Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-n7x5d Total loading time: 0.246 Render date: 2021-12-08T10:52:28.273Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

17 - Optimal Perceptron Learning: an On-line Bayesian Approach

Published online by Cambridge University Press:  28 January 2010

Sara Solla
Affiliation:
Physics and Astronomy, Northwestern University, Evanston, IL 60208,; Physiology, Northwestern University Medical School, Chicago, IL 60611, USA
Ole Winther
Affiliation:
CONNECT, The Niels Bohr Institute, 2100 Copenhagen Ø, Denmark; Theoretical Physics II, Lund University, S-223 62 Lund, Sweden
David Saad
Affiliation:
Aston University
Get access

Summary

Abstract

The recently proposed Bayesian approach to online learning is applied to learning a rule defined as a noisy single layer perceptron with either continuous or binary weights. In the Bayesian online approach the exact posterior distribution is approximated by a simpler parametric posterior that is updated online as new examples are incorporated to the dataset. In the case of continuous weights, the approximate posterior is chosen to be Gaussian. The computational complexity of the resulting online algorithm is found to be at least as high as that of the Bayesian offline approach, making the online approach less attractive. A Hebbian approximation based on casting the full covariance matrix into an isotropic diagonal form significantly reduces the computational complexity and yields a previously identified optimal Hebbian algorithm. In the case of binary weights, the approximate posterior is chosen to be a biased binary distribution. The resulting online algorithm is derived and shown to outperform several other online approaches to this problem.

Introduction

Neural networks are adaptive systems characterized by a set of parameters w, the weights and biases that specify the connectivity among the neuronal computational elements. Of particular interest is the ability of these systems to learn from examples. Traditional formulations of the learning problem are based on a dynamical prescription for the adaptation of the parameters w. The learning process thus generates a trajectory in w space that starts from a random initial assignment w0 and leads to a specific w* that is in some sense optimal.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1999

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.)
3
Cited by

Send book to Kindle

To send this book to your Kindle, first ensure no-reply@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 sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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.

  • Optimal Perceptron Learning: an On-line Bayesian Approach
    • By Sara Solla, Physics and Astronomy, Northwestern University, Evanston, IL 60208,; Physiology, Northwestern University Medical School, Chicago, IL 60611, USA, Ole Winther, CONNECT, The Niels Bohr Institute, 2100 Copenhagen Ø, Denmark; Theoretical Physics II, Lund University, S-223 62 Lund, Sweden
  • Edited by David Saad, Aston University
  • Book: On-Line Learning in Neural Networks
  • Online publication: 28 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511569920.018
Available formats
×

Send book to Dropbox

To send 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 sending content to Dropbox.

  • Optimal Perceptron Learning: an On-line Bayesian Approach
    • By Sara Solla, Physics and Astronomy, Northwestern University, Evanston, IL 60208,; Physiology, Northwestern University Medical School, Chicago, IL 60611, USA, Ole Winther, CONNECT, The Niels Bohr Institute, 2100 Copenhagen Ø, Denmark; Theoretical Physics II, Lund University, S-223 62 Lund, Sweden
  • Edited by David Saad, Aston University
  • Book: On-Line Learning in Neural Networks
  • Online publication: 28 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511569920.018
Available formats
×

Send book to Google Drive

To send 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 sending content to Google Drive.

  • Optimal Perceptron Learning: an On-line Bayesian Approach
    • By Sara Solla, Physics and Astronomy, Northwestern University, Evanston, IL 60208,; Physiology, Northwestern University Medical School, Chicago, IL 60611, USA, Ole Winther, CONNECT, The Niels Bohr Institute, 2100 Copenhagen Ø, Denmark; Theoretical Physics II, Lund University, S-223 62 Lund, Sweden
  • Edited by David Saad, Aston University
  • Book: On-Line Learning in Neural Networks
  • Online publication: 28 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511569920.018
Available formats
×