Rodeo: Sparse, greedy nonparametric regression

Rodeo: Sparse, greedy nonparametric regression

Rodeo: Sparse Nonparametric Regression in High Dimensions

We present a method for nonparametric regression that performs bandwidth selection and variable selection simultaneously. The approach is based on the technique of incrementally decreasing the bandwidth in directions where the gradient of the estimator with respect to bandwidth is large. When the unknown function satisfies a sparsity condition, our approach avoids the curse of dimensionality, a...

Sparse Nonparametric Density Estimation in High Dimensions Using the Rodeo

We consider the problem of estimating the joint density of a d-dimensional random vector X = (X1,X2, ...,Xd) when d is large. We assume that the density is a product of a parametric component and a nonparametric component which depends on an unknown subset of the variables. Using a modification of a recently developed nonparametric regression framework called rodeo (regularization of derivative...

Sparse Greedy Gaussian Process Regression

Peter Bartlett RSISE Australian National University Canberra, ACT, 0200 [email protected] We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m. In particular, computational requirements are O(n2m), storage is O(nm), the cost for prediction is 0 ( n) and the cost to com...

Structured Sparse Regression via Greedy Hard Thresholding

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard thresholding methods have proven to be extremely efficient, but such methods require NP hard projections when dealing with overlapping groups. In this paper, we show ...