Learning in high dimensions, noise, sparsity and treelets

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Description:	Nadler, B (Weizmann) Wednesday 09 January 2008, 16:30-17:30 Contemporary Frontiers in High-Dimensional Statistical Data Analysis

Created:

2008-01-21 11:30

Collection:

Statistical Theory and Methods for Complex, High-Dimensional Data

Publisher:

Isaac Newton Institute

Nadler, B

Language:

eng (English)

Credits:

Author:

Nadler, B


Abstract:	In recent years there is growing practical need to perform learning (classification,regression, etc) in high dimensional settings where p>>n. Consequently instead of the standard limit $n\to\infty$, learning algorithms are typically analyzed in the joint limit $p,n\to\infty$. In this talk we present a different approach, that keeps $p,n$ fixed, but considers noise as a small parameter. This resulting perturbation analysis reveals the importance of a robust low dimensional representation of the noise-free signals, the possible failure of simple variable selection methods and the key role of sparsity for the success of learning in high dimensions. We also discuss sparsity in a-priori unknown basis and a possible data-driven adaptive construction of such basis, called treelets. We present a few applications of our analysis, mainly to error-in-variables linear regression problems, principal component analysis, and rank determination. Related Links * http://arxiv.org/abs/0707.0481v1 - Treelets * http://www.wisdom.weizmann.ac.il/~nadler/Publications/bn11_pls2.pdf * http://www.wisdom.weizmann.ac.il/~nadler/Publications/publications.html

Abstract:

In recent years there is growing practical need to perform learning (classification,regression, etc) in high dimensional settings where p>>n. Consequently instead of the standard limit $n\to\infty$, learning algorithms are typically analyzed in the joint limit $p,n\to\infty$. In this talk we present a different approach, that keeps $p,n$ fixed, but considers noise as a small parameter. This resulting perturbation analysis reveals the importance of a robust low dimensional representation of the noise-free signals, the possible failure of simple variable selection methods and the key role of sparsity for the success of learning in high dimensions. We also discuss sparsity in a-priori unknown basis and a possible data-driven adaptive construction of such basis, called treelets. We present a few applications of our analysis, mainly to error-in-variables linear regression problems, principal component analysis, and rank determination.

Related Links

* http://arxiv.org/abs/0707.0481v1 - Treelets
* http://www.wisdom.weizmann.ac.il/~nadler/Publications/bn11_pls2.pdf
* http://www.wisdom.weizmann.ac.il/~nadler/Publications/publications.html

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