardo Fraiman , Badih Ghattas , Juan Kalemkerian

We develop a set of scalable Bayesian inference procedures for a general class of nonparametric regression models. Specifically, nonparametric Bayesian inferences are separately performed on each subset randomly split from a massive…

Statistics Theory · Mathematics 2019-09-05 Zuofeng Shang , Botao Hao , Guang Cheng

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

Methodology · Statistics 2021-08-26 Terrance D. Savitsky , Matthew R. Williams