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Projection onto A Nonnegative Max-Heap

Projection onto A Nonnegative Max-Heap

This video was recorded at Video Journal of Machine Learning Abstracts - Volume 2. We consider the problem of computing the Euclidean projection of a vector of length $p$ onto a non-negative max-heap - an ordered tree where the values of the nodes are all nonnegative and the value of any parent node is no less than the value(s) of its child node(s). This Euclidean projection plays a building block role in the optimization problem with a non-negative max-heap constraint. Such a constraint is desirable when the features follow an ordered tree structure, that is, a given feature is selected for the given regression/classification task only if its parent node is selected. In this paper, we show that such Euclidean projection problem admits an analytical solution and we develop a top-down... Show More
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