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Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of advances in equilibrium computation for probabilistic inference. In particular, we present formulations of inference problems in Markov random fields (MRFs) as computation of equilibria in a certain class of game-theoretic graphical models. While some previous work explores this direction, we still lack a more precise connection between variational probabilistic inference in MRFs and correlated equilibria. This paper sharpens the connection, which helps us exploit relatively more recent theoretical and empirical results from the literature on algorithmic and computational game theory on the tractable, polynomial-time computation of exact or approximate correlated equilibria in graphical games with arbitrary, loopy graph structure. Our work discusses how to design new algorithms with equally tractable guarantees for the computation of approximate variational inference in MRFs. In addition, inspired by a previously stated game-theoretic view of tree-reweighted message-passing techniques for belief inference as a zero-sum game, we propose a different, general-sum potential game to design approximate fictitious-play techniques. Empirical evaluations on synthetic experiments and on an application to soft de-noising on real-world image datasets illustrate the performance of our proposed approach and shed some light on the conditions under which the resulting belief inference algorithms may be most effective relative to standard state-of-the-art methods. 

Heat waves impact a wide array of human activities, including health, cooling energy demand, and infrastructure. Cities amplify many of these impacts by concentrating large populations and critical infrastructure in relatively small areas. In addition, heat waves are expected to become longer, more intense, and more frequent in North America. Here, we evaluate combined climate and urban surface impacts on localized heat wave metrics throughout the 21st century across two emissions scenarios (RCP4.5 and RCP8.5) for New York City (NYC), which houses the largest urban population in the United States. We account for local biases due to urban surfaces via bias correcting with observed records and urbanized 1‐km resolution dynamical downscaling simulations across selected time periods (2045–2049 and 2095–2099). Analysis of statistically downscaled global model output shows underestimation of uncorrected summer daily maximum temperatures, leading to lower heat wave intensity and duration projections. High‐resolution dynamical downscaling simulations reveal strong dependency of changes in event duration and intensity on geographical location and urban density. Event intensity changes are expected to be highest closer to the coast, where afternoon sea‐breezes have traditionally mitigated summer high temperatures. Meanwhile, event duration anomaly is largest over Manhattan, where the urban canopy is denser and taller.