Related papers: Optimal quantization for nonuniform discrete distr…
Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the…
In this paper, we first consider a family of constraints given by straight lines. For a uniform probability distribution, we determine the constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors…
In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$. We give an exact formula…
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…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely,…
This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
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…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given $k\geq 2$, let $\{S_j : 1\leq…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
We consider the problem of distributed feature quantization, where the goal is to enable a pretrained classifier at a central node to carry out its classification on features that are gathered from distributed nodes through communication…
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…
There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…
Quantization is essential for reducing the computational cost and memory usage of deep neural networks, enabling efficient inference on low-precision hardware. Despite the growing adoption of uniform and floating-point quantization schemes,…
Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…