Credibility evaluation of income data with hierarchical correlation reconstruction
This work addresses credibility assessment for income data in contexts like tax declarations, but it is incremental as it adapts an existing technique to a specific domain.
The paper tackles the problem of automatically evaluating the credibility of declared income using available household variables by adapting hierarchical correlation reconstruction (HCR) to model conditional probability distributions, resulting in a method that marks data points for manual verification based on predicted density thresholds.
In situations like tax declarations or analyzes of household budgets we would like to automatically evaluate credibility of exogenous variable (declared income) based on some available (endogenous) variables - we want to build a model and train it on provided data sample to predict (conditional) probability distribution of exogenous variable based on values of endogenous variables. Using Polish household budget survey data there will be discussed simple and systematic adaptation of hierarchical correlation reconstruction (HCR) technique for this purpose, which allows to combine interpretability of statistics with modelling of complex densities like in machine learning. For credibility evaluation we normalize marginal distribution of predicted variable to $ρ\approx 1$ uniform distribution on $[0,1]$ using empirical distribution function $(x=EDF(y)\in[0,1])$, then model density of its conditional distribution $(\textrm{Pr}(x_0|x_1 x_2\ldots))$ as a linear combination of orthonormal polynomials using coefficients modelled as linear combinations of features of the remaining variables. These coefficients can be calculated independently, have similar interpretation as cumulants, additionally allowing to directly reconstruct probability distribution. Values corresponding to high predicted density can be considered as credible, while low density suggests disagreement with statistics of data sample, for example to mark for manual verification a chosen percentage of data points evaluated as the least credible.