Robust fusion of unreliable data sources using error-correcting output codes

The emergence of big and dirty data era demands new distributed learning and inference solutions to tackle the problem of inference with corrupted data. The central goal of this chapter is to discuss the presence of corrupted data in the context of distributed inference networks (DINs) and discuss coding-theoretic strategies to ensure reliable inference performance in several practical scenarios. It discusses a generalization of the classical Byzantine Generals problem in the context of distributed inference to different topologies. Over the last three decades, research community has extensively studied the impact of imperfect transmission channels or sensor faults on distributed inference systems. However, corrupted (Byzantine) data models, considered in this chapter, are philosophically different from the imperfect channels or faulty sensor cases. Byzantines are intentional and intelligent and therefore can optimize over the data corruption parameters. While learning their behavior and actively countering them is a viable approach, this chapter presents a new paradigm of mitigation strategies that use coding-theoretic results. The general approach of error-correcting output codes (ECOC) for data fusion is presented and its applicability for several inference problems in practice dealing with unreliable data including Byzantines is shown. This approach is then shown to be applicable to a wider range of inference problems such as classification using crowdsourced data.