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Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
We propose a simple method to reproduce the ^1S_0 pairing properties of nuclear matter, which are obtained using a sophisticated model, by introducing a density-independent cutoff into the relativistic mean field model. This can be applied…
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix of the graph. In this survey article, we compute formulas…
We introduce an accurate, self-contained and automatic atom based numerical algorithm to characterize grain distributions in two dimensional Phase Field Crystal simulations. Four input parameters must be set by the user and their effect is…
We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an…
Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
When processing high-dimensional datasets, a common pre-processing step is feature selection. Filter-based feature selection algorithms are not tailored to a specific classification method, but rather rank the relevance of each feature with…
An algorithm to estimate motion from satellite imagery is presented. Dense displacement fields are computed from time-separated images of of significant convective activity using a Bayesian formulation of the motion estimation problem.…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
In this paper we present an interesting gadget based on the chain pair simplification problem under the discrete Fr\'echet distance (CPS-3F), which allows the construction of arbitrarily long paths that must be chosen in the simplification…
Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose ``disassembly and assembly of a graph'' algorithm which uses a solution of the problem on a…
In this paper numerical methods of computing distances between two Radon measures on R are discussed. Efficient algorithms for Wasserstein-type metrics are provided. In particular, we propose a novel algorithm to compute the flat metric…
We present a pipeline for parametric wireframe extraction from densely sampled point clouds. Our approach processes a scalar distance field that represents proximity to the nearest sharp feature curve. In intermediate stages, it detects…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…