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This paper focuses on the computational complexity of computing empirical plug-in estimates for causal effect queries. Given a causal graph and observational data, any identifiable causal query can be estimated from an expression over the observed variables, called the estimand. The estimand can then be evaluated by plugging in probabilities computed empirically from data. In contrast to conventional wisdom which assumes that high dimensional probabilistic functions will lead to exponential evaluation time, we show that estimand evaluation can be done efficiently, potentially in time linear in the data size, depending on the estimand's hypergraph. In particular, we show that both the treewidth and hypertree width of the estimand's structure bound the evaluation complexity, analogous to their role in bounding the complexity of inference in probabilistic graphical models. In settings with high dimensional functions, the hypertree width often provides a more effective bound, since the empirical distributions are sparse. 

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. 

The standard approach to answering an identifiable causaleffect query (e.g., P(Y |do(X)) given a causal diagram and observational data is to first generate an estimand, or probabilistic expression over the observable variables, which is then evaluated using the observational data. In this paper, we propose an alternative paradigm for answering causal-effect queries over discrete observable variables. We propose to instead learn the causal Bayesian network and its confounding latent variables directly from the observational data. Then, efficient probabilistic graphical model (PGM) algorithms can be applied to the learned model to answer queries. Perhaps surprisingly, we show that this model completion learning approach can be more effective than estimand approaches, particularly for larger models in which the estimand expressions become computationally difficult. We illustrate our method’s potential using a benchmark collection of Bayesian networks and synthetically generated causal models 

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. 

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. 

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. 

Bayesian Networks are useful for analyzing the properties of systems with large populations of interacting agents (e.g., in social modeling applications and distributed service applications). These networks typically have large functions (CPTs), making exact inference intractable. However, often these models have additive symmetry. In this paper we show how summation-based CPTs, especially in the presence of symmetry, can be computed efficiently through the usage of the Fast Fourier Transform (FFT). In particular, we propose an efficient method using the FFT for reducing the size of Conditional Probability Tables (CPTs) in Bayesian Networks with summation-based causal independence (CI). We show how to apply it directly towards the acceleration of Bucket Elimination, and we subsequently provide experimental results demonstrating the computational speedup provided by our method.