How Inductive Inference Strategies Discover Their Errors

Inductive Inference of Functions by Probabilistic Strategies

The following model of inductive inference is considered. Arbitrary numbering tau = {tau0, tau1, tau2, ...} of total functions N->N is fixed. A "black box" outputs the values f(0), f(1), ..., f(m), ... of some function f from the numbering tau. Processing these values by some algorithm (a strategy) F we try to identify a tau-index of f (i.e. a number n such that f = taun). Strategy F outputs an...

Inductive Inference

How genetic errors in GPCRs affect their function: Possible therapeutic strategies

Activating and inactivating mutations in numerous human G protein-coupled receptors (GPCRs) are associated with a wide range of disease phenotypes. Here we use several class A GPCRs with a particularly large set of identified disease-associated mutations, many of which were biochemically characterized, along with known GPCR structures and current models of GPCR activation, to understand the mol...

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...