Forest Density Estimation

Details Forest Density Estimation Forest Density Estimation

2010-01-10

arxiv.org/abs/1001.1557v2

Statistics

Machine Learning

Extended version of earlier paper titled "Tree density estimation"

Scientific paper

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 microarray data indicate that the methods are a practical alternative to Gaussian graphical models.

Affiliated with

Also associated with

No associations

Rating

Forest Density Estimation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Forest Density Estimation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Forest Density Estimation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-718704