  We introduce a general constructive setting of the density ratio estimation
problem as a solution of a (multidimensional) integral equation. In this
equation, not only its right hand side is known approximately, but also the
integral operator is defined approximately. We show that this ill-posed problem
has a rigorous solution and obtain the solution in a closed form. The key
element of this solution is the novel V-matrix, which captures the geometry of
the observed samples. We compare our method with three well-known previously
proposed ones. Our experimental results demonstrate the good potential of the
new approach.
