Bayesian optimization has been successful at global optimization of expensiveto-evaluate multimodal objective functions. However, unlike most optimization methods, Bayesian optimization typically does not use derivative information. In this paper we show how Bayesian optimization can exploit derivative information to find good solutions with fewer objective function evaluations. In particular, ...

We analyze the conjugate gradient (CG) method with preconditioning slightly variable from one iteration to the next. To maintain the optimal convergence properties, we consider a variant proposed by Axelsson that performs an explicit orthogonalization of the search directions vectors. For this method, which we refer to as flexible CG, we develop a theoretical analysis that shows that the conver...

Ubiquitous porosity gradients have a potentially important effect on the mixing of particle-bound tracers, such as 210Pb Mass-depth coordinates cannot be used to deal with these effects if values of the traditional mixing coefficient, D,, are required. This paper compares and evaluates three different means of dealing directly with porosity gradients while modeling bioturbation, i.e. mean const...

In animal embryos, morphogen gradients determine tissue patterning and morphogenesis. Shyer et al. provide evidence that, during vertebrate gut formation, tissue folding generates graded activity of signals required for subsequent steps of gut growth and differentiation, thereby revealing an intriguing link between tissue morphogenesis and morphogen gradient formation.

A common belief in high dimensional data analysis is that data is concentrated on a low dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on manifolds for dimension reduction for high dimensional data with few observations. We obtain generalization error bounds for the gradient estimates and show tha...