On estimating the large entries of a convolution

We give a Monte Carlo algorithm that computes an unbiased estimate of the convolution of two vectors. The variance of our estimate is small for entries of the convolution that are large; this corresponds to the situation in which convolution is used in pattern matching or template matching, where one is only interested in the largest entries of the resulting convolution vector. Experiments performed with our algorithm confirm the theory and suggest that, in contexts where one cares about only the large entries in the convolution, the algorithm can be a faster alternative to performing an FFT-based convolution