Convergent interactive inference with leaky joins

One of the primary challenges in graphical models is inference, or re-constructing a marginal probability from the graphical model’s factorized representation. While tractable for some graphs, the cost of inference grows exponentially with the graphical model’s complexity, necessitating approximation for more complex graphs. For interactive applications, latency is the dominant concern, making approximate inference the only feasible option. Unfortunately, approximate inference can be wasteful for interactive applications, as exact inference can still converge faster, even for moderately complex inference problems. In this paper, we propose a new family of convergent inference algorithms (CIAs) that bridge the gap between approximations and exact solutions, providing early, incrementally improving approximations that become exact after a finite period of time. We describe two specific CIAs based on a cryptographic technique called linear congruential generators, including a novel incremental join algorithm for dense relations called Leaky Joins. We conclude with experiments that demonstrate the utility of Leaky Joins for convergent inference: On both synthetic and real-world probabilistic graphical models, Leaky Joins converge to exact marginal probabilities almost as fast as state of the art exact inference algorithms, while simultaneously achieving approximations that are almost as good as state of the art approximation algorithms.