Related papers: Least Squares Estimation For Hierarchical Data

Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often…

With advancements in sensor technology, a heterogeneous set of data, containing samples of scalar, waveform signal, image, or even structured point cloud are becoming increasingly popular. Developing a statistical model, representing the…

Thanks to the broadband nature of the Distributed Acoustic Sensing (DAS) measurement, a roadside section of the Stanford DAS-2 array can record seismic signals from various sources. For example, it measures the earth's quasi-static…

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…

In this brief, we present an enhanced privacy-preserving distributed estimation algorithm, referred to as the ``Double-Private Algorithm," which combines the principles of both differential privacy (DP) and cryptography. The proposed…

Hierarchical data analysis is crucial in various fields for making discoveries. The linear mixed model is often used for training hierarchical data, but its parameter estimation is computationally expensive, especially with big data.…

Large-scale well-annotated datasets are of great importance for training an effective object detector. However, obtaining accurate bounding box annotations is laborious and demanding. Unfortunately, the resultant noisy bounding boxes could…

This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…

As data-privacy requirements are becoming increasingly stringent and statistical models based on sensitive data are being deployed and used more routinely, protecting data-privacy becomes pivotal. Partial Least Squares (PLS) regression is…

Distributed Acoustic Sensing (DAS) enables continuous monitoring of dynamic strain along tens of kilometers of optical fiber, generating massive datasets whose interpretation and automated analysis remain challenging. DAS measurements often…

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…

Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

We study privacy-preserving sparse linear regression in the high-dimensional regime, focusing on the LASSO estimator. We analyze two widely used mechanisms for differential privacy: output perturbation, which injects noise into the…

Some complex problems, such as image tagging and natural language processing, are very challenging for computers, where even state-of-the-art technology is yet able to provide satisfactory accuracy. Therefore, rather than relying solely on…

Detection of anomalies among a large number of processes is a fundamental task that has been studied in multiple research areas, with diverse applications spanning from spectrum access to cyber-security. Anomalous events are characterized…

Given full or partial information about a collection of points that lie close to a union of several subspaces, subspace clustering refers to the process of clustering the points according to their subspace and identifying the subspaces. One…

Disclosure avoidance (DA) systems are used to safeguard the confidentiality of data while allowing it to be analyzed and disseminated for analytic purposes. These methods, e.g., cell suppression, swapping, and k-anonymity, are commonly…

Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. We consider an array model within which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array…

A novel combination of two widely-used clustering algorithms is proposed here for the detection and reduction of high data density regions. The Density Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is used for the…