Related papers: Redundancies : An Omission in Probability Theory ?
Research on summarization has mainly been driven by empirical approaches, crafting systems to perform well on standard datasets with the notion of information Importance remaining latent. We argue that establishing theoretical models of…
We provide another proof to the EL Theorem. We show the tradeoff between compressibility of codebooks and their communication capacity. A resource bounded version of the EL Theorem is proven. This is used to prove three instances of…
The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own case - similarity shapes - the shape spaces are…
We perform the analysis of probabilistic assumptions of Bell's approach. We emphasize that J. Bell wrote about probability without to specify the concrete axiomatics of probability theory. The careful analysis demonstrated that…
The violation of Bell inequalities is often interpreted as showing that, if hidden variables exist, they must be contextual and non local. But they can also be explained questioning the probability space employed, or the validity of the…
The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d- dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities, is violated by quantum…
This paper contains an answer to the question of existence of regularities of the so called \textit{random in a broad sense} mass phenomena, asked by A. N. Kolmogorov in \cite{Kolmogorov}. It turns out that some family of finitely-additive…
This paper argues for the status of formal probability theory as a mathematical, rather than a scientific, theory. David Freedman and Philip Stark's concept of model based probabilities is examined and is used as a bridge between the formal…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…
In this paper, the feasibility of using finite totally ordered probability models under Alelinnas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional probability. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a…
We construct universal prediction systems in the spirit of Popper's falsifiability and Kolmogorov complexity and randomness. These prediction systems do not depend on any statistical assumptions (but under the IID assumption they dominate,…
Although the likelihood function is normalizeable with respect to the data there is no guarantee that the same holds with respect to the model parameters. This may lead to singularities in the expectation value integral of these parameters,…
We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…