Probabilistic Tractable Models in Mixed Discrete-Continuous Domains

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