From: Local differential privacy for unbalanced multivariate nominal attributes
A | Multiple unbalanced categorical data sets |
l | Number of attributes |
n | Number of participants |
\(k_i\) | Number of items of the i-th attribute |
d | Total number of items, \(d = \sum _ik_i\) |
\({\mathbf {a}}_j\) | j-th attributes of A, the length \(|{\mathbf {a}}_j|\) of which is \(k_j\) |
\({\mathbf {v}}_i\) | Private values possessed by the i-th user, the length \(|{\mathbf {v}}_i|\) of which is l |
\(v_{ij}\) | j-th value of \({\mathbf {v}}_i\) |
\({\mathbf {h}}_i\) | Private bit vector of i-th users, the length of which is d |
H | True histogram, \({\mathbf {H}} = \sum {\{{\mathbf {h}}_1, \ldots , {\mathbf {h}}_n\}}\) |
\(H'\) | Sanitized histogram of \({\mathbf {H}}\), \({\mathbf {H}}' = \sum {\{{\mathbf {h}}_1', \ldots , {\mathbf {h}}_n'\}}\) |
\(H''\) | Estimated histogram of \({\mathbf {H}}'\), \({\mathbf {H}}'' = \sum {\{{\mathbf {h}}_1'', \ldots , {\mathbf {h}}_n''\}}\) |
\(\epsilon _i\) | Privacy budget of the i-th attribute |
CF | Cardano formula |
NS | Newton-Raphson method |
SE | Square error |
NSE | Normalized square error, \(NSE = \frac{SE}{n}\) |