Entropy 13 (6):1076-1136 (
2011)
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Abstract
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.