相关论文: Statistics of Partial Minima

The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding…

This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…

The energy landscape for soft sphere packings exists in a high-dimensional space and plays host to an astronomical number of local minima in a hierarchical and ultrametric arrangement. Each point in the landscape is a configuration that can…

We consider the problem of estimating a $d$-dimensional discrete distribution from its samples observed under a $b$-bit communication constraint. In contrast to most previous results that largely focus on the global minimax error, we study…

Consider a random permutation of $kn$ objects that permutes $n$ disjoint blocks of size $k$ and then permutes elements within each block. Normalizing its cycle lengths by $kn$ gives a random partition of unity, and we derive the limit law…

We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ "anchors" lead to a global solution and a…

In the first paper of this series [S. Torquato, J. Chem. Phys. {\bf 136}, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in $d$-dimensional Euclidean space $\mathbb{R}^d$ were obtained,…

We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the…

Let $C\subset{\mathbb P}_K^2$ be an algebraic curve over a number field $K$, and denote by $d_K$ the degree of $K$ over ${\mathbb Q}$. We prove that the number of $K$-rational points of height at most $H$ in $C$ is bounded by $c…

We introduce and asses several Divide \& Conquer heuristic strategies aimed to solve large instances of the 0-1 Minimization Knapsack Problem. The method subdivides a large problem in two smaller ones (or recursive iterations of the same…

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…

In recent years, large high-dimensional data sets have become commonplace in a wide range of applications in science and commerce. Techniques for dimension reduction are of primary concern in statistical analysis. Projection methods play an…

Self similar 3D distributions of point-particles, with a given quasifractal dimension D, were generated on a Menger sponge model and then compared with \textit{2dfGRS} and \textit{Virgo project} data…

Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

This paper is essentially an exercise in studying the minima of a certain least squares optimization using the second partial derivative test. The motivation is to gain insight into an optimization-based solution to the problem of tracking…

We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in $[0, 1]^d$. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and…

The paper presents a formula for the reclassification of multidimensional data points (columns of real numbers, "objects", "vectors", etc.). This formula describes the change in the total squared error caused by reclassification of data…

Clustering is a fundamental problem in many scientific applications. Standard methods such as $k$-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal.…

We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…