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Found 18 papers, 3 papers with code
Inferring Change Points in High-Dimensional Linear Regression via Approximate Message Passing
We consider the problem of localizing change points in high-dimensional linear regression.
Spectral Estimators for Structured Generalized Linear Models via Approximate Message Passing
Our methodology is general, and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings.
Mixed Regression via Approximate Message Passing
For max-affine regression, we propose an algorithm that combines AMP with expectation-maximization to estimate intercepts of the model along with the signals.
Statistical-Computational Tradeoffs in Mixed Sparse Linear Regression
Via a simple reduction, this provides novel rigorous evidence for the existence of a computational barrier to solving exact support recovery in sparse phase retrieval with sample complexity $n = \tilde{o}(k^2)$.
Precise Asymptotics for Spectral Methods in Mixed Generalized Linear Models
In a mixed generalized linear model, the objective is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one.
Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices.
PCA Initialization for Approximate Message Passing in Rotationally Invariant Models
However, the existing analysis of AMP requires an initialization that is both correlated with the signal and independent of the noise, which is often unrealistic in practice.
Approximate Message Passing with Spectral Initialization for Generalized Linear Models
We consider the problem of estimating a signal from measurements obtained via a generalized linear model.
Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models
This allows us to compute the Bayes-optimal combination of $\hat{\boldsymbol x}^{\rm L}$ and $\hat{\boldsymbol x}^{\rm s}$, given the limiting distribution of the signal $\boldsymbol x$.
Estimation of Low-Rank Matrices via Approximate Message Passing
In this paper we present a practical algorithm that can achieve Bayes-optimal accuracy above the spectral threshold.
Empirical Bayes Estimators for High-Dimensional Sparse Vectors
An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the well-known soft-thresholding estimator.
A strong converse bound for multiple hypothesis testing, with applications to high-dimensional estimation
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator.
Multilayer Codes for Synchronization from Deletions
Consider two remote nodes, each having a binary sequence.
Information Theory Information Theory
Finite Sample Analysis of Approximate Message Passing Algorithms
The concentration inequality also indicates that the number of AMP iterations $t$ can grow no faster than order $\frac{\log n}{\log \log n}$ for the performance to be close to the state evolution predictions with high probability.
Cluster-Seeking James-Stein Estimators
The JS-estimator shrinks the observed vector towards the origin, and the risk reduction over the ML-estimator is greatest for $\boldsymbol{\theta}$ that lie close to the origin.
Capacity-achieving Sparse Superposition Codes via Approximate Message Passing Decoding
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity.
Lossy Compression via Sparse Linear Regression: Computationally Efficient Encoding and Decoding
The proposed encoding algorithm sequentially chooses columns of the design matrix to successively approximate the source sequence.
Lossy Compression via Sparse Linear Regression: Performance under Minimum-distance Encoding
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression.
