Abstract. Variational descriptions for various multiphase level set formulations involving curvature flow are discussed. A representation of n phases using n−1 level set functions is introduced having the advantage that constraints preventing overlaps or vacuum are not needed. The representation is then used in conjunction with our variational formulation to deduce a novel level set based algor...

Sparse Gaussian process methods that use inducing variables require the selection of the inducing inputs and the kernel hyperparameters. We introduce a variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound of the true log marginal likelihood. The key property of this formulation is that the inducing i...