More Web Proxy on the site http://driver.im/

Article

Generalized² Linear² models

Author:

Geoffrey J. GordonAuthors Info & Claims

NIPS'02: Proceedings of the 16th International Conference on Neural Information Processing Systems

Pages 593 - 600

Published: 01 January 2002 Publication History

Abstract

We introduce the Generalized² Linear² Model, a statistical estimator which combines features of nonlinear regression and factor analysis. A (GL)²M approximately decomposes a rectangular matrix X into a simpler representation f(g(A)h(B)). Here A and B are low-rank matrices, while f, g, and h arc link functions. (GL)²Ms include many useful models as special cases, including principal components analysis, exponential-family PCA, the infomax formulation of independent components analysis, linear regression, and generalized linear models. They also include new and interesting special cases, one of which we describe below. We also present an iterative procedure which optimizes the parameters of a (GL)²M. This procedure reduces to well-known algorithms for some of the special cases listed above; for other special cases, it is new.

References

[1]

T. K. Landauer, P. W. Foltz. and D. Laham. Introduction to latent semantic analysis. Discourse Processes, 25:259-284, 1998.

[2]

Jon M. Kleinberg. Authoritative sources in a hyperlinked environment. Journal of the ACM, 46(5):604-632, 1999.

Digital Library

[3]

M. Turk and A. Pentland. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 3(1):71-86, 1991.

Digital Library

[4]

Carlo Tomasi and Takeo Kanade. Shape and motion from image streams under orthography: a factorization method. Int. J. Computer Vision, 9(2):137-154, 1992.

Digital Library

[5]

D. P. O'Leary and S. Peleg. Digital image compression by outer product expansion. IEEE Tmns. Communications, 31:441-444, 1983.

[6]

P. McCullagh and J. A. Nelder. Generalized Linear Models. Chapman & Hall, London, 2nd edition, 1983.

[7]

Peter Auer, Mark Hebster, and Manfred K. Warmuth. Exponentially many local minima for single neurons. In NIPS, vol. 8. MIT Press, 1996.

Digital Library

[8]

R. Tyrell Rockafellar. Convex Analysis. Princeton University Press, New Jersey, 1970.

[9]

Geoffrey J. Gordon. Approximate Solutions to Markov Decision Processes. PhD thesis, Carnegie Mellon University, 1999.

Digital Library

[10]

Daniel Lee and H. Sebastian Seung. Algorithms for nonnegative matrix factorization. In NIPS, vol. 13. MIT Press, 2001.

[11]

Nathan Srebro. Personal communication, 2002.

[12]

Anthony J. Bell and Terrence J. Sejuowski. The 'independent components' of natural scenes are edge filters. Vision Research, 37(23):3327-3338, 1997.

[13]

Michael Collins, Sanjoy Dasgupta, and Robert Schapire. A generalization of principal component analysis to the exponential family. In NIPS, vol. 14. MIT Press, 2002.

[14]

D. Fox, W. Burgard, F. Dellaert, and S. Thrun. Monte Carlo localization: Efficient position estimation for mobile robots. In AAAI 1999.

Digital Library

[15]

Nicholas Roy and Geoffrey J. Gordon. Exponential family PCA for belief compression in POMDPs. In NIPS, vol. 15. MIT Press, 2003.

[16]

Sam Roweis. EM algorithms for PCA and SPCA. In NIPS, vol. 10. MIT Press, 1998.

Digital Library

Cited By

Singh AGordon G(2008)A unified view of matrix factorization modelsProceedings of the 2008th European Conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II10.5555/3121525.3121550(358-373)Online publication date: 15-Sep-2008
https://dl.acm.org/doi/10.5555/3121525.3121550
Srebro NJaakkola T(2003)Weighted low-rank approximationsProceedings of the Twentieth International Conference on International Conference on Machine Learning10.5555/3041838.3041929(720-727)Online publication date: 21-Aug-2003
https://dl.acm.org/doi/10.5555/3041838.3041929

Index Terms

Generalized² Linear² models
1. Computing methodologies
  1. Machine learning
    1. Machine learning approaches
      1. Factorization methods
        Canonical correlation analysis
  2. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
  2. Probability and statistics
    1. Statistical paradigms
      1. Regression analysis
        Robust regression
      2. Statistical graphics

Index terms have been assigned to the content through auto-classification.

Recommendations

Software component models: past, present and future
CBSE '14: Proceedings of the 17th international ACM Sigsoft symposium on Component-based software engineering

In the early years of the CBSE Symposium, much research was focused on identifying the desiderata of CBSE and developing different approaches to CBSE. However, a common framework for defining and analysing CBSE approaches with respect to these ...
Software Component Models

Component-based Development (CBD) is an important emerging topic in Software Engineering, promising long sought after benefits like increased reuse, reduced time-to-market and hence software production cost. The cornerstone of a CBD technology is its ...
Impossible differential cryptanalysis of reduced-round ARIA and Camellia

This paper studies the security of the block ciphers ARIA and Camellia against impossible differential cryptanalysis. Our work improves the best impossible differential cryptanalysis of ARIA and Camellia known so far. The designers of ARIA expected no ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Guide Proceedings

NIPS'02: Proceedings of the 16th International Conference on Neural Information Processing Systems

January 2002

1674 pages

Publisher

MIT Press

Cambridge, MA, United States

Publication History

Published: 01 January 2002

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 15 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Singh AGordon G(2008)A unified view of matrix factorization modelsProceedings of the 2008th European Conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II10.5555/3121525.3121550(358-373)Online publication date: 15-Sep-2008
https://dl.acm.org/doi/10.5555/3121525.3121550
Srebro NJaakkola T(2003)Weighted low-rank approximationsProceedings of the Twentieth International Conference on International Conference on Machine Learning10.5555/3041838.3041929(720-727)Online publication date: 21-Aug-2003
https://dl.acm.org/doi/10.5555/3041838.3041929

View Options

View options

Media

Figures

Other

Tables

View Table of Contents