Related papers: Bootstrapping Max Statistics in High Dimensions: N…
Split-plot or repeated measures designs are frequently used for planning experiments in the life or social sciences. Typical examples include the comparison of different treatments over time, where both factors may possess an additional…
This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…
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…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly…
The robust rank-order test (Fligner and Policello, 1981) was designed as an improvement of the non-parametric Wilcoxon-Mann-Whitney U-test to be more appropriate when the samples being compared have unequal variance. However, it tends to be…
Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…
We introduce a high-dimensional multiplier bootstrap for time series data based on capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
We propose a bootstrap-based test to detect a mean shift in a sequence of high-dimensional observations with unknown time-varying heteroscedasticity. The proposed test builds on the U-statistic based approach in Wang et al. (2022), targets…
We present a new fitting technique based on the parametric bootstrap method, which relies on the idea to produce artificial measurements using the estimated probability distribution of the experimental data. In order to investigate the main…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
Bootstrap is a principled and powerful frequentist statistical tool for uncertainty quantification. Unfortunately, standard bootstrap methods are computationally intensive due to the need of drawing a large i.i.d. bootstrap sample to…
Subsampled Newton methods approximate Hessian matrices through subsampling techniques, alleviating the cost of forming Hessian matrices but using sufficient curvature information. However, previous results require $\Omega (d)$ samples to…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…