Additive smoothing

In the field of statistical language modeling and statistics, additive smoothing is a technique used to smooth a distribution "p"("x") representing, for example, occurrences of a word "x" in a text.

The additively smoothed distribution is defined as:$p(x;delta)\; =\; frac\{p(x)\; +\; delta\}\{N\; +\; delta\; |X,$

where "δ" is a number typically between 0 and 1, "X" is the group of all sample groups (for example different words) and "N" is the number of all samples

: $N\; =\; sum\{x\; in\; X\}\; p(x).$

Additive smoothing is sometimes referred as Lidstone smoothing.

References

* SF Chen, J Goodman (1996). "An empirical study of smoothing techniques for language modeling". "Proceedings of the 34th annual meeting on Association for Computational Linguistics".