Combines PCA and AMP for better signal estimation in noisy data.
problem Estimating a rank-1 signal in rotationally invariant noise.
method Combines PCA and AMP, with PCA initialization at the start of AMP.
result Rigorous asymptotic characterization of the new estimator's performance.
AMP method reconstructs rank-one matrices from noisy data efficiently.
problem Reconstructing rank-one matrices with prior structural information from noisy observations.
method Approximate Message Passing (AMP) with random initialization.
result AMP from random initialization converges rapidly and globally.
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency. However, AMP suffers from serious convergence issues in contex…
New method improves sparse signal reconstruction using 1RSB-AMP.
problem Sparse signal reconstruction with improved accuracy.
method Developed 1RSB-AMP and 1RSB-SE for SCAD penalty minimization.
result 1RSB-AMP achieves improved reconstruction compared to RS-AMP.
Paper proposes AMP with spectral initialization for robust signal estimation.
problem Signal estimation from generalized linear model measurements with correlated initialization.
method Approximate message passing (AMP) with spectral initialization.
result Characterization of AMP with spectral initialization in high-dimensional limit.
This paper introduces SS-MAMP to address convergence issues in AMP algorithms.
problem Convergence issues in AMP algorithms for signal reconstruction.
method Proposes SS-MAMP algorithm framework for right-unitarily invariant sensing matrices and Lipschitz-continuous local processors.
result Covariance matrices of SS-MAMP are L-banded and convergent, ensuring optimal convergence.
New framework predicts AMP behavior in spiked models for finite iterations.
problem Understanding AMP dynamics in high-dimensional spiked models.
method Developed a non-asymptotic framework for AMP in spiked matrix estimation.
result Predicted AMP behavior for up to O(polylognn) iterations in Z2 synchronization. A new AMP-based method speeds up conformal prediction intervals.
problem Computational cost in building high-dimensional prediction intervals.
method Approximate Message Passing (AMP) to accelerate full conformal prediction.
result AMP-based method produces valid prediction intervals orders of magnitude faster.
AMP regularization improves deep learning models by favoring flat minima.
problem Improving deep learning model generalization and avoiding overfitting.
method AMP regularization uses adversarial model perturbation to minimize a norm-bounded perturbation of the empirical risk.
result AMP regularization leads to state-of-the-art performance across various deep architectures.
This paper applies AMP theory to improve learning tasks.
problem Improving learning efficiency by optimizing task-specific models.
method Uses aggregated Markov processes to reduce model complexity and enhance learning.
result Demonstrates how AMP theory can be effectively applied to stochastic learning.
Simple AMP algorithm robust to adversarial corruption.
problem Robust approximate message passing in spiked matrix models.
method Spectral pre-processing combined with robust spectral initialization.
result AMP output is close to correct for corrupted data.
This paper deals with chain graphs under the alternative Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. We also show that the extension of Meek's conjecture to AMP chain graphs does n…
We solve minimal separator problems in AMP chain graphs and improve structure learning algorithms.
problem Finding minimal separators in AMP chain graphs and learning their structure from data.
method We analyze and solve several versions of the minimal separator problem. We propose modifications to the PC-like algorithm and extend a decomposition-based method for AMP CGs.
result Our modifications of the PC-like algorithm and the LCD-AMP method improve structure learning and are more accurate and stable, especially in high-dimensional settings.
A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, today's denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorit…
The paper develops AMP theory for sparse and robust regression with polynomial iterations.
problem Challenges in high-dimensional statistical estimation due to asymptotic theory breakdown.
method Non-asymptotic distributional theory of AMP for sparse and robust regression.
result First finite-sample non-asymptotic distributional theory of AMP for polynomial iterations.
Unified tutorial on AMP for high-dimensional problems.
problem Structured high-dimensional statistical problems.
method Statistical perspective of AMP and its applications.
result Unified and strengthened results in AMP literature.
A fast, robust AMP algorithm for quadratic optimization problems.
problem Implementing robust approximate-message passing algorithms for quadratic optimization problems.
method Spectral pre-processing and mild modification of AMP algorithm iterates.
result Output solution close to AMP algorithm output for perturbed inputs.
Given the emerging global threat of antimicrobial resistance, new methods for next-generation antimicrobial design are urgently needed. We report a peptide generation framework PepCVAE, based on a semi-supervised variational autoencoder (VAE) model, for designing novel antimicrobial peptide (AMP) sequences. Our model l…
New AMP algorithms for rotationally invariant models with reduced complexity.
problem Signal estimation in generalized linear models with arbitrary spectral design matrices.
method Rotationally invariant approximate message passing (AMP) algorithms.
result Performance close to Vector AMP with significantly lower complexity.
Plug-and-play L-GM-AMP improves CS recovery for any i.i.d. source prior.
problem Efficiently recovering signals from compressed measurements with unknown priors.
method Deep learning with Gaussian-mixture model to approximate source prior, combined with learned denoising.
result L-GM-AMP achieves state-of-the-art performance without prior knowledge of source distribution.
AMP algorithms can be efficiently simulated by SDPs even with corrupted data.
problem Optimizing average-case optimization problems with corrupted data.
method Local statistics hierarchy semidefinite programs (SDPs) simulate AMP algorithms robustly.
result Robust guarantees for many AMP algorithms are offered, contrasting with strong lower bounds for SDPs.
