相关论文: Optimal False Discovery Control of Minimax Estimat…
We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…
This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not…
An explicit solution is derived for the Bellman inequality corresponding to minimax optimal dual control. The minimizing player determines control action as a function of past state measurements and inputs. The maximizing player selects…
High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…
The mitigation of false positives is an important issue when conducting multiple hypothesis testing. The most popular paradigm for false positives mitigation in high-dimensional applications is via the control of the false discovery rate…
Selecting relevant features associated with a given response variable is an important issue in many scientific fields. Quantifying quality and uncertainty of a selection result via false discovery rate (FDR) control has been of recent…
We study one-way matching of a pair of datasets with low rank signals. Under a stylized model, we first derive information-theoretic limits of matching under a mismatch proportion loss. We then show that linear assignment with projected…
In energy-efficient schemes, finding the optimal size of deep learning models is very important and has a broad impact. Meanwhile, recent studies have reported an unexpected phenomenon, the sparse double descent: as the model's sparsity…
We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the…
Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $\Omega(n^{2/3})$ dimension-free minimax regret lower…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
We show that, under a standard hardness assumption, there is no computationally efficient algorithm that given $n$ samples from an unknown distribution can give valid answers to $n^{3+o(1)}$ adaptively chosen statistical queries. A…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
The false discovery rate (FDR) and the false non-discovery rate (FNR), defined as the expected false discovery proportion (FDP) and the false non-discovery proportion (FNP), are the most popular benchmarks for multiple testing. Despite the…
In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one…
This paper considers point and interval estimation of the $\ell_q$ loss of an estimator in high-dimensional linear regression with random design. We establish the minimax rate for estimating the $\ell_{q}$ loss and the minimax expected…
Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we…
Variable selection has been widely used in data analysis for the past decades, and it becomes increasingly important in the Big Data era as there are usually hundreds of variables available in a dataset. To enhance interpretability of a…
While data-driven confounder selection requires careful consideration, it is frequently employed in observational studies. Widely recognized criteria for confounder selection include the minimal-set approach, which involves selecting…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…