PhilSci Archive

A General Theory of (Identification in the) Limit and Convergence (to the Truth)

Lin, Hanti A General Theory of (Identification in the) Limit and Convergence (to the Truth). UNSPECIFIED.

[img]
Preview
Text
limit and convergence 6.pdf

Download (296kB) | Preview

Abstract

I propose a new definition of identification in the limit (also called convergence to the truth), as a new success criterion that is meant to complement, rather than replacing, the classic definition due to Gold (1967). The new definition is designed to explain how it is possible to have successful learning in a kind of scenario that Gold's classic account ignores---the kind of scenario in which the entire infinite data stream to be presented incrementally to the learner is not presupposed to completely determine the correct learning target. From a purely mathematical point of view, the new definition employs a convergence concept that generalizes net convergence and sits in between pointwise convergence and uniform convergence. Two results are proved to suggest that the new definition provides a success criterion that is by no means weak: (i) Between the new identification in the limit and Gold's classic one, neither implies the other. (ii) If a learning method identifies the correct target in the limit in the new sense, any U-shaped learning involved therein has to be redundant and can be removed while maintaining the new kind of identification in the limit. I conclude that we should have (at least) two success criteria that correspond to two senses of identification in the limit: the classic one and the one proposed here. They are complementary: meeting any one of the two is good; meeting both at the same time, if possible, is even better.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Other
Creators:
CreatorsEmailORCID
Lin, Hantiika@ucdavis.edu
Keywords: Identification in the Limit, Convergence to the Truth, Language Learning, Enumerative Induction, Uniform Convergence, Net Convergence
Subjects: General Issues > Confirmation/Induction
General Issues > Formal Learning Theory
Depositing User: Dr. Hanti Lin
Date Deposited: 16 Mar 2017 14:54
Last Modified: 16 Mar 2017 14:54
Item ID: 12909
Subjects: General Issues > Confirmation/Induction
General Issues > Formal Learning Theory
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/12909

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item