skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


This content will become publicly available on August 1, 2026

Title: The impact of contamination and correlated design on the Lasso: An average case analysis
We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature.  more » « less
Award ID(s):
2045068
PAR ID:
10518765
Author(s) / Creator(s):
;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Statistics & Probability Letters
Volume:
223
Issue:
C
ISSN:
0167-7152
Page Range / eLocation ID:
110417
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S.; Katz, B.; Moore-Russo, D. (Ed.)
    We discuss two Dynamic Geometry Software applets designed as part of an Inquiry-Oriented instructional unit on determinants and share students' generalizations based on using the applet. Using the instructional design theory of Realistic Mathematics Education, our team developed a task sequence supporting students' guided reinvention of determinants. This unit leverages students' understanding of matrix transformations as distortion of space to meaningfully connect determinants to the transformation as the signed multiplicative change in area that objects in the domain undergo from the linear transformation. The applets are intended to provide students with feedback to help connect changes in the matrix to changes in the visualization of the linear transformation and, so, to changes in the determinant. Critically, the materials ask students to make generalizations while reflecting on their experiences using the applets. We discuss patterns among these generalizations and implications they have on the applets' design. 
    more » « less
  2. ; ; (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S.; Katz, B.; Moore-Russo, D. (Ed.)
    We discuss two Dynamic Geometry Software applets designed as part of an Inquiry-Oriented instructional unit on determinants and share students' generalizations based on using the applet. Using the instructional design theory of Realistic Mathematics Education, our team developed a task sequence supporting students' guided reinvention of determinants. This unit leverages students' understanding of matrix transformations as distortion of space to meaningfully connect determinants to the transformation as the signed multiplicative change in area that objects in the domain undergo from the linear transformation. The applets are intended to provide students with feedback to help connect changes in the matrix to changes in the visualization of the linear transformation and, so, to changes in the determinant. Critically, the materials ask students to make generalizations while reflecting on their experiences using the applets. We discuss patterns among these generalizations and implications they have on the applets' design. 
    more » « less
  3. ; ; (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S.; Katz, B.; Moore-Russo, D. (Ed.)
    We discuss two Dynamic Geometry Software applets designed as part of an Inquiry-Oriented instructional unit on determinants and share students' generalizations based on using the applet. Using the instructional design theory of Realistic Mathematics Education, our team developed a task sequence supporting students' guided reinvention of determinants. This unit leverages students' understanding of matrix transformations as distortion of space to meaningfully connect determinants to the transformation as the signed multiplicative change in area that objects in the domain undergo from the linear transformation. The applets are intended to provide students with feedback to help connect changes in the matrix to changes in the visualization of the linear transformation and, so, to changes in the determinant. Critically, the materials ask students to make generalizations while reflecting on their experiences using the applets. We discuss patterns among these generalizations and implications they have on the applets' design. 
    more » « less
  4. ; ; (, Journal of the Royal Statistical Society Series C: Applied Statistics)
    Abstract In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data. 
    more » « less
  5. ; ; ; ; (, IEEE Transactions on Control Systems Technology)
    null (Ed.)
    We present a method for dynamics-driven, user-interface design for a human-automation system via sensor selection. We define the user interface to be the output of a multiple-input-multiple-output (MIMO) linear time-invariant (LTI) system and formulate the design problem as one of selecting an output matrix from a given set of candidate output matrices. Necessary conditions for situation awareness are captured as additional constraints on the selection of the output matrix. These constraints depend on the level of trust the human has in the automation. We show that the resulting user-interface design problem is a combinatorial, set-cardinality minimization problem with set function constraints. We propose tractable algorithms to compute optimal or suboptimal solutions with suboptimality bounds. Our approaches exploit monotonicity and submodularity present in the design problem and rely on constraint programming and submodular maximization. We apply this method to the IEEE 118-bus, to construct correct-by-design interfaces under various operating scenarios. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email