Statistically and Computationally Efficient Variance Estimator for Kernel Ridge Regression

公共子空间的统计与计算最优估计与推断

Statistically and Computationally Optimal Estimation and Inference of Common Subspaces

针对多个对称低秩矩阵共享公共子空间的问题，提出基于投影梯度下降和谱平方和初始化的估计器，在强估计信噪比下达到最优 sinΘ 误差率，并在强推断信噪比下实现渐近正态分布的自适应置信区间。

Statistically consistent and computationally efficient inference of ancestral DNA sequences in the TKF91 model under dense taxon sampling

In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and branchings indicate past speciation events. Phylogenies are commonly estimated from molecular sequences, such as DNA sequences, collected from the species of interest. At a high level, the idea behind this inference is simple: the further apart in the Tree of Life are two species, the greater is the number of mutations to have accumulated in their genomes since their most recent common ancestor. In order to obtain a…

Approximate Kernel PCA Using Random Features: Computational vs. Statistical Trade-off

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistical consistency of most of these approximate kernel methods is not well understood except for kernel ridge regression wherein it has been shown that the random feature approximation is not only computationally efficient but also statistically consistent with a minimax optimal rate…

Scalable simultaneous inference in high-dimensional linear regression models

The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose pseudoinverse. Under a symmetry assumption on the available regressors, the estimators are normally distributed and accompanied by a closed-form expression for the standard errors that is free of tuning parameters. We study the numerical performance in Monte Carlo experiments that mimic the size of modern applications for which existing methods are computationall…

STARK通过自适应正则化来去噪空间转录组图像

STARK denoises spatial transcriptomics images via adaptive regularization

STARK通过自适应正则化和核方法有效去噪空间转录组图像，提升低测序深度下的细胞身份识别和基因表达插值能力。

Nonparametric Testing under Random Projection

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the specific kernel ridge regression setup, a simple distance-based test statistic is proposed. Notably, we derive the minimum number of random projections that is sufficient for achieving testing optimality in terms of the minimax rate. An adaptive testing procedure is further established without prior knowledge of regularity. One technical contribution is to establi…

大规模回归的随机投影

Random Projections For Large-Scale Regression

在大规模数据分析任务中，如果样本量和变量数量非常大，则拟合线性回归模型的计算成本非常高。随机投影被广泛用作机器学习和统计中的降维工具。我们讨论了随机投影在线性回归问题中的应用，以减少计算成本，并概述了推广误差的理论保证。可以表明，随机投影与最小二乘回归的组合导致与岭回归和主成分回归类似的恢复。我们还讨论了可能的改进时，平均多个随机投影，这种方法很容易并行实现。

Statistically Guided Divide-and-Conquer for Sparse Factorization of Large Matrix

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering, vector time series modeling, among others. The appeal of this factorization is owing to its power in discovering a highly-interpretable latent association network, either between samples and variables or between responses and predictors. However, many existing methods are either ad hoc without a general performance guarantee, or are computationally intensive…

On Estimation of Conditional Modes Using Multiple Quantile Regressions

We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate the conditional mode by finding the maximum of the estimated conditional density. The proposed method has two advantages in that it is computationally stable because it has no initial parameter dependencies, and it is statistically efficient with a fast convergence rate. Synthetic and real-world data experiments demonstrate the better performance of the prop…

固定k近邻密度泛函估计的双样本分析

Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators

我们提供有限样本分析的一般框架，使用k-最近邻统计估计泛函的非参数连续概率密度，包括熵和发散。不是将一致的密度估计值（这需要$k \to \infty$作为样本量$n \to \infty$）插入到感兴趣的泛函中，而是考虑固定k并执行偏差校正的估计值。这在计算上更有效，并且正如我们在某些情况下所示，在统计上，导致更快的收敛速度。我们的框架统一了几个以前的估计，其中大部分是我们的第一个有限样本保证。