Modelling problems containing a mixture of Boolean and numerical variables is a long-standing interest of Artificial Intelligence. However, performing inference and learning in hybrid domains is a particularly daunting task. The ability to model this kind of domains is crucial in "learning to design" tasks, that is, learning applications where the goal is to learn from examples how to perform automatic de novo design of novel objects. In this paper we present Structured Learning Modulo Theories, a max-margin approach for learning in hybrid domains based on Satisfiability Modulo Theories, which allows to combine Boolean reasoning and optimization over continuous linear arithmetical constraints. The main idea is to leverage a state-of-the-art generalized Satisfiability Modulo Theory solver for implementing the inference and separation oracles of Structured Output SVMs. We validate our method on artificial and real world scenarios.
The formalism Probabilistic Relational Models (PRM) couples discrete Bayesian Networks with a modeling formalism similar to UML class diagrams and has been used for architecture analysis. PRMs are well-suited to perform architecture analysis with respect to system qualities since they support both modeling and analysis within the same formalism. A particular strength of PRMs is the ability to perform meaningful analysis of domains where there is a high level of uncertainty, as is often the case when performing system quality analysis. However, the use of discrete Bayesian networks in PRMs complicates the analysis of continuous phenomena. The main contribution of this paper is the Hybrid Probabilistic Relational Models (HPRM) formalism which extends PRMs to enable continuous analysis thus extending the applicability for architecture analysis and especially for trade-off analysis of system qualities. HPRMs use hybrid Bayesian networks which allow combinations of discrete and continuous variables. In addition to presenting the HPRM formalism, the paper contains an example which details the use of HPRMs for architecture trade-off analysis. Abstract A scheme is presented for modeling and local computation of exact probabilities, means, and variances for mixed qualitative and quantitative variables. The models assume that the conditional distribution of the quantitative variables, given the qualitative, is multivariate Gaussian. The computational architecture is set up by forming a tree of belief universes, and the calculations are then performed by local message passing between universes. The asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure. Approximate methods when these are not appropriately fulfilled are sketched. It has earlier been shown how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation, thereby paving the way for exploiting probability-based models as parts of realistic systems for planning and decision support. The purpose of this article is to extend this computational s... We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities.