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Algorithmic Probability

Author : Marcel F. Neuts

Publisher : CRC Press

Page : 488 pages

File Size : 13,63 MB

Release : 1995-07-01

Category : Mathematics

ISBN : 9780412996917

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Book Description

This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes. A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.



Algorithmic Probability

Author : Fouad Sabry

Publisher : One Billion Knowledgeable

Page : 129 pages

File Size : 31,85 MB

Release : 2023-06-28

Category : Computers

ISBN :

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Book Description

What Is Algorithmic Probability In the field of algorithmic information theory, algorithmic probability is a mathematical method that assigns a prior probability to a given observation. This method is sometimes referred to as Solomonoff probability. In the 1960s, Ray Solomonoff was the one who came up with the idea. It has applications in the theory of inductive reasoning as well as the analysis of algorithms. Solomonoff combines Bayes' rule and the technique in order to derive probabilities of prediction for an algorithm's future outputs. He does this within the context of his broad theory of inductive inference. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Algorithmic Probability Chapter 2: Kolmogorov Complexity Chapter 3: Gregory Chaitin Chapter 4: Ray Solomonoff Chapter 5: Solomonoff's Theory of Inductive Inference Chapter 6: Algorithmic Information Theory Chapter 7: Algorithmically Random Sequence Chapter 8: Minimum Description Length Chapter 9: Computational Learning Theory Chapter 10: Inductive Probability (II) Answering the public top questions about algorithmic probability. (III) Real world examples for the usage of algorithmic probability in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of algorithmic probability' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of algorithmic probability.



Universal Artificial Intelligence

Author : Marcus Hutter

Publisher : Springer Science & Business Media

Page : 294 pages

File Size : 13,1 MB

Release : 2005-12-29

Category : Computers

ISBN : 3540268774

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Book Description

Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.



Algorithmic Probability and Combinatorics

Author : Manuel Lladser

Publisher : American Mathematical Soc.

Page : 251 pages

File Size : 11,65 MB

Release : 2010-07-30

Category : Mathematics

ISBN : 082184783X

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Book Description

This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.



Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

Author : David L. Dowe

Publisher : Springer

Page : 457 pages

File Size : 44,71 MB

Release : 2013-10-22

Category : Computers

ISBN : 3642449581

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Book Description

Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff (1926-2009), honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines (UTMs) could be used for universal Bayesian prediction and artificial intelligence (machine learning). This work continues to increasingly influence and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of (general) intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy.



Information Theory and Statistical Learning

Author : Frank Emmert-Streib

Publisher : Springer Science & Business Media

Page : 443 pages

File Size : 18,98 MB

Release : 2009

Category : Computers

ISBN : 0387848150

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Book Description

This interdisciplinary text offers theoretical and practical results of information theoretic methods used in statistical learning. It presents a comprehensive overview of the many different methods that have been developed in numerous contexts.



Probability and Computing

Author : Michael Mitzenmacher

Publisher : Cambridge University Press

Page : 372 pages

File Size : 11,64 MB

Release : 2005-01-31

Category : Computers

ISBN : 9780521835404

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Book Description

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.



Algorithmic Information Dynamics

Author : Hector Zenil

Publisher : Cambridge University Press

Page : 346 pages

File Size : 44,27 MB

Release : 2023-05-25

Category : Science

ISBN : 1108659268

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Book Description

Biological systems are extensively studied as interactions forming complex networks. Reconstructing causal knowledge from, and principles of, these networks from noisy and incomplete data is a challenge in the field of systems biology. Based on an online course hosted by the Santa Fe Institute Complexity Explorer, this book introduces the field of Algorithmic Information Dynamics, a model-driven approach to the study and manipulation of dynamical systems . It draws tools from network and systems biology as well as information theory, complexity science and dynamical systems to study natural and artificial phenomena in software space. It consists of a theoretical and methodological framework to guide an exploration and generate computable candidate models able to explain complex phenomena in particular adaptable adaptive systems, making the book valuable for graduate students and researchers in a wide number of fields in science from physics to cell biology to cognitive sciences.



Algorithmic Learning in a Random World

Author : Vladimir Vovk

Publisher : Springer Science & Business Media

Page : 344 pages

File Size : 38,4 MB

Release : 2005-03-22

Category : Computers

ISBN : 9780387001524

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Book Description

Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.