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A Philosophical Treatise of Universal Induction
 Entropy 2011
"... Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more ..."
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Cited by 11 (7 self)
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Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches.
One decade of universal artificial intelligence
 In Theoretical Foundations of Artificial General Intelligence
, 2012
"... The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers ..."
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Cited by 2 (2 self)
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The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book (Hutter, 2005), an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. While nowadays most AI researchers avoid discussing intelligence, the awardwinning PhD thesis (Legg, 2008) provided the philosophical embedding and investigated the UAIbased universal measure of rational intelligence, which is formal, objective and nonanthropocentric. Recently, effective approximations of AIXI have been derived and experimentally investigated in JAIR paper (Veness et al. 2011). This practical breakthrough has resulted in some impressive applications, finally muting earlier critique that UAI is only a theory. For the first time, without providing any domain knowledge, the same
Algorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence
, 2010
"... This article is a personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and philosophy. Intuitively, randomness is a lack of order or predictabil ..."
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This article is a personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and philosophy. Intuitively, randomness is a lack of order or predictability. If randomness is the opposite of determinism, then algorithmic randomness is the opposite of computability. Besides many other things, these concepts have been used to quantify Ockham’s razor, solve the induction problem, and define intelligence. Contents 1 Why were you initially drawn to the study of computation
Universal Prediction of Selected Bits
, 2011
"... Many learning tasks can be viewed as sequence prediction problems. For example, online classification can be converted to sequence prediction with the sequence being pairs of input/target data and where the goal is to correctly predict the target data given input data and previous input/target pairs ..."
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Many learning tasks can be viewed as sequence prediction problems. For example, online classification can be converted to sequence prediction with the sequence being pairs of input/target data and where the goal is to correctly predict the target data given input data and previous input/target pairs. Solomonoff induction is known to solve the general sequence prediction problem, but only if the entire sequence is sampled from a computable distribution. In the case of classification and discriminative learning though, only the targets need be structured (given the inputs). We show that the normalised version of Solomonoff induction can still be used in this case, and more generally that it can detect any recursive subpattern (regularity) within an otherwise completely unstructured sequence. It is also shown that the unnormalised
Chapter 5 One Decade of Universal Artificial Intelligence
"... The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers ..."
Abstract
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The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book [24] an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. While nowadays most AI researchers avoid discussing intelligence, the awardwinning PhD thesis [38] provided the philosophical embedding and investigated the UAIbased universal measure of rational intelligence, which is formal, objective and nonanthropocentric. Recently, effective approximations of AIXI have been derived and experimentally investigated in JAIR paper [79] This practical breakthrough has resulted in some impressive applications, finally muting earlier critique that UAI is only a theory. For the first time, without providing any domain knowledge, the same agent is able to selfadapt to a diverse range of interactive environments. For instance, AIXI is able to learn from scratch to play TicTacToe, Pacman, Kuhn Poker, and other games by trial and error, without even providing the rules of the games. These achievements give new hope that the grand goal of Artificial General Intelligence is not elusive. This chapter provides an informal overview of UAI in context. It attempts to gently introduce a very theoretical, formal, and mathematical subject, and discusses philosophical and technical ingredients, traits of intelligence, some social questions, and the past and future of UAI. “The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science.”