  A two--step Christoffel function based solution is proposed to distribution
regression problem. On the first step, to model distribution of observations
inside a bag, build Christoffel function for each bag of observations. Then, on
the second step, build outcome variable Christoffel function, but use the bag's
Christoffel function value at given point as the weight for the bag's outcome.
The approach allows the result to be obtained in closed form and then to be
evaluated numerically. While most of existing approaches minimize some kind an
error between outcome and prediction, the proposed approach is conceptually
different, because it uses Christoffel function for knowledge representation,
what is conceptually equivalent working with probabilities only. To receive
possible outcomes and their probabilities Gauss quadrature for second--step
measure can be built, then the nodes give possible outcomes and normalized
weights -- outcome probabilities. A library providing numerically stable
polynomial basis for these calculations is available, what make the proposed
approach practical.
