A simple measure of conditional dependence

We propose a coefficient of conditional dependence between two random variables Y and Z given set other X1,…,Xp, based on an i.i.d. sample. The has long list desirable properties, the most important which is that under absolutely no distributional assumptions, it converges to limit in [0,1], where 0 if only are conditionally independent 1 equal measurable function X1,…,Xp. Moreover, natural interpretation as nonlinear generalization familiar partial R2 statistic for measuring by regression. Using this statistic, we devise new variable selection algorithm, called Feature Ordering Conditional Independence (FOCI), model-free, tuning parameters, provably consistent sparsity assumptions. A number applications synthetic real data sets worked out.