Related papers: Optimality in Mean Estimation: Beyond Worst-Case, …
Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to…
Estimating the maximum mean finds a variety of applications in practice. In this paper, we study estimation of the maximum mean using an upper confidence bound (UCB) approach where the sampling budget is adaptively allocated to one of the…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
Estimating the geometric median of a dataset is a robust counterpart to mean estimation, and is a fundamental problem in computational geometry. Recently, [HSU24] gave an $(\varepsilon, \delta)$-differentially private algorithm obtaining an…
In numerous regular statistical models, median bias reduction (Kenne Pagui et al., 2017) has proven to be a noteworthy improvement over maximum likelihood, alternative to mean bias reduction. The estimator is obtained as solution to a…
We construct an algorithm, running in time $\tilde{\mathcal O}(N d + uK d)$, which is robust to outliers and heavy-tailed data and which achieves the subgaussian rate from [Lugosi, Mendelson] \begin{equation}\label{eq:intro_subgaus_rate}…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the…
We design an $(\varepsilon, \delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\Sigma$, that is adaptive to $\Sigma$. To within polylogarithmic factors, the estimator…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
The Median-of-Means (MoM) is a robust estimator widely used in machine learning that is known to be (minimax) optimal in scenarios where samples are i.i.d. In more grave scenarios, samples are contaminated by an adversary that can inspect…
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…
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…
Selecting the best alternative from a finite set represents a broad class of pure exploration problems. Traditional approaches to pure exploration have predominantly relied on Gaussian or sub-Gaussian assumptions on the performance…
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 consider the problem of mean estimation under user-level local differential privacy, where $n$ users are contributing through their local pool of data samples. Previous work assume that the number of data samples is the same across…
We study the robust mean estimation problem in high dimensions, where $\alpha <0.5$ fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…