Machine Learning
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Diagnosing extrapolation: tree-based density estimation
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Tree-based multivariate regression and density estimation with right-censored data
Journal of Multivariate Analysis
Interpretable Hierarchical Clustering by Constructing an Unsupervised Decision Tree
IEEE Transactions on Knowledge and Data Engineering
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
A Recursive Partitioning Decision Rule for Nonparametric Classification
IEEE Transactions on Computers
Indexing density models for incremental learning and anytime classification on data streams
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
All of Nonparametric Statistics
All of Nonparametric Statistics
Unsupervised discretization using tree-based density estimation
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
MLPACK: a scalable C++ machine learning library
The Journal of Machine Learning Research
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In this paper we develop density estimation trees (DETs), the natural analog of classification trees and regression trees, for the task of density estimation. We consider the estimation of a joint probability density function of a d-dimensional random vector X and define a piecewise constant estimator structured as a decision tree. The integrated squared error is minimized to learn the tree. We show that the method is nonparametric: under standard conditions of nonparametric density estimation, DETs are shown to be asymptotically consistent. In addition, being decision trees, DETs perform automatic feature selection. They empirically exhibit the interpretability, adaptability and feature selection properties of supervised decision trees while incurring slight loss in accuracy over other nonparametric density estimators. Hence they might be able to avoid the curse of dimensionality if the true density is sparse in dimensions. We believe that density estimation trees provide a new tool for exploratory data analysis with unique capabilities.