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

🤖 Plain-English Summary

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.

🔑 Key Findings

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

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