Related papers: A local lemma via entropy compression

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…

The analysis of decision making under uncertainty is closely related to the analysis of probabilistic inference. Indeed, much of the research into efficient methods for probabilistic inference in expert systems has been motivated by the…

Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient…

Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty…

We prove the convergence of solutions of nonlocal conservation laws to their local entropic counterpart for a fundamentally extended class of nonlocal kernels when these kernels approach a Dirac distribution. The nonlocal kernels are…

The hypergraph container lemma is a powerful tool in probabilistic combinatorics that has found many applications since it was first proved a decade ago. Roughly speaking, it asserts that the family of independent sets of every uniform…

We make use of an entropic property to establish a convergence theorem (Main Theorem), which reveals that the conditional entropy measures the asymptotic Gaussianity. As an application, we establish the {\it entropic conditional central…

Comparisons are made for the amount of agreement of the composite likelihood information criteria and their full likelihood counterparts when making decisions among the fits of different models, and some properties of penalty term for…

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…

In this paper, we propose a dictionary screening method for embedding compression in text classification tasks. The key purpose of this method is to evaluate the importance of each keyword in the dictionary. To this end, we first train a…

There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…

Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and…

We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…

The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the…

This study proposed an exhaustive stable/reproducible rule-mining algorithm combined to a classifier to generate both accurate and interpretable models. Our method first extracts rules (i.e., a conjunction of conditions about the values of…

Our previous paper applied a lopsided version of the Lov\'asz Local Lemma that allows negative dependency graphs to the space of random injections from an $m$-element set to an $n$-element set. Equivalently, the same story can be told about…

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…

We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…

We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of…