Related papers: Conditional automatic complexity and its metrics
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
Mutual information I in infinite sequences (and in their finite prefixes) is essential in theoretical analysis of many situations. Yet its right definition has been elusive for a long time. I address it by generalizing Kolmogorov Complexity…
The concepts of conditional mutual information (CMI) and normalized conditional mutual information (NCMI) are introduced to measure the concentration and separation performance of a classification deep neural network (DNN) in the output…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
Complexity measures are introduced, that quantify the change of the natural entropy fluctuations at different length scales in time-series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death…
Network maps of patent classes have been widely used to analyze the coherence and diversification of technology or knowledge positions of inventors, firms, industries, regions, and so on. To create such networks, a measure is required to…
An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several artitions, starting with the given pattern matrix or dissimilarity,…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
Although the notion of task similarity is potentially interesting in a wide range of areas such as curriculum learning or automated planning, it has mostly been tied to transfer learning. Transfer is based on the idea of reusing the…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
Given a stochastic process $\{A_n, n \geq 1\}$ taking values in natural numbers, the random continued fractions is defined as $[A_1, A_2, \cdots, A_n, \cdots]$ analogue to the continued fraction expansion of real numbers. Assume that…
Defining similarity measures is a requirement for some machine learning methods. One such method is case-based reasoning (CBR) where the similarity measure is used to retrieve the stored case or set of cases most similar to the query case.…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…
The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…