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Found 22 papers, 8 papers with code
Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise
We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise.
Theoretical Analysis of Leave-one-out Cross Validation for Non-differentiable Penalties under High-dimensional Settings
Despite a large and significant body of recent work focused on estimating the out-of-sample risk of regularized models in the high dimensional regime, a theoretical understanding of this problem for non-differentiable penalties such as generalized LASSO and nuclear norm is missing.
Approximate Leave-one-out Cross Validation for Regression with $\ell_1$ Regularizers (extended version)
Recent theoretical work showed that approximate leave-one-out cross validation (ALO) is a computationally efficient and statistically reliable estimate of LO (and OO) for generalized linear models with differentiable regularizers.
Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems
We consider an inverse problem $\mathbf{y}= f(\mathbf{Ax})$, where $\mathbf{x}\in\mathbb{R}^n$ is the signal of interest, $\mathbf{A}$ is the sensing matrix, $f$ is a nonlinear function and $\mathbf{y} \in \mathbb{R}^m$ is the measurement vector.
Analysis of Sensing Spectral for Signal Recovery under a Generalized Linear Model
We define a notion for the spikiness of the spectrum of $\mathbf{A}$ and show the importance of this measure in the performance of the EP.
Optimal Data Detection and Signal Estimation in Systems with Input Noise
Practical systems often suffer from hardware impairments that already appear during signal generation.
Sharp Concentration Results for Heavy-Tailed Distributions
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions.
Error bounds in estimating the out-of-sample prediction error using leave-one-out cross validation in high-dimensions
We study the problem of out-of-sample risk estimation in the high dimensional regime where both the sample size $n$ and number of features $p$ are large, and $n/p$ can be less than one.
Does SLOPE outperform bridge regression?
A recently proposed SLOPE estimator (arXiv:1407. 3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503. 08393).
Consistent Risk Estimation in Moderately High-Dimensional Linear Regression
This paper studies the problem of risk estimation under the moderately high-dimensional asymptotic setting $n, p \rightarrow \infty$ and $n/p \rightarrow \delta>1$ ($\delta$ is a fixed number), and proves the consistency of three risk estimates that have been successful in numerical studies, i. e., leave-one-out cross validation (LOOCV), approximate leave-one-out (ALO), and approximate message passing (AMP)-based techniques.
Benefits of over-parameterization with EM
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective.
Approximate Leave-One-Out for High-Dimensional Non-Differentiable Learning Problems
$\mathcal{C} \subset \mathbb{R}^{p}$ is a closed convex set.
Approximate Leave-One-Out for Fast Parameter Tuning in High Dimensions
Consider the following class of learning schemes: $$\hat{\boldsymbol{\beta}} := \arg\min_{\boldsymbol{\beta}}\;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbol{\beta}; y_j) + \lambda R(\boldsymbol{\beta}),\qquad\qquad (1) $$ where $\boldsymbol{x}_i \in \mathbb{R}^p$ and $y_i \in \mathbb{R}$ denote the $i^{\text{th}}$ feature and response variable respectively.
Approximate message passing for amplitude based optimization
We consider an $\ell_2$-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations.
A scalable estimate of the extra-sample prediction error via approximate leave-one-out
Motivated by the low bias of the leave-one-out cross validation (LO) method, we propose a computationally efficient closed-form approximate leave-one-out formula (ALO) for a large class of regularized estimators.
Methodology
Global analysis of Expectation Maximization for mixtures of two Gaussians
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models.
Consistent Parameter Estimation for LASSO and Approximate Message Passing
For instance the following basic questions have not yet been studied in the literature: (i) How does the size of the active set $\|\hat{\beta}^\lambda\|_0/p$ behave as a function of $\lambda$?
From Denoising to Compressed Sensing
A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.
Parameterless Optimal Approximate Message Passing
In particular, both the final reconstruction error and the convergence rate of the algorithm crucially rely on how the threshold parameter is set at each step of the algorithm.
Asymptotic Analysis of LASSOs Solution Path with Implications for Approximate Message Passing
This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements.
Iterative Thresholding Algorithm for Sparse Inverse Covariance Estimation
In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized covariance matrix estimation is presented.
The Noise-Sensitivity Phase Transition in Compressed Sensing
We develop formal expressions for the MSE of \hxl, and evaluate its worst-case formal noise sensitivity over all types of k-sparse signals.
Statistics Theory Information Theory Information Theory Statistics Theory
