NDLI: Predictive PAC Learnability: A Paradigm for Learning from Exchangeable Input Data

Content Provider	IEEE Xplore Digital Library
Author	Pestov, V.
Copyright Year	2010
Abstract	Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs $X_1, X_2, \ldots$. Inspired by the work of Berti and Rigo on a Glivenko–Cantelli theorem for exchangeable inputs, we propose a new paradigm, adequate for learning from exchangeable data: predictive PAC learnability. A learning rule $\mathcal L$ for a function class $\mathscr F$ is predictive PAC if for every $\e, \delta>0$ and each function $f\in {\mathscr F}$, whenever $\abs{\sigma}\geq s(\delta, \e)$, we have with confidence $1-\delta$ that the expected difference between $f(X_{n+1})$ and the image of $f\vert\sigma$ under $\mathcal L$ does not exceed $\e$ conditionally on $X_1, X_2, \ldots, X_n$. Thus, instead of learning the function $f$ as such, we are learning to a given accuracy $\e$ the predictive behaviour of $f$ at the future points $X_i(\omega)$, $i>n$ of the sample path. Using de Finetti's theorem, we show that if a universally separable function class $\mathscr F$ is distribution-free PAC learnable under i.i.d. inputs, then it is distribution-free predictive PAC learnable under exchangeable inputs, with a slightly worse sample complexity.
Starting Page	387
Ending Page	391
File Size	214287
Page Count	5
File Format	PDF
ISBN	9781424479641
DOI	10.1109/GrC.2010.102
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-08-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Exchangeable random variables Statistical learning de Finetti theorem Extraterrestrial measurements predictive PAC learnability Random variables Complexity theory Joints Convergence
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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