Related papers: Quantization for a probability distribution genera…
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…
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…
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…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…
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…
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…
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…
This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
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…
In this article, we study the approximation of a probability measure $\mu$ on $\mathbb{R}^{d}$ by its empirical measure $\hat{\mu}_{N}$ interpreted as a random quantization. As error criterion we consider an averaged $p$-th moment…
Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
In this paper, we have considered a uniform probability distribution supported by a stretched Sierpi\'nski triangle. For this probability measure, the optimal sets of $n$-means and the $n$th quantization errors are determined for all $n\geq…
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…
We investigate quantization coefficients for self-similar probability measures \mu on limit sets which are generated by systems S of infinitely many contractive similarities and by probabilistic vectors. The theory of quantization…
In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…
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…
In this paper, for a given family of constraints and the classical Cantor distribution we determine the constrained optimal sets of $n$-points, $n$th constrained quantization errors for all positive integers $n$. We also calculate the…