Probabilistic Tractable Models in Mixed Discrete-Continuous Domains

Abstract

We study the problem of the unsupervised learning of graphical models in mixed discrete-continuous domains. The problem of unsupervised learning of such models in discrete domains alone is notoriously challenging, compounded by the fact that inference is computationally demanding. The situation is generally believed to be significantly worse in discrete-continuous domains: estimating the unknown probability distribution of given samples is often limited in practice to a handful of parametric forms, and in addition to that, computing conditional queries needs to carefully handle low-probability regions in safety-critical applications. In recent years, the regime of tractable learning has emerged, which attempts to learn a graphical model that permits efficient inference. Most of the results in this regime are based on arithmetic circuits, for which inference is linear in the size of the obtained circuit. In this work, we show how, with minimal modifications, such regimes can be generalized by leveraging efficient density estimation schemes based on piecewise polynomial approximations. Our framework is realized on a recent computational abstraction that permits efficient inference for a range of queries in the underlying language. Our empirical results show that our approach is effective, and allows a study of the trade-off between the granularity of the learned model and its predictive power.

Discrete Dynamic Modeling Analysis of Data Mining Algorithm under the Background of Big Data in the Strategic Goal of Sustainable Development of College Physical Training

“…Establishment of Discrete Dynamic Model. In order to master the strengthening degree of diversified college students' physical training on different students' physical functions, Apriori algorithm is used for data mining and discrete dynamic modeling of college students' physical training data in a college, in order to achieve the purpose of sustainable development [20]. In the construction of discrete dynamic model, considering different training items in physical education class and different competition items in sports competition, the prediction vector of data positioning state is…”