相关论文: Random Worlds and Maximum Entropy

The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…

Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…

What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore…

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference…

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

We study approximation in the unit interval by rational numbers whose numerators are selected randomly with certain probabilities. Previous work showed that an analogue of Khintchine's Theorem holds in a similar random model and raised the…

We give a characterization of Maximum Entropy/Minimum Relative Entropy inference by providing two `strong entropy concentration' theorems. These theorems unify and generalize Jaynes' `concentration phenomenon' and Van Campenhout and Cover's…

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…

Social dilemmas have been regarded as the essence of evolution game theory, in which the prisoner's dilemma game is the most famous metaphor for the problem of cooperation. Recent findings revealed people's behavior violated the Sure Thing…

Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured,…

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive…

For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the…

We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…

Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…

In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…

I show that the maximum entropy principle can be replaced by a more natural assumption, that there exists a phenomenological function of entropy consistent with the microscopic model. The requirement of existence provides then a unique…

We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method. In contrast to BC, which uses…

Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…

The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…