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Spatial evolutionary games are used to model large systems of interacting agents. In earlier work, a method was developed using Bayesian Networks to approximate the population dynamics in these games. One advantage of that approach is that one can smoothly adjust the size of the network to get more accurate approximations. However, scaling the method up can be intractable if the number of strategies in the evolutionary game increases. In this paper, we propose a new method for computing more accurate approximations by using surrogate Bayesian Networks. Instead of doing inference on larger networks directly, we do it on a much smaller surrogate network extended with parameters that exploit the symmetry inherent to the domain. We learn the parameters on the surrogate network using KL-divergence as the loss function. We illustrate the value of this method empirically through a comparison on several evolutionary games. 

Monte Carlo methods are powerful tools for solving problems involving complex probability distributions. Despite their versatility, these methods often suffer from inefficiencies, especially when dealing with rare events. As such, importance sampling emerged as a prominent technique for alleviating these challenges. Recently, a new scheme called Abstraction Sampling was developed that incorporated stratification to importance sampling over graphical models. However, existing work only explored a limited set of abstraction functions that guide stratification. This study introduces three newclasses of abstraction functions combined with seven distinct partitioning schemes, resulting in twenty-one new abstraction functions, each motivated by theory and intuition from both search and sampling domains. An extensive empirical analysis onover 400problemscomparesthese newschemes highlighting several well-performing candidates. 

Monte Carlo methods are powerful tools for solving problems involving complex probability distributions. Despite their versatility, these methods often suffer from inefficiencies, especially when dealing with rare events. As such, importance sampling emerged as a prominent technique for alleviating these challenges. Recently, a new scheme called Abstraction Sampling was developed that incorporated stratification to importance sampling over graphical models. However, existing work only explored a limited set of abstraction functions that guide stratification. This study introduces three new classes of abstraction functions combined with seven distinct partitioning schemes, resulting in twenty-one new abstraction functions, each motivated by theory and intuition from both search and sampling domains. An extensive empirical analysis on over 400 problems compares these new schemes highlighting several well-performing candidates. 

Scientific computing has experienced a surge empowered by advancements in technologies such as neural networks. However, certain important tasks are less amenable to these technologies, benefiting from innovations to traditional inference schemes. One such task is protein re-design. Recently a new re-design algorithm, {AOBB-K\textsuperscript{*}}, was introduced and was competitive with state-of-the-art {BBK\textsuperscript{*}} on small protein re-design problems. However, {AOBB-K\textsuperscript{*}} did not scale well. In this work, we focus on scaling up {AOBB-K\textsuperscript{*}} and introduce three new versions: {AOBB-K\textsuperscript{*}}-b (boosted), {AOBB-K\textsuperscript{*}}-{DH} (with dynamic heuristics), and {AOBB-K\textsuperscript{*}}-{UFO} (with underflow optimization) that significantly enhance scalability. 

The importance of designing proteins, such as high affinity antibodies, has become ever more apparent. Computational Protein Design can cast such design problems as optimization tasks with the objective of maximizing K*, an approximation of binding affinity. Here we lay out a graphical model framework for K* optimization that enables use of compact AND/OR search algorithms. We designed an AND/OR branch-and-bound algorithm, AOBB-K*, for optimizing K* that is guided by a new K* heuristic and can incorporate specialized performance improvements with theoretical guarantees. As AOBB-K* is inspired by algorithms from the well studied task of Marginal MAP, this work provides a foundation for harnessing advancements in state-of-the-art mixed inference schemes and adapting them to protein design. 

Abstraction Sampling (AS) is a recently introduced enhancement of Importance Sampling that exploits stratification by using a notion of abstractions: groupings of similar nodes into abstract states. It was previously shown that AS performs particularly well when sampling over an AND/OR search space; however, existing schemes were limited to ``proper'' abstractions in order to ensure unbiasedness, severely hindering scalability. In this paper, we introduce AOAS, a new Abstraction Sampling scheme on AND/OR search spaces that allow more flexible use of abstractions by circumventing the properness requirement. We analyze the properties of this new algorithm and, in an extensive empirical evaluation on five benchmarks, over 480 problems, and comparing against other state of the art algorithms, illustrate AOAS's properties and show that it provides a far more powerful and competitive Abstraction Sampling framework.