Related papers: Optimal quantization for nonuniform discrete distr…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems,…
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when…
Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…
The goal of optimal quantization is to find the best approximation of a probability distribution by a discrete measure with finite support. When dealing with empirical distributions, this boils down to finding the best summary of the data…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
This paper examines the problem of computing a canonical smallest covering region for an arbitrary discrete probability distribution. This optimisation problem is similar to the classical 0-1 knapsack problem, but it involves optimisation…
Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum…
Constructing a discretization of a given set is a major problem in various theoretical and applied disciplines. An offset discretization of a set $X$ is obtained by taking the integer points inside a closed neighborhood of $X$ of a certain…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
We establish for dual quantization the counterpart of Kieffer's uniqueness result for compactly supported one dimensional probability distributions having a $\log$-concave density (also called strongly unimodal): for such distributions,…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. Recent advances using the distributed gradient…
Quantizing images into discrete representations has been a fundamental problem in unified generative modeling. Predominant approaches learn the discrete representation either in a deterministic manner by selecting the best-matching token or…
Quantization is essential to simplify DNN inference in edge applications. Existing uniform and non-uniform quantization methods, however, exhibit an inherent conflict between the representing range and representing resolution, and thereby…
There is a fundamental limit to what is knowable about atomic and molecular scale systems. This fuzziness is not always due to the act of measurement. Other contributing factors include system parameter uncertainty, functional uncertainty…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…