Dan Yao

Bio: Dan Yao is an academic researcher from Heriot-Watt University. The author has contributed to research in topics: Expectation propagation & Uncertainty quantification. The author has an hindex of 1, co-authored 3 publications receiving 1 citations.

Joint Robust Linear Regression and Anomaly Detection in Poisson noise using Expectation-Propagation

Abstract: In this paper, we propose a new Expectation-Propagation (EP) algorithm to address the problem of joint robust linear regression and sparse anomaly detection from data corrupted by Poisson noise. Adopting an approximate Bayesian approach, an EP method is derived to approximate the posterior distribution of interest. The method accounts not only for additive anomalies, but also for destructive anomalies, i.e., anomalies that can lead to observations with amplitudes lower than the expected signals. Experiments conducted with both synthetic and real data illustrate the potential benefits of the proposed EP method in joint spectral unmixing and anomaly detection in the photon-starved regime of a Lidar system.

Robust Linear Regression and Anomaly Detection in the Presence of Poisson Noise Using Expectation-Propagation

Abstract: This paper presents a family of approximate Bayesian methods for joint anomaly detection and linear regression in the presence of non-Gaussian noise Robust anomaly detection using non-convex sparsity-promoting regularization terms is generally challenging, in particular when additional uncertainty measures about the estimation process are needed, eg, posterior probabilities of anomaly presence The problem becomes even more challenging in the presence of non-Gaussian, (eg, Poisson distributed), additional constraints on the regression coefficients (eg, positivity) and when the anomalies present complex structures (eg, structured sparsity) Uncertainty quantification is classically addressed using Bayesian methods Specifically, Monte Carlo methods are the preferred tools to handle complex models Unfortunately, such simulation methods suffer from a significant computational cost and are thus not scalable for fast inference in high dimensional problems In this paper, we thus propose fast alternatives based on Expectation-Propagation (EP) methods, which aim at approximating complex distributions by more tractable models to simplify the inference process The main problem addressed in this paper is linear regression and (sparse) anomaly detection in the presence of noisy measurements The aim of this paper is to demonstrate the potential benefits and assess the performance of such EP-based methods The results obtained illustrate that approximate methods can provide satisfactory results with a reasonable computational cost It is important to note that the proposed methods are sufficiently generic to be used in other applications involving condition monitoring

Patch-Based Image Restoration using Expectation Propagation.

Abstract: This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can suffer from scalability issues in high-dimensional inference problems such as image restoration. To address this issue, EP is used here to approximate the posterior distributions using products of multivariate Gaussian densities. Moreover, imposing structural constraints on the covariance matrices of these densities allows for greater scalability and distributed computation. While the method is naturally suited to handle additive Gaussian observation noise, it can also be extended to non-Gaussian noise. Experiments conducted for denoising, inpainting and deconvolution problems with Gaussian and Poisson noise illustrate the potential benefits of such flexible approximate Bayesian method for uncertainty quantification in imaging problems, at a reduced computational cost compared to sampling techniques.

Fast Scalable Image Restoration Using Total Variation Priors and Expectation Propagation

Abstract: This paper presents a scalable approximate Bayesian method for image restoration using Total Variation (TV) priors, with the ability to offer uncertainty quantification. In contrast to most optimization methods based on maximum a posteriori estimation, we use the Expectation Propagation (EP) framework to approximate minimum mean squared error (MMSE) estimates and marginal (pixel-wise) variances, without resorting to Monte Carlo sampling. For the classical anisotropic TV-based prior, we also propose an iterative scheme to automatically adjust the regularization parameter via Expectation Maximization (EM). Using Gaussian approximating densities with diagonal covariance matrices, the resulting method allows highly parallelizable steps and can scale to large images for denoising, deconvolution, and compressive sensing (CS) problems. The simulation results illustrate that such EP methods can provide a posteriori estimates on par with those obtained via sampling methods but at a fraction of the computational cost. Moreover, EP does not exhibit strong underestimation of posteriori variances, in contrast to variational Bayes alternatives.

Joint Robust Linear Regression and Anomaly Detection in Poisson noise using Expectation-Propagation

Abstract: In this paper, we propose a new Expectation-Propagation (EP) algorithm to address the problem of joint robust linear regression and sparse anomaly detection from data corrupted by Poisson noise. Adopting an approximate Bayesian approach, an EP method is derived to approximate the posterior distribution of interest. The method accounts not only for additive anomalies, but also for destructive anomalies, i.e., anomalies that can lead to observations with amplitudes lower than the expected signals. Experiments conducted with both synthetic and real data illustrate the potential benefits of the proposed EP method in joint spectral unmixing and anomaly detection in the photon-starved regime of a Lidar system.