Complexity-based induction systems: Comparisons and convergence theorems

By Ray J. Solomonoff. 1978

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Citations in the corpus

Deep learning in neural networks: An overview (2014, neutral): “…of a solution candidate by the length of the shortest program that computes it (e.g., Blumer, Ehrenfeucht, Haussler, & Warmuth, 1987; Chaitin, 1966; Grünwald,Myung, & Pitt, 2005; Kolmogorov, 1965b; Levin, 1973a; Li & Vitányi, 1997; Rissanen, 1986; Solomonoff, 1964, 1978;Wallace & Boulton, 1968).”
Delusion, Survival, and Intelligent Agents (2011, methodology): “The prediction scheme can be, for example, Solomonoﬀ induction [6]; i.e, for a universal prior ρ , the prediction is ˆ o t = arg max o ∈O ρ ( o | h ) .”
The Fastest and Shortest Algorithm for all Well-Defined Problems (2000, methodology): “This has been put into a rigorous scheme by [18] and proved to be optimal in [19, 7].”
Formalizing Two Problems of Realistic World-Models (2015, background): “Solomonoff (1964) formalized an induction problem faced by agents which must learn to predict an environment which does not contain the agent, and this formalism has inspired the development of many useful tools, including Kolmogorov complexity and Hutter’s AIXI.”
Asymptotic non-learnability of universal agents with computable horizon functions (2013, background): “Solomonoff showed that M converges to the true generator μ (the true environment q0 gets more and more weight in M), when the size of the sequence grows [13].”
Transfer Learning using Kolmogorov Complexity: Basic Theory and Empirical Evaluations (2007, result): “This result was first proved in[14], and extended variously in [11; 12].”
An Approximation of the Universal Intelligence Measure (2011, background): “This is a mathematical, non-anthropocentric definition of intelligence that draws on a range of proposed informal definitions of intelligence, algorithmic information theory [14], Solomonoff’s model of universal inductive inference [17,18], and Hutter’s AIXI theory of universal artificial intelligen”
Maximizing Fun by Creating Data with Easily Reducible Subjective Complexity (2013, background): “Consider Solomonoff's theoretically optimal, universal way of predicting the future (Hutter 2005; Li and Vitányi 1997; Solomonoff 1964, 1978).”
A tutorial introduction to the minimum description length principle (2004, background): “Solomonoff’s ideas were later extended by several authors, leading to an ‘idealized’ version of MDL [Solomonoff 1978; Li and Vitányi 1997; Gács, Tromp, and Vitányi 2001].”
A Formal Solution to the Grain of Truth Problem (2016, background): “:= 2 , whereK(T ) denotes the length of the shortest input to some universal Turing machine that encodesT [Sol78].”