Related papers: A Multiscale Scan Statistic for Adaptive Submatrix…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…
Given an observation $\mathbf Y \in \mathbb{R}^{d_1\times d_2}$ from the model $\mathbf Y = \mathbf X + \mathbf E$ where $\mathbf X$ is constant and $\mathbf E$ has i.i.d. $N(0,1)$ entries, we consider the problem of detecting a planted…
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
We consider the problem of detecting an elevated mean on an interval with unknown location and length in the univariate Gaussian sequence model. Recent results have shown that using scale-dependent critical values for the scan statistic…
Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…
Matrix form data sets arise in many areas, so there are lots of works about the matrix regression models. One special model of these models is the adaptive nuclear norm regularized trace regression, which has been proven have good…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…
While a broad range of techniques have been proposed to tackle distribution shift, the simple baseline of training on an $\textit{undersampled}$ balanced dataset often achieves close to state-of-the-art-accuracy across several popular…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…