Characteristic Circuits
This addresses the problem of probabilistic reasoning under uncertainty for heterogeneous data domains, offering a novel method that is not incremental.
The paper tackles the challenge of learning probabilistic models on heterogeneous data where closed-form densities are unavailable, by introducing characteristic circuits (CCs) that operate in the spectral domain, and shows that CCs outperform state-of-the-art density estimators on benchmark datasets.
In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. Probabilistic circuits (PCs), a prominent family of tractable probabilistic models, offer a remedy to this challenge by composing simple, tractable distributions into a high-dimensional probability distribution. However, learning PCs on heterogeneous data is challenging and densities of some parametric distributions are not available in closed form, limiting their potential use. We introduce characteristic circuits (CCs), a family of tractable probabilistic models providing a unified formalization of distributions over heterogeneous data in the spectral domain. The one-to-one relationship between characteristic functions and probability measures enables us to learn high-dimensional distributions on heterogeneous data domains and facilitates efficient probabilistic inference even when no closed-form density function is available. We show that the structure and parameters of CCs can be learned efficiently from the data and find that CCs outperform state-of-the-art density estimators for heterogeneous data domains on common benchmark data sets.