Topological separations in inductive inference

Robust Separations in Inductive Inference

Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. Barzdin proposed a way of ruling out such examples, and conjectured that one of the earliest results of inductive inference theory would fall if his method were used We refute Barzdin’s conjecture. We propose a new line of research examining robust separations; these ar...

Inductive Inference

Subjectivity in Inductive Inference

This paper examines circumstances under which subjectivity enhances the effectiveness of inductive reasoning. We consider a game in which Fate chooses a data generating process and agents are characterized by inference rules that may be purely objective (or data-based) or may incorporate subjective considerations. The basic intuition is that agents who invoke no subjective considerations are do...

Fixed Parameter Inductive Inference

We investigate a particular inductive inference problem where we are given as input a finite set of ordered triples of the form (wi, bi, ti) such that wi is a bit string, bi is a single bit, and ti is a positive integer written in unary. A machine M is said to match such a triple if M outputs bi on input wi in at most ti steps. We proceed to investigate the fixed parameter problems where we fix...

Statistics as Inductive Inference

This chapter concerns the relation between statistics and inductive logic. I start by describing induction in formal terms, and I introduce a general notion of probabilistic inductive inference. This provides a setting in which statistical procedures and inductive logics can be captured. Specifically, I discuss three statistical procedures (hypotheses testing, parameter estimation, and Bayesian...