Papers › Accelerated Experimental Design for Pairwise Comparisons

Accelerated Experimental Design for Pairwise Comparisons

18 Jan 2019arXiv:1901.06080archive 2025-07-28

Yuan Guo, Jennifer Dy, Deniz Erdogmus, Jayashree Kalpathy-Cramer, Susan Ostmo, J. Peter Campbell, Michael F. Chiang, Stratis Ioannidis

Pairwise comparison labels are more informative and less variable than class labels, but generating them poses a challenge: their number grows quadratically in the dataset size. We study a natural experimental design objective, namely, D-optimality, that can be used to identify which K pairwise comparisons to generate. This objective is known to perform well in practice, and is submodular, making the selection approximable via the greedy algorithm. A na\"ive greedy implementation has O(N²d²K) complexity, where N is the dataset size, d is the feature space dimension, and K is the number of generated comparisons. We show that, by exploiting the inherent geometry of the dataset--namely, that it consists of pairwise comparisons--the greedy algorithm's complexity can be reduced to O(N²(K+d)+N(dK+d²) +d²K). We apply the same acceleration also to the so-called lazy greedy algorithm. When combined, the above improvements lead to an execution time of less than 1 hour for a dataset with 10⁸ comparisons; the na\"ive greedy algorithm on the same dataset would require more than 10 days to terminate.

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