Learning Combinations of Sigmoids Through Gradient Estimation

TL;DR

This paper introduces a novel gradient estimation and clustering method to learn parameters of regression models with hidden units, specifically focusing on linear combinations of sigmoids, with proven guarantees.

Contribution

It presents a new approach for learning sigmoid combinations by estimating and clustering gradients, providing the first non-asymptotic guarantees for such models.

Findings

Gradients concentrate around hidden unit parameters

Non-asymptotic bounds on sample complexity

Method successfully identifies sigmoid parameters

Abstract

We develop a new approach to learn the parameters of regression models with hidden variables. In a nutshell, we estimate the gradient of the regression function at a set of random points, and cluster the estimated gradients. The centers of the clusters are used as estimates for the parameters of hidden units. We justify this approach by studying a toy model, whereby the regression function is a linear combination of sigmoids. We prove that indeed the estimated gradients concentrate around the parameter vectors of the hidden units, and provide non-asymptotic bounds on the number of required samples. To the best of our knowledge, no comparable guarantees have been proven for linear combinations of sigmoids.