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COLT
2010
Springer

Forest Density Estimation

10 years 9 months ago
Forest Density Estimation
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univariate marginals, and apply Kruskal's algorithm to estimate the optimal forest on held out data. We prove an oracle inequality on the excess risk of the resulting estimator relative to the risk of the best forest. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. We prove that finding a maximum weight spanning forest with restricted tree size is NP-hard, and develop an approximation algorithm for this problem. Viewing the tree size as a complexity parameter, we then select a forest using data splitting, and prove bounds on excess risk and structure selection consistency of the procedure. Experiments with simulated data and m...
Anupam Gupta, John D. Lafferty, Han Liu, Larry A.
Added 10 Feb 2011
Updated 10 Feb 2011
Type Journal
Year 2010
Where COLT
Authors Anupam Gupta, John D. Lafferty, Han Liu, Larry A. Wasserman, Min Xu
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