Improved message passing for inference in densely connected systems

An improved inference method for densely connected systems is presented. The approach is based on passing condensed messages between variables, representing macroscopic averages of microscopic messages. We extend previous work that showed promising results in cases where the solution space is contiguous to cases where fragmentation occurs. We apply the method to the signal detection problem of Code Division Multiple Access (CDMA) for demonstrating its potential. A highly efficient practical algorithm is also derived on the basis of insight gained from the analysis. © EDP Sciences.

Message passing for task redistribution on sparse graphs

The problem of resource allocation in sparse graphs with real variables is studied using methods of statistical physics. An efficient distributed algorithm is devised on the basis of insight gained from the analysis and is examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

Message-passing algorithms for optimal utilization of cognitive radio networks

Cognitive Radio has been proposed as a key technology to significantly improve spectrum usage in wireless networks by enabling unlicensed users to access unused resource. We present new algorithms that are needed for the implementation of opportunistic scheduling policies that maximize the throughput utilization of resources by secondary users, under maximum interference constraints imposed by existing primary users. Our approach is based on the Belief Propagation (BP) algorithm, which is advantageous due to its simplicity and potential for distributed implementation. We examine convergence properties and evaluate the performance of the proposed BP algorithms via simulations and demonstrate that the results compare favorably with a benchmark greedy strategy. © 2013 IEEE.

Message-passing for inference and optimization of real variables on sparse graphs

The inference and optimization in sparse graphs with real variables is studied using methods of statistical mechanics. Efficient distributed algorithms for the resource allocation problem are devised. Numerical simulations show excellent performance and full agreement with the theoretical results. © Springer-Verlag Berlin Heidelberg 2006.

Message passing for distributed optimisation of power allocation with renewable resources

The increase in renewable energy generators introduced into the electricity grid is putting pressure on its stability and management as predictions of renewable energy sources cannot be accurate or fully controlled. This, with the additional pressure of fluctuations in demand, presents a problem more complex than the current methods of controlling electricity distribution were designed for. A global approximate and distributed optimisation method for power allocation that accommodates uncertainties and volatility is suggested and analysed. It is based on a probabilistic method known as message passing [1], which has deep links to statistical physics methodology. This principled method of optimisation is based on local calculations and inherently accommodates uncertainties; it is of modest computational complexity and provides good approximate solutions.We consider uncertainty and fluctuations drawn from a Gaussian distribution and incorporate them into the message-passing algorithm. We see the effect that increasing uncertainty has on the transmission cost and how the placement of volatile nodes within a grid, such as renewable generators or consumers, effects it.

Efficient Bayesian inference for learning in the Ising linear perceptron and signal detection in CDMA

Efficient new Bayesian inference technique is employed for studying critical properties of the Ising linear perceptron and for signal detection in code division multiple access (CDMA). The approach is based on a recently introduced message passing technique for densely connected systems. Here we study both critical and non-critical regimes. Results obtained in the non-critical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also studied. © 2006 Elsevier B.V. All rights reserved.

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

Inference by belief propagation in composite systems

We devise a message passing algorithm for probabilistic inference in composite systems, consisting of a large number of variables, that exhibit weak random interactions among all variables and strong interactions with a small subset of randomly chosen variables; the relative strength of the two interactions is controlled by a free parameter. We examine the performance of the algorithm numerically on a number of systems of this type for varying mixing parameter values.

Improved detection in CDMA for biased sources

We consider the detection of biased information sources in the ubiquitous code-division multiple-access (CDMA) scheme. We propose a simple modification to both the popular single-user matched-filter detector and a recently introduced near-optimal message-passing-based multiuser detector. This modification allows for detecting modulated biased sources directly with no need for source coding. Analytical results and simulations with excellent agreement are provided, demonstrating substantial improvement in bit error rate in comparison with the unmodified detectors and the alternative of source compression. The robustness of error-performance improvement is shown under practical model settings, including bias estimation mismatch and finite-length spreading codes. © 2007 IOP Publishing Ltd.

The interplay between microscopic and mesoscopic structures in complex networks

Understanding a complex network's structure holds the key to understanding its function. The physics community has contributed a multitude of methods and analyses to this cross-disciplinary endeavor. Structural features exist on both the microscopic level, resulting from differences between single node properties, and the mesoscopic level resulting from properties shared by groups of nodes. Disentangling the determinants of network structure on these different scales has remained a major, and so far unsolved, challenge. Here we show how multiscale generative probabilistic exponential random graph models combined with efficient, distributive message-passing inference techniques can be used to achieve this separation of scales, leading to improved detection accuracy of latent classes as demonstrated on benchmark problems. It sheds new light on the statistical significance of motif-distributions in neural networks and improves the link-prediction accuracy as exemplified for gene-disease associations in the highly consequential Online Mendelian Inheritance in Man database. © 2011 Reichardt et al.

