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.
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 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…
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…
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the independence models represented by a set of directed and acyclic graphs under conditioning. This impli…
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…
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…
We address the problem of finding a minimal separator in an Andersson-Madigan-Perlman chain graph (AMP CG), namely, finding a set Z of nodes that separates a given nonadjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial-time algorit…
An intervention may have an effect on units other than those to which it was administered. This phenomenon is called interference and it usually goes unmodeled. In this paper, we propose to combine Lauritzen-Wermuth-Frydenberg and Andersson-Madigan-Perlman chain graphs to create a new class of causal models that can re…
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.
Paper tackles robust graph matching in dense graphs with AMP type algorithm.
problem Matching recovery between correlated Gaussian Wigner matrices with adversarial perturbations.
method Approximate Message Passing (AMP) type iterative algorithm with time-dependent matrix multiplication.
result Algorithm succeeds in polynomial time for non-vanishing correlation and small perturbations.
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
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.
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.
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. 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.
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.
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.
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.
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.
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.
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.
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.
Proposes a non-conjugate model selection method for chain event graphs.
problem Existing model selection algorithms for chain event graphs rely on conjugate priors, which is unrealistic for many real-world applications.
method Proposes a mixture modelling approach to model selection in chain event graphs that does not rely on conjugacy.
result The proposed method is more scalable and robust than existing algorithms.
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.
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…
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.
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.
GNNs improve supply chain analytics with real-world benchmarks.
problem Limited research on applying GNNs to supply chain management.
method Conceptual discussions, detailed formulations, examples, mathematical definitions, and task guidelines.
result GNN-based models outperform other methods by 10-40% in various supply chain tasks.
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.
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.
In this paper, we extend Meek's conjecture (Meek 1997) from directed and acyclic graphs to chain graphs, and prove that the extended conjecture is true. Specifically, we prove that if a chain graph H is an independence map of the independence model induced by another chain graph G, then (i) G can be transformed into H …
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.
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.
stCEG models spatial events using Chain Event Graphs in R.
problem Modeling events over spatial areas.
method Full specification of CEG models from data, interactive plots, web GUI.
result First software for CEGs with full model customisation.
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…
FS-GCLSTM predicts stock returns by leveraging value-chain relationships.
problem Traditional time series models fail to capture complex interdependencies in modern markets.
method FS-GCLSTM integrates value-chain networks and graph convolutions to predict stock returns.
result FS-GCLSTM consistently delivers superior portfolio performance compared to traditional models.
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.
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.
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.
Study of Bayes optimal learning in high-dimensional linear regression with network side information.
problem Bayes optimal learning in high-dimensional linear regression with network side information.
method Introduce a Reg-Graph model and an iterative AMP algorithm for Bayes optimality under general conditions.
result Characterization of the limiting mutual information between latent signal and data observed.
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…
New AMP algorithm detects change points in high-dimensional GLMs.
problem Detecting change points in high-dimensional GLMs.
method Approximate Message Passing (AMP) algorithm for estimating signals and change points.
result Characterization of AMP algorithm's performance in high-dimensional limit.
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.