A Bayesian Perspective on Uncertainty Quantification for Estimated Graph Signals
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can be reinterpreted as finding the mean of a posterior Gaussian distribution, with a covariance matrix shaped by the graph structure. In this perspective, assumptions of signal smoothness as well as bandlimitedness are naturally expressible as the choice of certain prior distributions; noisy, noise-free or partial observations are expressible in terms of certain likelihood models. In addition to providing a point estimate, as most standard estimation strategies do, our probabilistic framework enables us to characterize the shape of the estimated signal distribution around the estimate in terms of the posterior covariance matrix.
Code (0)
등록된 구현이 없습니다.
Tasks
ImputationUncertainty QuantificationSimilar Papers 제목 키워드 기반
Benchmarking Uncertainty Quantification on Biosignal Classification Tasks under Dataset Shift
A biosignal is a signal that can be continuously measured from human bodies, such as respiratory sounds, heart activity (ECG), brain waves (EEG), etc, based on which, machine learning models have been developed with very…
BenchmarkingClassificationEEGElectroencephalogram (EEG)+1Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagation
This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal relations among time-h…
Causal DiscoveryUncertainty QuantificationHomodyned K-distribution: parameter estimation and uncertainty quantification using Bayesian neural networks
Quantitative ultrasound (QUS) allows estimating the intrinsic tissue properties. Speckle statistics are the QUS parameters that describe the first order statistics of ultrasound (US) envelope data. The parameters of Homo…
parameter estimationUncertainty QuantificationUncertainty Quantification With Noise Injection in Neural Networks: A Bayesian Perspective
Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robu…
Bayesian InferenceUncertainty QuantificationMulti-fidelity Machine Learning for Uncertainty Quantification and Optimization
In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly…
Bayesian OptimizationUncertainty Quantification