Fast Real-Time DC State Estimation in Electric Power Systems Using Belief Propagation

We propose a fast real-time state estimator based on the belief propagation algorithm for the power system state estimation. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrix-based state estimation methods, the belief propagation approach is robust to ill-conditioned scenarios caused by significant differences between measurement variances, thus resulting in a solution that eliminates observability analysis. Using the DC model, we numerically demonstrate the performance of the state estimator in a realistic real-time system model with asynchronous measurements. We note that the extension to the AC state estimation is possible within the same framework.Comment: 6 pages; 7 figures; submitted in the IEEE International Conference on Smart Grid Communications (SmartGridComm 2017

Inference of causality in epidemics on temporal contact networks

Investigating into the past history of an epidemic outbreak is a paramount problem in epidemiology. Based on observations about the state of individuals, on the knowledge of the network of contacts and on a mathematical model for the epidemic process, the problem consists in describing some features of the posterior distribution of unobserved past events, such as the source, potential transmissions, and undetected positive cases. Several methods have been proposed for the study of these inference problems on discrete-time, synchronous epidemic models on networks, including naive Bayes, centrality measures, accelerated Monte-Carlo approaches and Belief Propagation. However, most traced real networks consist of short-time contacts on continuous time. A possibility that has been adopted is to discretize time line into identical intervals, a method that becomes more and more precise as the length of the intervals vanishes. Unfortunately, the computational time of the inference methods increase with the number of intervals, turning a sufficiently precise inference procedure often impractical. We show here an extension of the Belief Propagation method that is able to deal with a model of continuous-time events, without resorting to time discretization. We also investigate the effect of time discretization on the quality of the inference

A closure for the Master Equation starting from the Dynamic Cavity Method

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner, and which performs better on several important classes of problems.Comment: arXiv admin note: text overlap with arXiv:2205.0075

Non-parametric belief propagation for mobile mapping sensor fusion

© 2016 Wuhan University. Published by Informa UK Limited, trading as Taylor & Francis Group. Many different forms of sensor fusion have been proposed each with its own niche. We propose a method of fusing multiple different sensor types. Our approach is built on the discrete belief propagation to fuse photogrammetry with GPS to generate three-dimensional (3D) point clouds. We propose using a non-parametric belief propagation similar to Sudderth et al’s work to fuse different sensors. This technique allows continuous variables to be used, is trivially parallel making it suitable for modern many-core processors, and easily accommodates varying types and combinations of sensors. By defining the relationships between common sensors, a graph containing sensor readings can be automatically generated from sensor data without knowing a priori the availability or reliability of the sensors. This allows the use of unreliable sensors which firstly, may start and stop providing data at any time and secondly, the integration of new sensor types simply by defining their relationship with existing sensors. These features allow a flexible framework to be developed which is suitable for many tasks. Using an abstract algorithm, we can instead focus on the relationships between sensors. Where possible we use the existing relationships between sensors rather than developing new ones. These relationships are used in a belief propagation algorithm to calculate the marginal probabilities of the network. In this paper, we present the initial results from this technique and the intended course for future work

Kernel Belief Propagation

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results