Related papers: Decomposition Bounds for Marginal MAP
This work presents a parallel variant of the algorithm introduced in [Acceleration of block coordinate descent methods with identification strategies Comput. Optim. Appl. 72(3):609--640, 2019] to minimize the sum of a partially separable…
The challenge of mapping indoor environments is addressed. Typical heuristic algorithms for solving the motion planning problem are frontier-based methods, that are especially effective when the environment is completely unknown. However,…
A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…
Recent advancements in multi-modal large language models have propelled the development of joint probabilistic models capable of both image understanding and generation. However, we have identified that recent methods suffer from loss of…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
We solve the inverse problem of deblurring a pixelized image of Jupiter using regularized deconvolution and by sample-based Bayesian inference. By efficiently sampling the marginal posterior distribution for hyperparameters, then the full…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We introduce a novel bias-variance decomposition for a range of strictly convex margin losses, including the logistic loss (minimized by the classic LogitBoost algorithm), as well as the squared margin loss and canonical boosting loss.…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
Multi-sector capacity expansion models play a crucial role in energy planning by providing decision support for policymaking in technology development. To ensure reliable support, these models require high technological, spatial, and…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our methods are particularly well suited for convex quadratic programming problems…
Multi-agent planning (MAP) approaches have been typically conceived for independent or loosely-coupled problems to enhance the benefits of distributed planning between autonomous agents as solving this type of problems require less…