相关论文: Deterministic Extractors for Additive Sources

The notion of semi-random sources, also known as Santha-Vazirani (SV) sources, stands for a sequence of n bits, where the dependence of the i'th bit on the previous i-1 bits is limited for every $i\in[n]$. If the dependence of the i'th bit…

We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…

Generative models, particularly Generative Adversarial Networks (GANs), often suffer from a lack of output diversity, frequently generating similar samples rather than a wide range of variations. This paper introduces a novel generalization…

We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…

Following a growing number of studies that, over the past 15 years, have established entropy inequalities via ideas and tools from additive combinatorics, in this work we obtain a number of new bounds for the differential entropy of sums,…

We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by…

We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…

Sampling from flat modes in discrete spaces is a crucial yet underexplored problem. Flat modes represent robust solutions and have broad applications in combinatorial optimization and discrete generative modeling. However, existing sampling…

The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…

Various combinatorial classes such as outerplanar graphs and maps, series-parallel graphs, substitution-closed classes of permutations and many more allow bijective encodings by so-called enriched trees, which are rooted trees with…

In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which…

Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…

We study the common ancestor type distribution in a $2$-type Moran model with population size $N$, mutation and selection, and in the deterministic limit regime arising in the former when $N$ tends to infinity, without any rescaling of…

We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…

In light of the recent advancements in machine learning, we propose a novel approach to neutron source distribution estimation through the utilisation of probabilistic generative models. The estimation is based on a Monte Carlo particle…

We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…

If part of a population is hidden but two or more sources are available that each cover parts of this population, dual- or multiple-system(s) estimation can be applied to estimate this population. For this it is common to use the log-linear…