Median trick

The median trick is a generic approach that increases the chances of a probabilistic algorithm to succeed.[1] Apparently first used in 1986[2] by Jerrum et al.[3] for approximate counting algorithms, the technique was later applied to a broad selection of classification and regression problems.[2]

The idea of median trick is very simple: run the randomized algorithm with numeric output multiple times, and use the median of the obtained results as a final answer. For example, for sublinear in time algorithms the same algorithm can be run repeatedly (or in parallel) over random subsets of input data, and, per Chernoff inequality, the median of the results will converge to solution very fast.[4] For the algorithms that are sublinear in space (e.g., counting the distinct elements of a stream), different randomizations of the algorithm (say, with different hash functions) should be used for repeated runs over the same data.[5]