Probabilistic Tractable Models in Mixed Discrete-Continuou s Domains
DATA INTELLIGENCE(2022)
摘要
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 need 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.
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关键词
Graphical models,Tractable inference,Hybrid domains,Weighted model integration
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