相关论文: Thin Partitions: Isoperimetric Inequalities and Sa…

Neural network ensembling is a common and robust way to increase model efficiency. In this paper, we propose a new neural network ensemble algorithm based on Audibert's empirical star algorithm. We provide optimal theoretical minimax bound…

Next generation radio telescopes, like the Square Kilometre Array, will acquire an unprecedented amount of data for radio astronomy. The development of fast, parallelisable or distributed algorithms for handling such large-scale data sets…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

We study the expected star discrepancy under a newly designed class of non-equal volume partitions. The main contributions are twofold. First, we establish a strong partition principle for the star discrepancy, showing that our newly…

A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…

In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…

Due to the current lack of large-scale datasets at the million-scale level, tasks involving panoramic images predominantly rely on existing two-dimensional pre-trained image benchmark models as backbone networks. However, these networks are…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…

X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…

A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…

We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…

Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental constraints project onto a subspace of viable…

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

Two commonly arising computational tasks in Bayesian learning are Optimization (Maximum A Posteriori estimation) and Sampling (from the posterior distribution). In the convex case these two problems are efficiently reducible to each other.…

In this work, we propose a new segmentation algorithm for images containing convex objects present in multiple shapes with a high degree of overlap. The proposed algorithm is carried out in two steps, first we identify the visible contours,…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…