Advances in High Dimensional Function Estimation by Adaptive Annealing

The problem of high-dimensional function estimation is discussed including the need for joint consideration of issues of approximation, estimation and computation, and the role of information theory in understanding the relationships.  Flexible accurate function modeling arises by allowance of arbitrary order interactions among explanatory variables or by allowance of general ridge basis expansions.  However, the number of candidate basis functions becomes exponentially large in the number of variables, more than can be feasibly computed by standard greedy basis search algorithms.  We discuss a class of stochastic search strategies we call adaptive annealling and the prospects for computationally feasible and accurate search with these strategies for certain smoothly parameterized classes of basis functions. This work is joint with Xi Luo and Sabyasachi Chatterjee.