The design of fault tolerant software for loosely coupled distributed systems

Requirements for systems to continue to operate satisfactorily in the presence of faults has led to the development of techniques for the construction of fault tolerant software. This thesis addresses the problem of error detection and recovery in distributed systems which consist of a set of communicating sequential processes. A method is presented for the `a priori' design of conversations for this class of distributed system. Petri nets are used to represent the state and to solve state reachability problems for concurrent systems. The dynamic behaviour of the system can be characterised by a state-change table derived from the state reachability tree. Systematic conversation generation is possible by defining a closed boundary on any branch of the state-change table. By relating the state-change table to process attributes it ensures all necessary processes are included in the conversation. The method also ensures properly nested conversations. An implementation of the conversation scheme using the concurrent language occam is proposed. The structure of the conversation is defined using the special features of occam. The proposed implementation gives a structure which is independent of the application and is independent of the number of processes involved. Finally, the integrity of inter-process communications is investigated. The basic communication primitives used in message passing systems are seen to have deficiencies when applied to systems with safety implications. Using a Petri net model a boundary for a time-out mechanism is proposed which will increase the integrity of a system which involves inter-process communications.

Finding structures in information networks using the affinity network

This thesis proposes a novel graphical model for inference called the Affinity Network,which displays the closeness between pairs of variables and is an alternative to Bayesian Networks and Dependency Networks. The Affinity Network shares some similarities with Bayesian Networks and Dependency Networks but avoids their heuristic and stochastic graph construction algorithms by using a message passing scheme. A comparison with the above two instances of graphical models is given for sparse discrete and continuous medical data and data taken from the UCI machine learning repository. The experimental study reveals that the Affinity Network graphs tend to be more accurate on the basis of an exhaustive search with the small datasets. Moreover, the graph construction algorithm is faster than the other two methods with huge datasets. The Affinity Network is also applied to data produced by a synchronised system. A detailed analysis and numerical investigation into this dynamical system is provided and it is shown that the Affinity Network can be used to characterise its emergent behaviour even in the presence of noise.

Using min-sum loopy belief propagation for decentralised supply chain formation

Modern business trends such as agile manufacturing and virtual corporations require high levels of flexibility and responsiveness to consumer demand, and require the ability to quickly and efficiently select trading partners. Automated computational techniques for supply chain formation have the potential to provide significant advantages in terms of speed and efficiency over the traditional manual approach to partner selection. Automated supply chain formation is the process of determining the participants within a supply chain and the terms of the exchanges made between these participants. In this thesis we present an automated technique for supply chain formation based upon the min-sum loopy belief propagation algorithm (LBP). LBP is a decentralised and distributed message-passing algorithm which allows participants to share their beliefs about the optimal structure of the supply chain based upon their costs, capabilities and requirements. We propose a novel framework for the application of LBP to the existing state-of-the-art case of the decentralised supply chain formation problem, and extend this framework to allow for application to further novel and established problem cases. Specifically, the contributions made by this thesis are: • A novel framework to allow for the application of LBP to the decentralised supply chain formation scenario investigated using the current state-of-the-art approach. Our experimental analysis indicates that LBP is able to match or outperform this approach for the vast majority of problem instances tested. • A new solution goal for supply chain formation in which economically motivated producers aim to maximise their profits by intelligently altering their profit margins. We propose a rational pricing strategy that allows producers to earn significantly greater profits than a comparable LBP-based profitmaking approach. • An LBP-based framework which allows the algorithm to be used to solve supply chain formation problems in which goods are exchanged in multiple units, a first for a fully decentralised technique. As well as multiple-unit exchanges, we also model in this scenario realistic constraints such as factory capacities and input-to-output ratios. LBP continues to be able to match or outperform an extended version of the existing state-of-the-art approach in this scenario. • Introduction of a dynamic supply chain formation scenario in which participants are able to alter their properties or to enter or leave the process at any time. Our results suggest that LBP is able to deal easily with individual occurences of these alterations and that performance degrades gracefully when they occur in larger numbers.

Decentralised supply chain formation:a belief propagation-based approach

Decentralised supply chain formation involves determining the set of producers within a network able to supply goods to one or more consumers at the lowest cost. This problem is frequently tackled using auctions and negotiations. In this paper we show how it can be cast as an optimisation of a pairwise cost function. Optimising this class of functions is NP-hard but good approximations to the global minimum can be obtained using Loopy Belief Propagation (LBP). Here we detail a LBP-based approach to the supply chain formation problem, involving decentralised message-passing between potential participants. Our approach is evaluated against a well-known double-auction method and an optimal centralised technique, showing several improvements: it obtains better solutions for most networks that admit a competitive equilibrium Competitive equilibrium as defined in [3] is used as a means of classifying results on certain networks to allow for minor inefficiencies in their auction protocol and agent bidding strategies. while also solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions.

Decentralized supply chain formation using max-sum loopy belief propagation

Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation-based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP-hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max-sum LBP-based approach to the supply chain formation problem, involving decentralized message-passing between supply chain participants. Our approach is evaluated against a well-known decentralized double-auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non-negative surplus and agents not in the allocation would acquire non-positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions. © 2012 Wiley Periodicals, Inc.