Inductive inference and unsolvability

1991 ◽  
Vol 56 (3) ◽  
pp. 891-900 ◽  
Author(s):  
Leonard M. Adleman ◽  
M. Blum
Keyword(s):  
Recursive Function ◽  
Inductive Inference ◽  
Inference Problem ◽  
Halting Problem ◽  
Index Problem ◽  
Unsolvable Problems

AbtractIt is shown that many different problems have the same degree of unsolvability. Among these problems are:The Inductive Inference Problem. Infer in the limit an index for a recursive function f presented as f(0), f(1),f(2),….The Recursive Index Problem. Decide in the limit if i is the index of a total recursive function.The Zero Nonvariant Problem. Decide in the limit if a recursive function f presented as f(0), f(1), f(2),… has value unequal to zero for infinitely many arguments.Finally, it is shown that these unsolvable problems are strictly easier than the halting problem.

Mechanical learners pay a price for Bayesianism

1988 ◽  
Vol 53 (4) ◽  
pp. 1245-1251 ◽  
Author(s):  
Daniel N. Osherson ◽  
Michael Stob ◽  
Scott Weinstein
Keyword(s):  
Turing Machine ◽  
Posterior Probability ◽  
Inductive Inference ◽  
Inference Problem ◽  
Inference Problems ◽  
Bayes’S Theorem ◽  
Bayes's Theorem ◽  
Is Failure ◽  
Bayesian Strategy

The price is failure on a class of inductive inference problems that are easily solved, in contrast, by nonBayesian mechanical learners. By “mechanical” is meant “simulable by Turing machine”.One of the central tenets of Bayesianism, which is common to the heterogeneous collection of views which fall under this rubric, is that hypothesis change proceeds via conditionalization on accumulated evidence, the posterior probability of a given hypothesis on the evidence being computed using Bayes's theorem. We show that this strategy for hypothesis change precludes the solution of certain problems of inductive inference by mechanical means—problems which are solvable by mechanical means when the restriction to this Bayesian strategy is lifted. Our discussion proceeds as follows. After some technical preliminaries, the concept of (formal) learner is introduced along with a criterion of inferential success. Next we specify a class of inductive inference problems, and then define the notion of “Bayesian behavior” on those problems. Finally, we exhibit an inductive inference problem from the specified class such that (a) some nonmechanical Bayesian learner solves the problem, (b) some nonBayesian mechanical learner solves the problem, (c) some mechanical learner manifests Bayesian behavior on the problem, but (d) no mechanical Bayesian learner solves the problem.Insofar as possible terminology and notation are drawn from Osherson, Stob, and Weinstein [1986].

scholarly journals The complexity of learning SUBSEQ(A)

2009 ◽  
Vol 74 (3) ◽  
pp. 939-975
Author(s):  
Stephen Fenner ◽  
William Gasarch ◽  
Brian Postow
Keyword(s):  
Inductive Inference ◽  
Finite Alphabet ◽  
Inference Problem

AbstractHigman essentially showed that ifA is anylanguage then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings inA. Lets1,s2,s3,… be the standard lexico-graphic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem:A(s1),A(s2),A(s3),…, learn, in the limit, a DFA for SUBSEQ(A). We consider this model of learning and the variants of it that are usually studied in Inductive Inference: anomalies, mind-changes, teams, and combinations thereof.This paper is a significant revision and expansion of an earlier conference version [10].

Degree problems for modular machines

1980 ◽  
Vol 45 (3) ◽  
pp. 510-528 ◽  
Author(s):  
Daniel E. Cohen
Keyword(s):  
Group Theory ◽  
Turing Machine ◽  
Recursive Function ◽  
Related Result ◽  
Turing Degrees ◽  
General Sense ◽  
Halting Problem ◽  
The Right

