Sublinear algorithms for testing monotone and unimodal distributions

The complexity of testing properties of monotone and unimodal distributions, when given access only to samples of the distribution, is investigated. Two kinds of sublineartime algorithms--those for testing monotonicity and those that take advantage of monotonicity--are provided. The first algorithm tests if a given distribution on [n] is monotone or far away from any monotone distribution in L1-norm; this algorithm uses ~O( n) samples and is shown to be nearly optimal. The next algorithm, given a joint distribution on [n]?[n], tests if it is monotone or is far away from any monotone distribution in L1-norm; this algorithm uses ~O(n3/2 ) samples. The problems of testing if two monotone distributions are close in L1-norm and if two random variables with a monotone joint distribution are close to being independent in L1-norm are also considered. Algorithms for these problems that use only poly(log n) samples are presented. The closeness and independence testing algorithms for monotone d...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Tugkan Batu, Ravi Kumar, Ronitt Rubinfeld
• Keywords: Algorithms, Monotone Distributions, Monotone Joint Distribution, STOC 2004, Unimodal Distributions