Related papers: Finding Low Star Discrepancy 3D Kronecker Point Se…
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Korobov point sets in the unit cube. It was observed recently that this new characteristic allows us to obtain optimal rate of…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we show an upper bound on the star discrepancy of order…
Several applications in communication, control, and learning require approximating target distributions to within small informational divergence (I-divergence). The additional requirement of invertibility usually leads to using encoders…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\'z}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}} s \ve^{-2}$. This is equivalent to the fact that for any…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Astrometric calibration of images with a small field of view is often inferior to the internal accuracy of the source detections due to the small number of accessible guide stars. One important experiment with such challenges is the Hubble…
The spherical cap discrepancy is a prominent measure of uniformity for sets on the d-dimensional sphere. It is particularly important for estimating the integration error for certain classes of functions on the sphere. Building on a…
Methods to determine abundances of the elements in the atmospheres of F, G, and K stars with precisions of 0.01-0.03 dex are reviewed. Such high-precision stellar abundances have led to the discovery of unexpected phenomena and relations…
Spectral clustering is a well-known technique which identifies $k$ clusters in an undirected graph with weight matrix $W\in\mathbb{R}^{n\times n}$ by exploiting its graph Laplacian $L(W)$, whose eigenvalues $0=\lambda_1\leq \lambda_2 \leq…
With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over…
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…
We establish sharp non-asymptotic probabilistic bounds for the star discrepancy of double-infinite random matrices -- a canonical model for sequences of random point sets in high dimensions. By integrating the recently proved…
We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set consisting of $N$ points chosen uniformly at random in the $s$-dimensional unit cube $[0,1]^s$ with probability at least $1-\exp(-\Theta(s))$…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O(n^1/2). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In…
We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most $t$ sets. We give an algorithm that finds a coloring with discrepancy $O((t \log n \log s)^{1/2})$ where $s$ is the…
We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of our results. First, among…