Related papers: Depth Distribution in High Dimensions

Suppose the data consist of a set $S$ of points $x_j$, $1\leq j \leq J$, distributed in a bounded domain $D\subset R^N$, where $N$ is a large number. An algorithm is given for finding the sets $L_k$ of dimension $k\ll N$, $k=1,2,...K$, in a…

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least $(1-\eps)$…

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…

We apply a recently developed framework for analyzing the convergence of stochastic algorithms to the general problem of large-scale nonconvex composite optimization more generally, and nonconvex likelihood maximization in particular. Our…

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…

In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…

We propose a new approach for the problem of relative depth estimation from a single image. Instead of directly regressing over depth scores, we formulate the problem as estimation of a probability distribution over depth and aim to learn…

Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…

In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…

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 $O(n+ 1/\varepsilon^{d-1})$…

A disk graph is an intersection graph of disks in the Euclidean plane, where the disks correspond to the vertices of the graph and a pair of vertices are adjacent if and only if their corresponding disks intersect. The problem of…

Deep learning has achieved tremendous success with independent and identically distributed (i.i.d.) data. However, the performance of neural networks often degenerates drastically when encountering out-of-distribution (OoD) data, i.e., when…

Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…

In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…

Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges…

In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…

Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…

The process of aggregation is ubiquitous in almost all deep nets models. It functions as an important mechanism for consolidating deep features into a more compact representation, whilst increasing robustness to overfitting and providing…

Let $V$ be the set of real common solutions to $F = (f_1, \ldots, f_s)$ in $\mathbb{R}[x_1, \ldots, x_n]$ and $D$ be the maximum total degree of the $f_i$'s. We design an algorithm which on input $F$ computes the dimension of $V$. Letting…

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…