Noise Addition

Synonyms

Additive noise

Definition

Noise addition is a masking method for statistical disclosure control of numerical microdata that consists of adding random noise to original microdata.

Key Points

The noise addition algorithms in the literature are:

• 1. Masking by uncorrelated noise addition. The vector of observations x_j for the jth attribute of the original dataset X_j is replaced by a vector

  $$ {z}_j={x}_j+{\upepsilon}_j $$

  where ɛ_j is a vector of normally distributed errors drawn from a random variable ${\varepsilon}_j\sim N\left(0,{\sigma}_{\varepsilon_j}^2\right)$, such that Cov(ε_t, ε_l) = 0 for all t ≠ l. This does not preserve variances nor correlations.

• 2. Masking by correlated noise addition. Correlated noise addition also preserves means and additionally allows preservation of correlation coefficients. The difference with the previous method is that the covariance matrix of the errors is now proportional to the covariance matrix of the original data, i.e., ε ∼ N(0, Σ_ε),...