Related papers: An information theory for preferences
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A…
Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficiency, the former model being preferable. The implications of this fact are discussed,…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
The method of optimizing entropy is used to (i) conduct Asymptotic Hypothesis Testing and (ii) determine the particle distribution for which Entropy is maximized. This paper focuses on two related applications of Information Theory:…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
Expected utility maximization problems in mathematical finance lead to a generalization of the classical definition of entropy. It is demonstrated that a necessary and sufficient condition for the second law of thermodynamics to operate is…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
In random expected utility (Gul and Pesendorfer, 2006), the distribution of preferences is uniquely recoverable from random choice. This paper shows through two examples that such uniqueness fails in general if risk preferences are random…
Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between…
This paper proposes a systematic framework to design a classification model that yields a classifier which optimizes a utility function based on prior knowledge. Specifically, as the data size grows, we prove that the produced classifier…
The classical Density Functional Theory (DFT) is introduced as an application of entropic inference for inhomogeneous fluids at thermal equilibrium. It is shown that entropic inference reproduces the variational principle of DFT when…
We ascertain the modularity-like objective function whose optimization is equivalent to the maximum likelihood in annotated networks. We demonstrate that the modularity-like objective function is a linear combination of modularity and…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…