Fast Kd-Trees for the Kullback-Leibler Divergence and Other Decomposable Bregman Divergences

The contributions of the paper span theoretical and implementational results. Compared to a linear search, we achieve two orders of magnitude speedup for practical scenarios in dimension up to 100.

⚡ This is an original paraphrased summary — not copied from the abstract. Full paper available at the source link below.

• 1 First, we prove that Kd-trees can be extended to ℝ^d with the distance measured by an arbitrary Bregman divergence.
• 2 Perhaps surprisingly, this shows that the triangle inequality is not necessary for correct pruning in Kd-trees.
• 3 Second, we offer an efficient algorithm and C++ implementation for nearest neighbour search for decomposable Bregman divergences.

This research advances how AI systems learn, reason, and solve problems — with direct implications for automation and scientific discovery.

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