Related papers: Universal Compression of Envelope Classes: Tight C…

Learning-based lossless image compression employs pixel-based or subimage-based auto-regression for probability estimation, which achieves desirable performances. However, the existing works only consider context dependencies in one…

We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild…

It is known that, by accounting for the multiboson interferences up to a finite order, the output distribution of noisy Boson Sampling, with distinguishability of bosons serving as noise, can be approximately sampled from in a time…

Quantum advantage, benchmarking the computational power of quantum machines outperforming all classical computers in a specific task, represents a crucial milestone in developing quantum computers and has been driving different physical…

In this paper, we propose improved estimation method for logistic regression based on subsamples taken according the optimal subsampling probabilities developed in Wang et al. 2018 Both asymptotic results and numerical results show that the…

We study different notions of pointwise redundancy in variable-length lossy source coding. We present a construction of one-shot variable-length lossy source coding schemes using the Poisson functional representation, and give bounds on its…

BosonSampling and Random Circuit Sampling are important both as a theoretical tool for separating quantum and classical computation, and as an experimental means of demonstrating quantum speedups. Prior works have shown that average-case…

In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…

Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…

In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…

The traditional methods for data compression are typically based on the symbol-level statistics, with the information source modeled as a long sequence of i.i.d. random variables or a stochastic process, thus establishing the fundamental…

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 describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…

This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…

We present a one-shot method for compressing large labeled graphs called Random Edge Coding. When paired with a parameter-free model based on P\'olya's Urn, the worst-case computational and memory complexities scale quasi-linearly and…