Modular machines were introduced in [1] and [2], where they were used to give simple proofs of various unsolvability results in group theory. Here we discuss the degrees of the halting, word, and confluence problems for modular machines, both for their own sake and in the hope that the results may be useful in group theory (see [4] for an application of a related result to group theory).In the course of the analysis, I found it convenient to compare degrees of these problems for a Turing machine T and for a Turing machine T1 obtained from T by enlarging the alphabet but retaining the same quintuples (or quadruples). The results were surprising. The degree for a problem of T1 depends not just on the corresponding degree for T, but also on the degrees of the corresponding problems when T is restricted to a semi-infinite tape (both semi-infinite to the right and semi-infinite to the left). For the halting and confluence problems, the Turing degrees of the problems for these three machines can be any r.e. degrees. In particular the halting problem of T can be solvable, while that of T1 has any r.e. degree.A machine M (in the general sense) consists of a countable set of configurations (together with a numbering, which we usually take for granted), a recursive subset of configurations called the terminal configurations, and a recursive function, written C ⇒ C′, on the set of configurations. If, for some n ≥ 0, we have C = C0 ⇒ C1 ⇒ … ⇒ Cn = C′, we write C → C′. We say M halts from C if C → C′ for some terminal C′.

The Effect of Stage of Development and Financial Health on Auditor Decision Behavior in the Going-Concern Task

1999 ◽  
Vol 18 (1) ◽  
pp. 37-54 ◽  
Author(s):  
Andrew J. Rosman ◽  
Inshik Seol ◽  
Stanley F. Biggs
Keyword(s):  
Information Acquisition ◽  
Type I ◽  
Type Ii ◽  
Financial Health ◽  
Inference Problem ◽  
Going Concern ◽  
Start Up ◽  
Mitigating Factors ◽  
Type Ii Errors ◽  
Problem Representations

The effect of different task settings within an industry on auditor behavior is examined for the going-concern task. Using an interactive computer process-tracing method, experienced auditors from four Big 6 accounting firms examined cases based on real data that differed on two dimensions of task settings: stage of organizational development (start-up and mature) and financial health (bankrupt and nonbankrupt). Auditors made judgments about each entity's ability to continue as a going concern and, if they had substantial doubt about continued existence, they listed evidence they would seek as mitigating factors. There are seven principal results. First, information acquisition and, by inference, problem representations were sensitive to differences in task settings. Second, financial mitigating factors dominated nonfinancial mitigating factors in both start-up and mature settings. Third, auditors' behavior reflected configural processing. Fourth, categorizing information into financial and nonfinancial dimensions was critical to understanding how auditors' information acquisition and, by inference, problem representations differed across settings. Fifth, Type I errors (determining that a healthy company is a going-concern problem) differed from correct judgments in terms of information acquisition, although Type II errors (determining that a problem company is viable) did not. This may indicate that Type II errors are primarily due to deficiencies in other stages of processing, such as evaluation. Sixth, auditors who were more accurate tended to follow flexible strategies for financial information acquisition. Finally, accurate performance in the going-concern task was found to be related to acquiring (1) fewer information cues, (2) proportionately more liquidity information and (3) nonfinancial information earlier in the process.

Introduction

2018 ◽  
Author(s):  
Jacob Stegenga
Keyword(s):  
Medical Practice ◽  
Evidence Based Medicine ◽  
Inductive Inference ◽  
Formal Theory ◽  
Practice Research ◽  
Evidence Based ◽  
Master Argument ◽  
Medical Interventions ◽  
Concepts Of Disease ◽  
Based Medicine

This chapter introduces the book, describes the key arguments of each chapter, and summarizes the master argument for medical nihilism. It offers a brief survey of prominent articulations of medical nihilism throughout history, and describes the contemporary evidence-based medicine movement, to set the stage for the skeptical arguments. The main arguments are based on an analysis of the concepts of disease and effectiveness, the malleability of methods in medical research, and widespread empirical findings which suggest that many medical interventions are barely effective. The chapter-level arguments are unified by our best formal theory of inductive inference in what is called the master argument for medical nihilism. The book closes by considering what medical nihilism entails for medical practice, research, and regulation.

