I recently got dataset for 37000 households with declared income and a few dozens of other variables of various types: continuous, discrete, binary.
The task is to automatically (unsupervised) evaluate credibility of declared income based on the remaining variables: evaluate if it agrees with statistics of the sample.
Normalize the income to uniform distribution on [0,1] using empirical distribution function like in copula theory. Thanks of it, modeled density of conditional distribution of this variable seems a proper way to evaluate credibility (?) Here are examples of pairwise dependencies of such normalized variables - would be rho=1 if independent, inhomogeneity allows to predict different conditional distribution of income based on the second variable (e.g. for 70 year old, extreme value is less credible):
To combine predictions from multiple variables, I just used linear regression: of cumulant-like polynomial coefficients of predicted variable, as linear combinations of features of the remaining variables (e.g. their contribution to j-th moment) - works nicely, here are some predicted densities:
I would like to compare it with some standard approach, but don't know what to use?
KDE doesn't seem useful here (?) - what other ML methods can be used to model such complex conditional continuous probability distributions?