TY - GEN ID - discovery10175941 AV - public CY - Online conference A1 - Rudi, Alessandro A1 - Ciliberto, Carlo KW - Kernel methods KW - Statistical Learning Theory KW - Positive Definite Models KW - Probabilistic Inference KW - Bayesian Inference KW - Decision Theory KW - Density Estimation KW - Probability Representation EP - 12 SN - 1049-5258 T3 - Advances in Neural Information Processing Systems Y1 - 2021/11/09/ UR - https://proceedings.neurips.cc/paper_files/paper/2021/hash/a1b63b36ba67b15d2f47da55cdb8018d-Abstract.html N2 - Finding a good way to model probability densities is key to probabilistic inference. An ideal model should be able to concisely approximate any probability while being also compatible with two main operations: multiplications of two models (product rule) and marginalization with respect to a subset of the random variables (sum rule). In this work, we show that a recently proposed class of positive semi-definite (PSD) models for non-negative functions is particularly suited to this end. In particular, we characterize both approximation and generalization capabilities of PSD models, showing that they enjoy strong theoretical guarantees. Moreover, we show that we can perform efficiently both sum and product rule in closed form via matrix operations, enjoying the same versatility of mixture models. Our results open the way to applications of PSD models to density estimation, decision theory, and inference. PB - NeurIPS Proceedings TI - PSD Representations for Effective Probability Models N1 - This version is the version of record. For information on re-use, please refer to the publisher?s terms and conditions. ER -