Related papers: Extending the scope of the small-ball method
We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The goal is to embed a heavy-ball type of momentum into the Fast Gradient Method (FGM). For this purpose, we devise a generalization…
We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to…
We propose a transductive Laplacian-regularized inference for few-shot tasks. Given any feature embedding learned from the base classes, we minimize a quadratic binary-assignment function containing two terms: (1) a unary term assigning…
In this note, we provide upper bounds on the expectation of the supremum of empirical processes indexed by H\"older classes of any smoothness and for any distribution supported on a bounded set in $\mathbb R^d$. These results can be…
This note shows that some assumption on small balls probability, frequently used in the domain of functional statistics, implies that the considered functional space is of finite dimension. To complete this result an example of L2 process…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
In this short note we study the asymptotic behaviour of the minima over compact intervals of Gaussian processes, whose paths are not necessarily smooth. We show that, beyond the logarithmic large deviation Gaussian estimates, this problem…
In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…
The issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
This study aims at contributing to lower bounds for empirical compatibility constants or empirical restricted eigenvalues. This is of importance in compressed sensing and theory for $\ell_1$-regularized estimators. Let $X$ be an $n \times…
A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties…
A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the empirical copula. One popular way of approximating its sampling distribution consists of…
Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…