Related papers: Statistical-Computational Trade-offs for Density E…

The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…

In classical statistics and distribution testing, it is often assumed that elements can be sampled from some distribution $P$, and that when an element $x$ is sampled, the probability $P$ of sampling $x$ is also known. Recent work in…

We present a polynomial-time reduction from solving noisy linear equations over $\mathbb{Z}/q\mathbb{Z}$ in dimension $\Theta(k\log n/\mathsf{poly}(\log k,\log q,\log\log n))$ with a uniformly random coefficient matrix to noisy linear…

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…

Let $P$ be a set of $n$ colored points. We develop efficient data structures that store $P$ and can answer chromatic $k$-nearest neighbor ($k$-NN) queries. Such a query consists of a query point $q$ and a number $k$, and asks for the color…

In the problem of semialgebraic range searching, we are to preprocess a set of points in $\mathbb{R}^D$ such that the subset of points inside a semialgebraic region described by $O(1)$ polynomial inequalities of degree $\Delta$ can be found…

This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…

Given a graph and an integer $k$, Densest $k$-Subgraph is the algorithmic task of finding the subgraph on $k$ vertices with the maximum number of edges. This is a fundamental problem that has been subject to intense study for decades, with…

Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where…

Functions of the ratio of the densities $p/q$ are widely used in machine learning to quantify the discrepancy between the two distributions $p$ and $q$. For high-dimensional distributions, binary classification-based density ratio…

$\newcommand{\dist}{\operatorname{dist}}$ In this paper we define the notion of a probabilistic neighborhood in spatial data: Let a set $P$ of $n$ points in $\mathbb{R}^d$, a query point $q \in \mathbb{R}^d$, a distance metric $\dist$, and…

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…

This paper proposes an easy-to-compute upper bound for the overlap index between two probability distributions without requiring any knowledge of the distribution models. The computation of our bound is time-efficient and memory-efficient…

We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…

We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…

This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this…