Related papers: An Efficient Algorithm for Matrix-Valued and Vecto…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant…
Bayesian inference in high-dimensional discrete-input additive noise models is a fundamental challenge in communication systems, as the support of the required joint a posteriori probability (APP) mass function grows exponentially with the…
Several algorithms have been used for mass transfer between particles undergoing advective and macro-dispersive random walks. The mass transfer between particles is required for general reactions on, and among, particles. The mass transfer…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
We propose a communication efficient quasi-Newton method for large-scale multi-agent convex composite optimization. We assume the setting of a network of agents that cooperatively solve a global minimization problem with strongly convex…
We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every…
We develop an Optimal Transportation Meshfree (OTM) particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle…
Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and…