Constrained Bayesian Networks: Theory, Optimization, and Applications
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data for the learning of causal network structure or probability values at nodes are available. Constrained Bayesian Networks generalize a Bayesian Network such that probabilities can be symbolic, arithmetic expressions and where the meaning of the network is constrained by finitely many formulas from the theory of the reals. A formal semantics for constrained Bayesian Networks over first-order logic of the reals is given, which enables non-linear and non-convex optimisation algorithms that rely on decision procedures for this logic, and supports the composition of several constrained Bayesian Networks. A non-trivial case study in arms control, where few or no data are available to assess the effectiveness of an arms inspection process, evaluates our approach. An open-access prototype implementation of these foundations and their algorithms uses the SMT solver Z3 as decision procedure, leverages an open-source package for Bayesian inference to symbolic computation, and is evaluated experimentally.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceSimilar Papers 제목 키워드 기반
Information Theoretic Bayesian Optimization over the Probability Simplex
Bayesian optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilitie…
Constrained Bayesian Optimization under Bivariate Gaussian Process with Application to Cure Process Optimization
Bayesian Optimization, leveraging Gaussian process models, has proven to be a powerful tool for minimizing expensive-to-evaluate objective functions by efficiently exploring the search space. Extensions such as constrain…
Bayesian OptimizationGaussian ProcessesConstrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation
Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional …
Active LearningBayesian OptimizationDrug DiscoveryHyperparameter OptimizationInformation-theoretic Bayesian Optimization: Survey and Tutorial
Several scenarios require the optimization of non-convex black-box functions, that are noisy expensive to evaluate functions with unknown analytical expression, whose gradients are hence not accessible. For example, the …
Bayesian OptimizationSurveyExcursion Search for Constrained Bayesian Optimization under a Limited Budget of Failures
When learning to ride a bike, a child falls down a number of times before achieving the first success. As falling down usually has only mild consequences, it can be seen as a tolerable failure in exchange for a faster le…
Bayesian Optimization