Related papers: Outperforming the Best 1D Low-Discrepancy Construc…
A fundamental open problem in learning theory is to characterize the best-case teaching dimension $\operatorname{TS}_{\min}$ of a concept class $\mathcal{C}$ with finite VC dimension $d$. Resolving this problem will, in particular, settle…
In this paper, we study the problem of {\em $k$-center clustering with outliers}. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a…
Motivated by the successful use of greedy algorithms for Reduced Basis Methods, a greedy method is proposed that selects N input data in an asymptotically optimal way to solve well-posed operator equations using these N data. The operator…
In this paper, we establish new advances in the theory started by T. Oikhberg in [15] where the author joins greedy approximation theory with the use of sequences with gaps. Concretely, we address and partially answer three open questions…
Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…
We study $(\alpha,\beta)$-spanners for weighted graphs. We propose a simple greedy completion procedure which starts from a sparse initial graph, and repeatedly fixes pairs of vertices with a bad stretch, generalizing Kunedsen's additive…
Decision Tree is a classic formulation of active learning: given $n$ hypotheses with nonnegative weights summing to 1 and a set of tests that each partition the hypotheses, output a decision tree using the provided tests that uniquely…
Examples are constructed of sparse subsequences of the integers for which the associated maximal averages operator is of weak type (1,1). A consequence, by transference, is that an almost everywhere L^1 -- type ergodic theorem holds for…
Although a generic uniformly distributed sequence has Poissonian pair correlations, only one explicit example has been found up to now. Additionally, it is even known that many classes of uniformly distributed sequences, like van der Corput…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…
Consider the Hitting Set problem where, for a given universe $\mathcal{X} = \left\{ 1, ... , n \right\}$ and a collection of subsets $\mathcal{S}_1, ... , \mathcal{S}_m$, one seeks to identify the smallest subset of $\mathcal{X}$ which has…
Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the…
We study the properties of points in $[0,1]^d$ generated by applying Hilbert's space-filling curve to uniformly distributed points in $[0,1]$. For deterministic sampling we obtain a discrepancy of $O(n^{-1/d})$ for $d\ge2$. For random…
We revisit the problem of computing an optimal partial cover of points by intervals. We show that the greedy algorithm computes a permutation $\Pi = \pi_1, \pi_2,\ldots$ of the intervals that is $3/4$-competitive for any prefix of $k$…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput sequences can be defined for abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is…
The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based…
Let $n$ and $\ell$ be positive integers. Recent papers by Kreher, Stinson and Veitch have explored variants of the problem of ordering the points in a triple system (such as a Steiner triple system, directed triple system or Mendelsohn…