Related papers: Greedy Algorithms for Approximating the Diameter o…

A major problem in data augmentation is to ensure that the generated new samples cover the search space. This is a challenging problem and requires exploration for data augmentation policies to ensure their effectiveness in covering the…

$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$…

We prove algorithmic and hardness results for the problem of finding the largest set of a fixed diameter in the Euclidean space. In particular, we prove that if $A^*$ is the largest subset of diameter $r$ of $n$ points in the Euclidean…

Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in \cite{BCDDPW,DPW}, where…

Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…

We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…

We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…

Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network…

Current practice in parameter space exploration in euclidean space is dominated by randomized sampling or design of experiment methods. The biggest issue with these methods is not keeping track of what part of parameter space has been…

The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…

The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…

In large scale machine learning and data mining problems with high feature dimensionality, the Euclidean distance between data points can be uninformative, and Distance Metric Learning (DML) is often desired to learn a proper similarity…

We study the following range searching problem in high-dimensional Euclidean spaces: given a finite set $P\subset \mathbb{R}^d$, where each $p\in P$ is assigned a weight $w_p$, and radius $r>0$, we need to preprocess $P$ into a data…

We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…

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…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

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…

Motivated by modern applications such as computerized adaptive testing, sequential rank aggregation, and heterogeneous data source selection, we study the problem of active sequential estimation, which involves adaptively selecting…