Related papers: Sample Complexity Bounds for Robust Mean Estimatio…
In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or Case-wise Contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
Generalizing treatment effects from a randomized trial to a target population requires the assumption that potential outcome distributions are invariant across populations after conditioning on observed covariates. This assumption fails…
Generalization under distribution shift remains a core challenge in modern machine learning, yet existing learning bound theory is limited to narrow, idealized settings and is non-estimable from samples. In this paper, we bridge the gap…
The problem of communicating sensor measurements over shared networks is prevalent in many modern large-scale distributed systems such as cyber-physical systems, wireless sensor networks, and the internet of things. Due to bandwidth…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…
This paper studies the construction of adaptive confidence intervals under Huber's contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of…
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…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
We consider a Gaussian contamination (i.e., mixture) model where the contamination manifests itself as a change in variance. We study this model in various asymptotic regimes, in parallel with the work of Ingster (1997) and Donoho and Jin…
When machine learning models are deployed on a test distribution different from the training distribution, they can perform poorly, but overestimate their performance. In this work, we aim to better estimate a model's performance under…
Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
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…
This paper studies active learning in the context of robust statistics. Specifically, we propose a variant of the Best Arm Identification problem for \emph{contaminated bandits}, where each arm pull has probability $\varepsilon$ of…
We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result…
We study the problem of mean estimation for high-dimensional distributions, assuming access to a statistical query oracle for the distribution. For a normed space $X = (\mathbb{R}^d, \|\cdot\|_X)$ and a distribution supported on vectors $x…
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…