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The theory of constrained quantization has been recently introduced by Pandey and Roychowdhury. In this paper, they have further generalized their previous definition of constrained quantization and studied the constrained quantization for…

Dynamical Systems · Mathematics 2024-05-02 Megha Pandey , Mrinal K. Roychowdhury

Quantization of a probability measure means representing it with a finite set of Dirac masses that approximates the input distribution well enough (in some metric space of probability measures). Various methods exists to do so, but the…

Machine Learning · Statistics 2024-02-12 Gabriel Turinici

Quantized Neural Networks (QNNs), which use low bitwidth numbers for representing parameters and performing computations, have been proposed to reduce the computation complexity, storage size and memory usage. In QNNs, parameters and…

Computer Vision and Pattern Recognition · Computer Science 2017-06-23 Shuchang Zhou , Yuzhi Wang , He Wen , Qinyao He , Yuheng Zou

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

Mathematical Physics · Physics 2015-05-28 E. M. F. Curado , J. P. Gazeau , Ligia M. C. S. Rodrigues

This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…

Information Theory · Computer Science 2016-11-15 Naci Saldi , Tamás Linder , Serdar Yüksel

Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$,…

Quantum Physics · Physics 2018-10-25 Michał Horodecki , Jonathan Oppenheim , Carlo Sparaciari

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…

Other Statistics · Statistics 2018-03-05 Hien D. Nguyen , Geoffrey J. McLachlan

Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…

Machine Learning · Statistics 2025-09-09 Logan S. McCarty

Quantization is a widely used technique to compress and accelerate deep neural networks. However, conventional quantization methods use the same bit-width for all (or most of) the layers, which often suffer significant accuracy degradation…

Computer Vision and Pattern Recognition · Computer Science 2021-10-14 Weihan Chen , Peisong Wang , Jian Cheng

In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular $m$-sided polygons inscribed in a circle. The result shows that the quantization…

Dynamical Systems · Mathematics 2021-02-22 Joel Hansen , Itzamar Marquez , Mrinal K. Roychowdhury , Eduardo Torres

Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…

Information Theory · Computer Science 2022-02-08 Peter Harremoës

We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…

Computation and Language · Computer Science 2007-05-23 Lillian Lee

The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…

Statistical Mechanics · Physics 2020-10-28 Qiuping A. Wang

We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…

Optimization and Control · Mathematics 2025-10-02 Markus Hegland , C. Yalçın Kaya

We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…

Quantum Physics · Physics 2015-06-11 Ulrike Herzog

In this paper, we study unconstrained distributed optimization strongly convex problems, in which the exchange of information in the network is captured by a directed graph topology over digital channels that have limited capacity (and…

Systems and Control · Electrical Eng. & Systems 2023-09-12 Apostolos I. Rikos , Wei Jiang , Themistoklis Charalambous , Karl H. Johansson

In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…

Data Structures and Algorithms · Computer Science 2013-05-02 Mohit Singh , Nisheeth K. Vishnoi

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…

Artificial Intelligence · Computer Science 2016-08-16 David Bellot , Pierre Bessiere

Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply…

Quantum Physics · Physics 2017-01-04 Alfredo Luis , Gonzalo Donoso

This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the…

Machine Learning · Statistics 2026-01-26 Kai Ming Ting , Ye Zhu , Hang Zhang , Tianrun Liang