Related papers: A Minimax Theory for Adaptive Data Analysis

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between…

We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of…

Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report…

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…

We study schemes and lower bounds for distributed minimax statistical estimation over a Gaussian multiple-access channel (MAC) under squared error loss, in a framework combining statistical estimation and wireless communication. First, we…

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 propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…

In this work, we improve on the upper and lower bounds for the regret of online learning with strongly observable undirected feedback graphs. The best known upper bound for this problem is $\mathcal{O}\bigl(\sqrt{\alpha T\ln K}\bigr)$,…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each…

We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that…

We investigate lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo under any adaptation strategy. In particular, we prove general lower bounds in total variation and on the weak convergence rate under general…

Consider a kidney-exchange application where we want to find a max-matching in a random graph. To find whether an edge $e$ exists, we need to perform an expensive test, in which case the edge $e$ appears independently with a \emph{known}…

We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…

This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…

This paper studies the statistical theory of batch data reinforcement learning with function approximation. Consider the off-policy evaluation problem, which is to estimate the cumulative value of a new target policy from logged history…

We prove a new minimax theorem connecting the worst-case Bayesian regret and minimax regret under partial monitoring with no assumptions on the space of signals or decisions of the adversary. We then generalise the information-theoretic…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…