11,838 research outputs found
Algorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence
This article is a brief 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.Comment: 9 LaTeX page
A Stochastic Complexity Perspective of Induction in Economics and Inference in Dynamics
Rissanen's fertile and pioneering minimum description length principle (MDL) has been viewed from the point of view of statistical estimation theory, information theory, as stochastic complexity theory -.i.e., a computable approximation to Kolomogorov Complexity - or Solomonoff's recursion theoretic induction principle or as analogous to Kolmogorov's sufficient statistics. All these - and many more - interpretations are valid, interesting and fertile. In this paper I view it from two points of view: those of an algorithmic economist and a dynamical system theorist. >From these points of view I suggest, first, a recasting of Jevons's sceptical vision of induction in the light of MDL; and a complexity interpretation of an undecidable question in dynamics.
Ultimate Intelligence Part I: Physical Completeness and Objectivity of Induction
We propose that Solomonoff induction is complete in the physical sense via
several strong physical arguments. We also argue that Solomonoff induction is
fully applicable to quantum mechanics. We show how to choose an objective
reference machine for universal induction by defining a physical message
complexity and physical message probability, and argue that this choice
dissolves some well-known objections to universal induction. We also introduce
many more variants of physical message complexity based on energy and action,
and discuss the ramifications of our proposals.Comment: Under review at AGI-2015 conference. An early draft was submitted to
ALT-2014. This paper is now being split into two papers, one philosophical,
and one more technical. We intend that all installments of the paper series
will be on the arxi
Solomonoff Induction Violates Nicod's Criterion
Nicod's criterion states that observing a black raven is evidence for the
hypothesis H that all ravens are black. We show that Solomonoff induction does
not satisfy Nicod's criterion: there are time steps in which observing black
ravens decreases the belief in H. Moreover, while observing any computable
infinite string compatible with H, the belief in H decreases infinitely often
when using the unnormalized Solomonoff prior, but only finitely often when
using the normalized Solomonoff prior. We argue that the fault is not with
Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201
No Free Lunch versus Occam's Razor in Supervised Learning
The No Free Lunch theorems are often used to argue that domain specific
knowledge is required to design successful algorithms. We use algorithmic
information theory to argue the case for a universal bias allowing an algorithm
to succeed in all interesting problem domains. Additionally, we give a new
algorithm for off-line classification, inspired by Solomonoff induction, with
good performance on all structured problems under reasonable assumptions. This
includes a proof of the efficacy of the well-known heuristic of randomly
selecting training data in the hope of reducing misclassification rates.Comment: 16 LaTeX pages, 1 figur
Modeling Epistemological Principles for Bias Mitigation in AI Systems: An Illustration in Hiring Decisions
Artificial Intelligence (AI) has been used extensively in automatic decision
making in a broad variety of scenarios, ranging from credit ratings for loans
to recommendations of movies. Traditional design guidelines for AI models focus
essentially on accuracy maximization, but recent work has shown that
economically irrational and socially unacceptable scenarios of discrimination
and unfairness are likely to arise unless these issues are explicitly
addressed. This undesirable behavior has several possible sources, such as
biased datasets used for training that may not be detected in black-box models.
After pointing out connections between such bias of AI and the problem of
induction, we focus on Popper's contributions after Hume's, which offer a
logical theory of preferences. An AI model can be preferred over others on
purely rational grounds after one or more attempts at refutation based on
accuracy and fairness. Inspired by such epistemological principles, this paper
proposes a structured approach to mitigate discrimination and unfairness caused
by bias in AI systems. In the proposed computational framework, models are
selected and enhanced after attempts at refutation. To illustrate our
discussion, we focus on hiring decision scenarios where an AI system filters in
which job applicants should go to the interview phase
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