Skip to main content Accessibility help
×
Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-29T00:42:38.668Z Has data issue: false hasContentIssue false

7 - Learning Boolean Functions with Queries

from Part III - Learning Theory and Cryptography

Published online by Cambridge University Press:  05 June 2013

Robert H. Sloan
Affiliation:
University of Illinois at Chicago
Balázs Szörényi
Affiliation:
University of Szeged
György Turán
Affiliation:
University of Illinois at Chicago
Yves Crama
Affiliation:
Université de Liège, Belgium
Get access

Summary

Introduction

The objective of machine learning is to acquire knowledge from available information in an automated manner. As an example, one can think of obtaining rules for medical diagnosis, based on a database of patients with their test results and diagnoses. If we make the simplifying assumption that data are represented as binary vectors of a fixed length and the rule to be learned classifies these vectors into two classes, then the task is that of learning, or identifying a Boolean function. This simplifying assumption is realistic in some cases, and it provides a good intuition for more general learning problems in others.

The notion of learning is somewhat elusive, and there are a large number of approaches to defining precisely what is meant by learning. A probabilistic notion, PAC (probably approximately correct) learning, based on random sampling of examples of the function to be learned, is discussed by Anthony in Chapter 6 of this volume. Here we discuss a different approach called learning by queries, introduced by Angluin in the 1980s [5]. In this model, it is known in advance that the function to be learned belongs to some given class of functions, and the learner's objective is to identify this function exactly by asking questions, or queries, about it. The prespecified class is called the target class, or concept class, and the function to be learned is called the target function, the target concept, or simply the target.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×