Related papers: Optimal Quantization For Mixed Distributions
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…
Finite precision approximations of discrete probability distributions are considered, applicable for distribution synthesis, e.g., probabilistic shaping. Two algorithms are presented that find the optimal $M$-type approximation $Q$ of a…
Though mostly used as a clustering algorithm, k-means are originally designed as a quantization algorithm. Namely, it aims at providing a compression of a probability distribution with k points. Building upon [21, 33], we try to investigate…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - density quantization - is introduced which…
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…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
We approximate the uniform measure on an equilateral triangle by a measure supported on $n$ points. We find the optimal sets of points ($n$-means) and corresponding approximation (quantization) error for $n\leq4$, give numerical…
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…
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces $\mathbb{R}^k$ by introducing and analyzing the notions of the $n$th constrained quantization error, constrained…
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…
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
A method to compute the optimal success probability of discrimination of N arbitrary quantum states is presented, based on the decomposition of any N-outcome measurement into sequences of nested two-outcome ones. In this way the…
In this paper, we have considered a uniform distribution on a regular polygon with $k$-sides for some $k\geq 3$ and the set of all its $k$ vertices as a conditional set. For the uniform distribution under the conditional set first, for all…
Distributed optimization finds many applications in machine learning, signal processing, and control systems. In these real-world applications, the constraints of communication networks, particularly limited bandwidth, necessitate…
Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility…
We study the problem of distributed mean estimation and optimization under communication constraints. We propose a correlated quantization protocol whose leading term in the error guarantee depends on the mean deviation of data points…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…
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…