相关论文: Random Worlds and Maximum Entropy
A definable set $X$ in the first-order language of rings defines a family of random vectors: for each finite field $\mathbb{F}_q$, let the distribution be supported and uniform on the $\mathbb{F}_q$-rational points of $X$. We employ results…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
How to generate provably true randomness with minimal assumptions? This question is important not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible…
The question of what is the total entropy of the universe, how it compares to the maximal entropy of de Sitter space, and how it is distributed across the universe's components, bears considerable importance for a number of reasons. Here,…
Three steps in the development of the maximum likelihood (ML) method are presented. At first, the application of the ML method and Fisher information notion in the model selection analysis is described (Chapter 1). The fundamentals of…
A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
It is often thought that the existence of other worlds cannot be scientifically verified and therefore should be treated as philosophical speculation. In this article, I describe several methods for determining if other worlds exist, even…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback-Leibler distance or relative entropy as a selection criterion. Yet that will raise…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is accomplished by including the…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional…
The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…