Optimal randomized classification trees

Optimal Partitioning for Classification and Regression Trees

In designing a decision tree for classification or regression, one selects at each node a feature to be tested, and partitions the range of that feature into a small number of bins, each bin corresponding to a child of the node. When the feature’s range is discrete with N unordered outcomes, the optimal partition, that is, the partition minimizing an expected loss, is usually found by an exhaus...

Near-Minimax Optimal Classification with Dyadic Classification Trees

This paper reports on a family of computationally practical classifiers that converge to the Bayes error at near-minimax optimal rates for a variety of distributions. The classifiers are based on dyadic classification trees (DCTs), which involve adaptively pruned partitions of the feature space. A key aspect of DCTs is their spatial adaptivity, which enables local (rather than global) fitting o...

Optimal randomized classification in adversarial settings

The problem of learning to distinguish good inputs from malicious has come to be known as adversarial classification emphasizing the fact that, unlike traditional classification, the adversary can manipulate input instances to avoid being so classified. We offer the first general theoretical analysis of the problem of adversarial classification, resolving several important open questions in the...

Globally Optimal Fuzzy Decision Trees for Classification and Regression

ÐA fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure. This extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods, while remaining easily interpretable. Fuzzification is achieved by superimposing a fu...

Optimal Trees