Type Inference: Some Results, Some Problems1

1993 ◽  
Vol 19 (1-2) ◽  
pp. 87-125
Author(s):  
Paola Giannini ◽  
Furio Honsell ◽  
Simona Ronchi Della Rocca
Keyword(s):  
Large Class ◽  
Higher Order ◽  
Type Inference ◽  
Principal Type ◽  
Open Problems ◽  
Inference Problem ◽  
Type Assignment ◽  
Unification Problem

In this paper we investigate the type inference problem for a large class of type assignment systems for the λ-calculus. This is the problem of determining if a term has a type in a given system. We discuss, in particular, a collection of type assignment systems which correspond to the typed systems of Barendregt’s “cube”. Type dependencies being shown redundant, we focus on the strongest of all, Fω, the type assignment version of the system Fω of Girard. In order to manipulate uniformly type inferences we give a syntax directed presentation of Fω and introduce the notions of scheme and of principal type scheme. Making essential use of them, we succeed in reducing the type inference problem for Fω to a restriction of the higher order semi-unification problem and in showing that the conditional type inference problem for Fω is undecidable. Throughout the paper we call attention to open problems and formulate some conjectures.

scholarly journals ModularBoost: an efficient network inference algorithm based on module decomposition

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Xinyu Li ◽  
Wei Zhang ◽  
Jianming Zhang ◽  
Guang Li
Keyword(s):  
Network Inference ◽  
Detection Methods ◽  
Inference Problem ◽  
Topological Constraints ◽  
Inference Algorithms ◽  
Module Detection ◽  
Series Expression ◽  
Gene Modules ◽  
Inference Methods ◽  
Complicated Task

Abstract Background Given expression data, gene regulatory network(GRN) inference approaches try to determine regulatory relations. However, current inference methods ignore the inherent topological characters of GRN to some extent, leading to structures that lack clear biological explanation. To increase the biophysical meanings of inferred networks, this study performed data-driven module detection before network inference. Gene modules were identified by decomposition-based methods. Results ICA-decomposition based module detection methods have been used to detect functional modules directly from transcriptomic data. Experiments about time-series expression, curated and scRNA-seq datasets suggested that the advantages of the proposed ModularBoost method over established methods, especially in the efficiency and accuracy. For scRNA-seq datasets, the ModularBoost method outperformed other candidate inference algorithms. Conclusions As a complicated task, GRN inference can be decomposed into several tasks of reduced complexity. Using identified gene modules as topological constraints, the initial inference problem can be accomplished by inferring intra-modular and inter-modular interactions respectively. Experimental outcomes suggest that the proposed ModularBoost method can improve the accuracy and efficiency of inference algorithms by introducing topological constraints.

scholarly journals Improving Ecological Inference by Predicting Individual Ethnicity from Voter Registration Records

2016 ◽  
Vol 24 (2) ◽  
pp. 263-272 ◽  
Author(s):  
Kosuke Imai ◽  
Kabir Khanna
Keyword(s):  
Mean Squared Error ◽  
False Positive Rate ◽  
True Positive Rate ◽  
Voter Registration ◽  
Racial Groups ◽  
Ecological Inference ◽  
Inference Problem ◽  
Individual Level ◽  
Positive Rate ◽  
Election Results

In both political behavior research and voting rights litigation, turnout and vote choice for different racial groups are often inferred using aggregate election results and racial composition. Over the past several decades, many statistical methods have been proposed to address this ecological inference problem. We propose an alternative method to reduce aggregation bias by predicting individual-level ethnicity from voter registration records. Building on the existing methodological literature, we use Bayes's rule to combine the Census Bureau's Surname List with various information from geocoded voter registration records. We evaluate the performance of the proposed methodology using approximately nine million voter registration records from Florida, where self-reported ethnicity is available. We find that it is possible to reduce the false positive rate among Black and Latino voters to 6% and 3%, respectively, while maintaining the true positive rate above 80%. Moreover, we use our predictions to estimate turnout by race and find that our estimates yields substantially less amounts of bias and root mean squared error than standard ecological inference estimates. We provide open-source software to implement the proposed methodology.

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