Related papers: Data Structures for Density Estimation
In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…
One way of characterizing the topological and structural properties of vertices and edges in a graph is by using structural similarity measures. Measures like Cosine, Jaccard and Dice compute the similarities restricted to the immediate…
We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…
The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set $S$ of $n$ points in $\mathbb{R}^d$, a point $y\in \mathbb{R}^d$, and an integer $2 \leq k \leq d$, find an affine combination…
We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…
We study the Densest At-Least-$k$-Subgraph (DAL$k$S) problem, in which we are given an undirected graph $G$ and an integer $k$, and the goal is to find a subgraph of $G$ with at least $k$ vertices with maximum density. The best-known…
Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
The key to out-of-distribution detection is density estimation of the in-distribution data or of its feature representations. This is particularly challenging for dense anomaly detection in domains where the in-distribution data has a…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
Robust mean estimation is one of the most important problems in statistics: given a set of samples in $\mathbb{R}^d$ where an $\alpha$ fraction are drawn from some distribution $D$ and the rest are adversarially corrupted, we aim to…
Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena…
Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of…