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In situations like tax declarations or analyzes of household budgets we wouldlike to automatically evaluate credibility of exogenous variable (declaredincome) based on some available (endogenous) variables - we want to build amodel and train it on provided data sample to predict (conditional) probabilitydistribution of exogenous variable based on values of endogenous variables.Using Polish household budget survey data there will be discussed simple andsystematic adaptation of hierarchical correlation reconstruction (HCR)technique for this purpose, which allows to combine interpretability ofstatistics with modelling of complex densities like in machine learning. Forcredibility evaluation we normalize marginal distribution of predicted variableto $\rho\approx 1$ uniform distribution on $[0,1]$ using empirical distributionfunction $(x=EDF(y)\in[0,1])$, then model density of its conditionaldistribution $(\textrm{Pr}(x_0|x_1 x_2\ldots))$ as a linear combination oforthonormal polynomials using coefficients modelled as linear combinations offeatures of the remaining variables. These coefficients can be calculatedindependently, have similar interpretation as cumulants, additionally allowingto directly reconstruct probability distribution. Values corresponding to highpredicted density can be considered as credible, while low density suggestsdisagreement with statistics of data sample, for example to mark for manualverification a chosen percentage of data points evaluated as the leastcredible.

Credibility evaluation of income data with hierarchical correlation reconstruction