Related papers: Optimal quantization for nonuniform discrete distr…
Methods for quantifying the similarity of datasets are relevant in applications where two or more datasets, or their underlying distributions, need to be compared, ranging from two- and k-sample testing to applications in machine learning…
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…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of…
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…
Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…
Sampling and quantization are crucial in digital signal processing, but quantization introduces errors, particularly due to distribution mismatch between input signals and quantizers. Existing methods to reduce this error require precise…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
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,…
We gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. We evaluate the maximum quantile over a class of distributions defined only by constraints…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of…
The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…