Design of Compressed Sensing Systems via Density-Evolution Framework for Structure Recovery in Graphical Models

• URL: http://arxiv.org/abs/2203.09636v1
• Date: Thu, 17 Mar 2022 22:16:38 GMT
• Title: Design of Compressed Sensing Systems via Density-Evolution Framework for Structure Recovery in Graphical Models
• Authors: Muralikrishnna G. Sethuraman, Hang Zhang, Faramarz Fekri
• Abstract summary: It has been shown that learning the structure of Bayesian networks from observational data is an NP-Hard problem. We propose a novel density-evolution based framework for optimizing compressed linear measurement systems. We show that the structure of GBN can indeed be recovered from resulting compressed measurements.
• Score: 10.667885727418705
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It has been shown that the task of learning the structure of Bayesian networks (BN) from observational data is an NP-Hard problem. Although there have been attempts made to tackle this problem, these solutions assume direct access to the observational data which may not be practical in certain applications. In this paper, we explore the feasibility of recovering the structure of Gaussian Bayesian Network (GBN) from compressed (low dimensional and indirect) measurements. We propose a novel density-evolution based framework for optimizing compressed linear measurement systems that would, by design, allow for more accurate retrieval of the covariance matrix and thereby the graph structure. In particular, under the assumption that both the covariance matrix and the graph are sparse, we show that the structure of GBN can indeed be recovered from resulting compressed measurements. The numerical simulations show that our sensing systems outperform the state of the art with respect to Maximum absolute error (MAE) and have comparable performance with respect to precision and recall, without any need for ad-hoc parameter tuning.

Related papers

• Graph Structure Learning with Interpretable Bayesian Neural Networks [10.957528713294874]
  We introduce novel iterations with independently interpretable parameters. These parameters influence characteristics of the estimated graph, such as edge sparsity. After unrolling these iterations, prior knowledge over such graph characteristics shape prior distributions. Fast execution and parameter efficiency allow for high-fidelity posterior approximation.
  arXiv  Detail & Related papers  (2024-06-20T23:27:41Z)
• Leveraging SPD Matrices on Riemannian Manifolds in Quantum Classical Hybrid Models for Structural Health Monitoring [0.0]
  Realtime finite element modeling of bridges assists modern structural health monitoring systems by providing comprehensive insights into structural integrity. FEM computational cost and the need for realtime analysis pose significant challenges. In this study, we propose a novel hybrid quantum classical Multilayer Perceptron pipeline.
  arXiv  Detail & Related papers  (2024-06-06T13:21:28Z)
• DA-Flow: Dual Attention Normalizing Flow for Skeleton-based Video Anomaly Detection [52.74152717667157]
  We propose a lightweight module called Dual Attention Module (DAM) for capturing cross-dimension interaction relationships in-temporal skeletal data. It employs the frame attention mechanism to identify the most significant frames and the skeleton attention mechanism to capture broader relationships across fixed partitions with minimal parameters and flops.
  arXiv  Detail & Related papers  (2024-06-05T06:18:03Z)
• Gaussian Ensemble Belief Propagation for Efficient Inference in High-Dimensional Systems [3.6773638205393198]
  Efficient inference in high-dimensional models is a central challenge in machine learning. We introduce the Ensemble Kalman Filter (EnKF) and Gaussian Belief Propagation (GaBP) GEnBP updates ensembles of prior samples into posterior samples by passing low-rank local messages over the edges of a graphical model.
  arXiv  Detail & Related papers  (2024-02-13T03:31:36Z)
• Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
  Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
  arXiv  Detail & Related papers  (2024-02-03T19:00:19Z)
• Dimensionality Reduction as Probabilistic Inference [10.714603218784175]
  Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. We introduce the ProbDR variational framework, which interprets a wide range of classical DR algorithms as probabilistic inference algorithms in this framework.
  arXiv  Detail & Related papers  (2023-04-15T23:48:59Z)
• Bayesian Structure Learning with Generative Flow Networks [85.84396514570373]
  In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) from data. Recently, a class of probabilistic models, called Generative Flow Networks (GFlowNets), have been introduced as a general framework for generative modeling. We show that our approach, called DAG-GFlowNet, provides an accurate approximation of the posterior over DAGs.
  arXiv  Detail & Related papers  (2022-02-28T15:53:10Z)
• Efficient Micro-Structured Weight Unification and Pruning for Neural Network Compression [56.83861738731913]
  Deep Neural Network (DNN) models are essential for practical applications, especially for resource limited devices. Previous unstructured or structured weight pruning methods can hardly truly accelerate inference. We propose a generalized weight unification framework at a hardware compatible micro-structured level to achieve high amount of compression and acceleration.
  arXiv  Detail & Related papers  (2021-06-15T17:22:59Z)
• Efficient Semi-Implicit Variational Inference [65.07058307271329]
  We propose an efficient and scalable semi-implicit extrapolational (SIVI) Our method maps SIVI's evidence to a rigorous inference of lower gradient values.
  arXiv  Detail & Related papers  (2021-01-15T11:39:09Z)
• Graph Convolutional Neural Networks for Body Force Prediction [0.0]
  A graph based data-driven model is presented to perform inference on fields defined on an unstructured mesh. The network can infer from field samples at different resolutions, and is invariant to the order in which the measurements within each sample are presented.
  arXiv  Detail & Related papers  (2020-12-03T19:53:47Z)
• Augmented Parallel-Pyramid Net for Attention Guided Pose-Estimation [90.28365183660438]
  This paper proposes an augmented parallel-pyramid net with attention partial module and differentiable auto-data augmentation. We define a new pose search space where the sequences of data augmentations are formulated as a trainable and operational CNN component. Notably, our method achieves the top-1 accuracy on the challenging COCO keypoint benchmark and the state-of-the-art results on the MPII datasets.
  arXiv  Detail & Related papers  (2020-03-17T03:52:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.