We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes according to it. We show how this factorization makes it possible to perform infe…
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the regime where the problem dimension is large but finite. For concreteness, we co…
New algorithm improves signal reconstruction from noisy measurements with side information.
problem Reconstructing unknown signals from noisy linear measurements with side information.
method Integrates side information into approximate message passing (AMP) and tracks performance using state evolution.
result AMP-SI performance is accurately predicted by state evolution.
Unified framework for AMP iterations using graph indexing.
problem Complex high-dimensional statistical inference problems.
method Graph-based indexing of AMP iterations, modular proof of state evolution.
result Unified SE equations for AMP iterations indexed by graphs.
Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they can run orders of magnitude faster than exis…
Novel AMP framework for multi-environment transfer learning.
problem Characterizing risk of Lasso-based transfer learning estimators.
method Multi-Environment Generalized Long AMP (multi-environment GLAMP) framework.
result Precise characterization of the risk of three Lasso-based transfer learning estimators.
AMP algorithm for matrix tensor product model provides recovery conditions.
problem Generalization of standard spiked matrix models with multiple pairwise observations.
method Approximate message passing with optimal weighing and combining of estimates.
result Asymptotically exact performance description and necessary/sufficient recovery conditions.
Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machin…
New method combines regional HIV prevention trial data without sharing individual patient info.
problem Regional differences in HIV prevention efficacy, privacy concerns, and data sharing limitations.
method Federated learning approach that combines site-specific estimators via L1-regularization.
result Improved precision in estimating region-specific survival curves.
Study on identifying AMP chain graph models under known and unknown component decompositions.
problem Identifying AMP chain graph models with known and unknown chain component decompositions.
method Analyzes conditions for identifiability of AMP models and proposes algorithms for structure recovery.
result Conditions for DAG identifiability in AMP models extend equal variance criteria for Bayes nets.
New AMP algorithms improve multi-layer signal reconstruction.
problem Reconstructing signals and hidden variables from multi-layer networks with rotationally invariant weights.
method Developed multi-layer rotationally invariant generalized AMP (ML-RI-GAMP) algorithms and state evolution recursion.
result ML-RI-GAMP outperforms existing methods in terms of lower complexity and similar performance.
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show tha…
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error …
RBM learns in high dimensions via AMP and GD, reaching optimal weak recovery.
problem Learning from high-dimensional data with RBM.
method AMP and GD analysis for RBM training in high dimensions.
result RBM reaches optimal weak recovery threshold in spiked covariance model.
Bayes-optimal limits in PCA with structured noise are determined.
problem Analyzing statistical dependencies in measurement noise for high-dimensional inference.
method Study of spiked matrix model with low-order polynomial orthogonal noise, providing Bayes-optimal limits and proposing a novel AMP.
result A novel AMP algorithm reaches the information-theoretic limits for more general priors.
This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meek's conjecture to AMP chain graphs does not hold…
We compare various notions of weak subsolutions to degenerate complex Monge-Amp{è}re flows, showing that they all coincide. This allows us to show that the viscosity solution coincides with the envelope of pluripotential subsolutions. Dedicated to Duong Hong Phong on the occasion of his 65th birthday.
The paper constructs invariant Calabi-Yau structures on complexified symmetric spaces.
problem Constructing invariant Calabi-Yau structures on complexified symmetric spaces.
method Solutions of a Monge-Ampère type equation.
result Existence of solutions to the Monge-Ampère type equation.
This study optimizes multi-modal learning thresholds and algorithms in high dimensions.
problem Optimizing multi-modal learning performance in high-dimensional data.
method Analytical quantification and derivation of AMP algorithm with state evolution analysis.
result Bayes-optimal performance and recovery thresholds derived for multi-modal data.
New AMP algorithm estimates signals and latent variables in mixed regression models.
problem Estimating signals and latent variables in mixed regression models.
method Approximate Message Passing (AMP) algorithm for matrix GLM.
result State evolution recursion and optimal denoising functions for precise error minimization.
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not onl…
SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty. This non-separable penalty renders many existing techniques invalid or inconclusive in analyzing the SLOPE solution. In this pa…
EB-PCA reduces noise in high-dimensional PCA by estimating a joint prior distribution.
problem High-dimensional PCA noise in samples comparable to or larger than data.
method Empirical Bayes PCA using Kiefer-Wolfowitz MLE, random matrix theory, and AMP algorithm.
result EB-PCA achieves Bayes-optimal accuracy in spiked models and significantly improves over PCA in simulations and real data.
Any regular Gaussian probability distribution that can be represented by an AMP chain graph (CG) can be expressed as a system of linear equations with correlated errors whose structure depends on the CG. However, the CG represents the errors implicitly, as no nodes in the CG correspond to the errors. We propose in this…
Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.
problem Parameter estimation from generalized linear models with complex correlation structures.
method Spectral initialization and approximate message passing (AMP) algorithm.
result Established rigorous performance guarantees for spectral initialization and AMP.
The study shows how to accurately estimate embedding vectors in high dimensions.
problem How to accurately estimate embedding vectors in high-dimensional spaces.
method A simple probability model and a variant of low-rank approximate message passing (AMP) method.
result The AMP approach enables precise predictions of the accuracy of the estimation in certain high-dimensional limits.