Related papers: Mean Estimation in High-Dimensional Binary Markov …

We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and…

We study the task of high-dimensional entangled mean estimation in the subset-of-signals model. Specifically, given $N$ independent random points $x_1,\ldots,x_N$ in $\mathbb{R}^D$ and a parameter $\alpha \in (0, 1)$ such that each $x_i$ is…

We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$…

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…

We consider the problem of robust mean and location estimation w.r.t. any pseudo-norm of the form $x\in\mathbb{R}^d\to ||x||_S = \sup_{v\in S}<v,x>$ where $S$ is any symmetric subset of $\mathbb{R}^d$. We show that the deviation-optimal…

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…

Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

We study mean estimation for a Gaussian distribution with identity covariance in $\mathbb{R}^d$ under a missing data scheme termed realizable $\epsilon$-contamination model. In this model an adversary can choose a function $r(x)$ between 0…

We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection…

We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…

This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of…

We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…

Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

We present differentially private algorithms for high-dimensional mean estimation. Previous private estimators on distributions over $\mathbb{R}^d$ suffer from a curse of dimensionality, as they require $\Omega(d^{1/2})$ samples to achieve…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…