The Generalized Lasso for Sub-Gaussian Measurements With Dithered Quantization

Thrampoulidis, Christos; Rawat, Ankit Singh

doi:10.1109/tit.2020.2965733

Cited by 20 publications

(33 citation statements)

References 23 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3) Upper bounding the convergence rate: Union bounding the events (17) and (19), we obtain upper and lower bounds on the singular values of [X 1] with the desired probability. Hence, we can bound the convergence rate of PGD as follows.…”

Section: Proof Of Theorem 35 For Subexponential Samplesmentioning

confidence: 99%

Quickly Finding the Best Linear Model in High Dimensions via Projected Gradient Descent

Sattar

Oymak

2020

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

We study the problem of finding the best linear model that can minimize least-squares loss given a dataset. While this problem is trivial in the low-dimensional regime, it becomes more interesting in high-dimensions where the population minimizer is assumed to lie on a manifold such as sparse vectors. We propose projected gradient descent (PGD) algorithm to estimate the population minimizer in the finite sample regime. We establish linear convergence rate and data-dependent estimation error bounds for PGD. Our contributions include: 1) The results are established for heavier tailed sub-exponential distributions besides sub-gaussian. 2) We directly analyze the empirical risk minimization and do not require a realizable model that connects input data and labels. 3) Our PGD algorithm is augmented to learn the bias terms which boosts the performance. The numerical experiments validate our theoretical results.

show abstract

Section: Proof Of Theorem 35 For Subexponential Samplesmentioning

confidence: 99%

Quickly Finding the Best Linear Model in High Dimensions via Projected Gradient Descent

Sattar

Oymak

2020

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…In particular, Corollary IV.1 is a special case of the main theorem in [29]. Several other interesting extensions of the result by Plan and Vershynin have recently appeared in the literature, e.g., [14], [16], [15], [32]. However, [29] is the only one to give results that are sharp in the flavor of this paper.…”

Section: A Least-squaresmentioning

confidence: 81%

Sharp Guarantees for Solving Random Equations with One-Bit Information

Taheri

Pedarsani

Thrampoulidis

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

Self Cite

View full text Add to dashboard Cite

We study the performance of a wide class of convex optimization-based estimators for recovering a signal from corrupted one-bit measurements in high-dimensions. Our general result predicts sharply the performance of such estimators in the linear asymptotic regime when the measurement vectors have entries IID Gaussian. This includes, as a special case, the previously studied least-squares estimator and various novel results for other popular estimators such as least-absolute deviations, hinge-loss and logistic-loss. Importantly, we exploit the fact that our analysis holds for generic convex loss functions to prove a bound on the best achievable performance across the entire class of estimators. Numerical simulations corroborate our theoretical findings and suggest they are accurate even for relatively small problem dimensions.

show abstract

“…In particular, Corollary 2 is a special case of the main theorem in [ 43 ]. Several other interesting extensions of the result by Plan and Vershynin have recently appeared in the literature (e.g., [ 41 , 62 , 63 , 64 ]). However, the one in [ 43 ] is the only one to give results that are sharp in the flavor of this paper.…”

Section: Appendix A1 Derivativesmentioning

confidence: 90%

Sharp Guarantees and Optimal Performance for Inference in Binary and Gaussian-Mixture Models

Taheri

Pedarsani

Thrampoulidis

2021

Entropy

Self Cite

View full text Add to dashboard Cite

We study convex empirical risk minimization for high-dimensional inference in binary linear classification under both discriminative binary linear models, as well as generative Gaussian-mixture models. Our first result sharply predicts the statistical performance of such estimators in the proportional asymptotic regime under isotropic Gaussian features. Importantly, the predictions hold for a wide class of convex loss functions, which we exploit to prove bounds on the best achievable performance. Notably, we show that the proposed bounds are tight for popular binary models (such as signed and logistic) and for the Gaussian-mixture model by constructing appropriate loss functions that achieve it. Our numerical simulations suggest that the theory is accurate even for relatively small problem dimensions and that it enjoys a certain universality property.

show abstract

The Generalized Lasso for Sub-Gaussian Measurements With Dithered Quantization

Cited by 20 publications

References 23 publications

Quickly Finding the Best Linear Model in High Dimensions via Projected Gradient Descent

Quickly Finding the Best Linear Model in High Dimensions via Projected Gradient Descent

Sharp Guarantees for Solving Random Equations with One-Bit Information

Sharp Guarantees and Optimal Performance for Inference in Binary and Gaussian-Mixture Models

Contact Info

Product

Resources

About