Probabilistic graphical models are used in a wide range of machine learning applications. From reasoning about protein interactions (Jaimovich et al., 2006) to stereo vision (Sun, Shum, and Zheng, 2002), graphical models have facilitated the application of probabilistic methods to challenging machine learning problems. A core operation in probabilistic graphical models is inference – the process of computing the probability of an event given particular observations. Although inference is NP-complete in general, there are several popular approximate inference algorithms that typically perform well in practice. Unfortunately, the approximate inference algorithms are still computationally intensive and therefore can benefit from parallelization. In this chapter, we parallelize loopy belief propagation (or loopy BP in short), which is used in a wide range of ML applications (Jaimovich et al., 2006; Sun et al., 2002; Lan et al., 2006; Baron, Sarvotham, and Baraniuk, 2010; Singla and Domingos, 2008).

We begin by briefly reviewing the sequential BP algorithm as well as the necessary background in probabilistic graphical models. We then present a collection of parallel shared memory BP algorithms that demonstrate the importance of scheduling in parallel BP. Next, we develop the Splash BP algorithm, which combines new scheduling ideas to address the limitations of existing sequential BP algorithms and achieve theoretically optimal parallel performance. Finally, we present how to efficiently implement loopy BP algorithms in the distributed parallel setting by addressing the challenges of distributed state and load balancing.