Single and Multiple Index Models

author: Pradeep Ravikumar, Department of Computer Science, University of Texas at Austin
published: Jan. 16, 2013,   recorded: December 2012,   views: 4615


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Statistical estimation in the high-dimensional setting, with more variables than samples, has been the focus of considerable research over the last decade. It is now well understood that consistent estimation is still possible under such high-dimensional settings provided we impose suitable constraints on the model space. These structural constraints are however typically easier to impose when the statistical model has a finite-dimensional parametric form. A natural approach to extend these to the non-parametric setting is to work with semi-parametric models, and impose these structural constraints on the parametric component of the semi-parametric model. In this talk, we consider the semi-parametric model class of single and multiple index models. Here, the regression function is assumed to be a sum of univariate functions of linear projections of the data. We show that we can combine "classical nonparametrics" (projection pursuit regression and backfitting) with a "variational principle" based on convex optimization to address the difficult optimization problems arising in estimating such models. In particular, we show that the standard maximum-likelihood based approach is non-convex and brittle, but we can use Bregman divergences to derive a computationally tractable backfitting procedure. We demonstrate the utility of this modeling approach in a retinal modeling application.

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Reviews and comments:

Comment1 OlivaRobinson, January 13, 2022 at 12:47 p.m.:

When it comes to models of databases, there are two major ones. The single-index model and the multiple index model. This video lecture is a great resource for those who are interested in learning about the Single and Multiple Index models. It covers an overview of what these models are, their use cases, and how they can be applied in real-life situations. Well, I have to read article because I need to know how I would get a job after learning things like this because I need to use these things to earn some money in a professional way.

Comment2 Print Daily Calendar, July 19, 2022 at 10:16 a.m.:

You knocked me off my feet!

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