I will talk about a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1, . . . , Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0, 1], where the limit is 0 if and only if Y and Z are conditionally independent given X1, . . . , Xp, and is 1 if and only if Y is equal to a measurable function of Z given X1, . . . , Xp. I will then present a new variable selection algorithm based on this statistic, called Feature Ordering by Conditional Independence (FOCI), which is model-free, has no tuning parameters, and is provably consistent under sparsity assumptions.
This is based on joint work with Mona Azadkia
The Statistics Seminars for Winter Quarter will be held in Room 380C of Sloan Mathematics Center in the Main Quad at 4:30pm on Tuesdays. Refreshments are served at 4pm in the Lounge on the first floor of Sequoia Hall.