Related papers: On Information (pseudo) Metric
Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
There are various mathematical models proposed in the recent literature for estimating the h-index through bibliometric measures, such as number of articles (P) and citations received (C). These models have been previously empirically…
We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however…
We derive bounds for the Orlicz norm of the deviation of a random variable defined on $\mathbb{R}^n$ from its Gaussian mean value. The random variables are assumed to be smooth and the bound itself depends on the Orlicz norm of the…
In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…
The isomorphism problem in the ergodic theory is revisited from the perspective of information spectrum approach, an approach that has been developed to investigate coding problems for non-ergodic random processes in information theory. It…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Techniques for decision making with knowledge of linear constraints on condition probabilities are examined. These constraints arise naturally in many situations: upper and lower condition probabilities are known; an ordering among the…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual…
Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is…
In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…
This is a short note for some basics of information geometry from thermodynamics and Callen's themostatistics.
Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be…
In a previous paper (C. Cafaro et al., 2012), we compared an uncorrelated 3D Gaussian statistical model to an uncorrelated 2D Gaussian statistical model obtained from the former model by introducing a constraint that resembles the quantum…