Additive smoothing
In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts x = ⟨ x 1 , x 2 , … , x d ⟩ {\displaystyle \mathbf {x} =\langle x_{1},x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts gives the estimator θ ^ i = x i + α N + α d ( i = 1 , … , d ) , {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\alpha }{N+\alpha d}}\qquad (i=1,\ldots ,d),} where the smoothed count x ^ i = N θ ^ i {\displaystyle {\hat {x}}_{i}=N{\hat {\theta }}_{i}} , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below).