Related papers: Least Squares Estimation For Hierarchical Data

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…

Implementing accurate Distribution System State Estimation (DSSE) faces several challenges, among which the lack of observability and the high density of the distribution system. While data-driven alternatives based on Machine Learning…

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…

Measuring the stability of conclusions derived from Ordinary Least Squares linear regression is critically important, but most metrics either only measure local stability (i.e. against infinitesimal changes in the data), or are only…

The U.S. Census Bureau collects and publishes detailed demographic data about Americans which are heavily used by researchers and policymakers. The Bureau has recently adopted the framework of differential privacy in an effort to improve…

Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

Due to the over-emphasize of the quantity of data, the data quality has often been overlooked. However, not all training data points contribute equally to learning. In particular, if mislabeled, it might actively damage the performance of…

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…

This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information…

Learning with noisy labels has gained increasing attention because the inevitable imperfect labels in real-world scenarios can substantially hurt the deep model performance. Recent studies tend to regard low-loss samples as clean ones and…

Inspired by recent developments in subdivision schemes founded on the Weighted Least Squares technique, we construct linear approximants for noisy data in which the weighting strategy minimizes the output variance, thereby establishing a…

A central problem in releasing aggregate information about sensitive data is to do so accurately while providing a privacy guarantee on the output. Recent work focuses on the class of linear queries, which include basic counting queries,…

In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonly…

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion -- the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation…

Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…

Distributed acoustic sensing (DAS) is a novel enabling technology that can turn existing fibre optic networks to distributed acoustic sensors. However, it faces the challenges of transmitting, storing, and processing massive streams of data…

This report summarizes major findings from an independent evaluation of 2020 census operations. The American Statistical Association 2020 Census Quality Indicators Task Force selected the authors to conduct the evaluation using nonpublic…

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent…

Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we…