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We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…
In this paper, We propose a general Riemannian proximal optimization algorithm with guaranteed convergence to solve Markov decision process (MDP) problems. To model policy functions in MDP, we employ Gaussian mixture model (GMM) and…
Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the…
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…
We introduce Probabilistic Gaussian Homotopy (PGH), a probability-space continuation framework for nonconvex optimization. Unlike classical Gaussian homotopy, which smooths the objective and uniformly averages gradients, PGH deforms the…
Recently, the task of image generation has attracted much attention. In particular, the recent empirical successes of the Markov Chain Monte Carlo (MCMC) technique of Langevin Dynamics have prompted a number of theoretical advances; despite…
It is common in pose graph optimization (PGO) algorithms to assume that noise in the translations and rotations of relative pose measurements is uncorrelated. However, existing work shows that in practice these measurements can be highly…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
This paper is concerned with the problem of defining and estimating statistics for distributions on spaces such as Riemannian manifolds and more general metric spaces. The challenge comes, in part, from the fact that statistics such as…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
The Birkhoff polytope (the convex hull of the set of permutation matrices) is frequently invoked in formulating relaxations of optimization problems over permutations. The Birkhoff polytope is represented using $\Theta(n^2)$ variables and…
For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different…
Ptychography is now integrated as a tool in mainstream microscopy allowing quantitative and high-resolution imaging capabilities over a wide field of view. However, its ultimate performance is inevitably limited by the available coherent…
Compact and discriminative visual codebooks are preferred in many visual recognition tasks. In the literature, a number of works have taken the approach of hierarchically merging visual words of an initial large-sized codebook, but…
Pairwise compatibility calculation is at the core of most fragments-reconstruction algorithms, in particular those designed to solve different types of the jigsaw puzzle problem. However, most existing approaches fail, or aren't designed to…
Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can…
We consider interpolation-based derivative-free optimization in settings where only some derivatives are available. Such situations arise naturally in scientific computing applications involving simulations, adjoint-enabled components,…