Rudi, Alessandro;
Ciliberto, Carlo;
(2021)
PSD Representations for Effective Probability Models.
In: Ranzato, M and Beygelzimer, A and Dauphin, Y and Liang, PS and Vaughan, JW, (eds.)
Advances in Neural Information Processing Systems 34 (NeurIPS 2021).
NeurIPS Proceedings: Online conference.
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Abstract
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.
| Type: | Proceedings paper |
|---|---|
| Title: | PSD Representations for Effective Probability Models |
| Event: | 35th Conference on Neural Information Processing Systems (NeurIPS 2021) |
| Location: | ELECTR NETWORK |
| Dates: | 6 Dec 2021 - 14 Dec 2021 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.neurips.cc/paper_files/paper/2... |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Kernel methods, Statistical Learning Theory, Positive Definite Models, Probabilistic Inference, Bayesian Inference, Decision Theory, Density Estimation, Probability Representation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10175941 |
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