1 research outputs found
Accelerated Experimental Design for Pairwise Comparisons
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 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 complexity, where is the
dataset size, is the feature space dimension, and 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 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 comparisons; the na\"ive greedy algorithm on the same
dataset would require more than 10 days to terminate