The max-product algorithm, a local message-passing scheme that attempts to compute the most probable assignment (MAP) of a given probability distribution, has been successfully employed as a method of approximate inference for applications arising in coding theory, computer vision, and machine learning. However, the max-product algorithm is not guaranteed to converge to the MAP assignment, and if it does, is not guaranteed to recover the MAP assignment. Alternative convergent message-passing schemes have been proposed to overcome these difficulties. This work provides a systematic study of such message-passing algorithms that extends the known results by exhibiting new sufficient conditions for convergence to local and/or global optima, providing a combinatorial characterization of these optima based on graph covers, and describing a new convergent and correct message-passing algorithm whose derivation unifies many of the known convergent message-passing algorithms. While convergent and correct message-passing algorithms represent a step forward in the analysis of max-product style message-passing algorithms, the conditions needed to guarantee convergence to a global optimum can be too restrictive in both theory and practice. This limitation of convergent and correct message-passing schemes is characterized by graph covers and illustrated by example.Comment: A complete rework and expansion of the previous version

Abstract. Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One can prove a coinduction step showing that some property is preserved by one step of the approximation process, then automatically infer by the coinduction principle that the property holds of the limit object. This can often be used to avoid complicated analytic arguments involving limits and convergence, replacing them with simpler algebraic arguments. This paper examines the application of this principle in a variety of areas, including infinite streams, Markov chains, Markov decision processes, and non-well-founded sets. These results point to the usefulness of coinduction as a general proof technique.

We consider the following activity recognition task: given a video, infer the set of activities being performed in the video and assign each frame to an activity. This task can be solved using modern deep learning architectures based on neural networks or conventional classifiers such as linear models and decision trees. While neural networks exhibit superior predictive performance as compared with decision trees and linear models, they are also uninterpretable and less explainable. We address this accuracy‐explanability gap using a novel framework that feeds the output of a deep neural network to an interpretable, tractable probabilistic model called dynamic cutset networks, and performs joint reasoning over the two to answer questions. The neural network helps achieve high accuracy while dynamic cutset networks because of their polytime probabilistic reasoning capabilities make the system more explainable. We demonstrate the efficacy of our approach by using it to build three prototype systems that solve human‐machine tasks having varying levels of difficulty using cooking videos as an accessible domain. We describe high‐level technical details and key lessons learned in our human subjects evaluations of these systems.

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