{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/quantum-kernel-mixtures-for-probabilistic","title":"Kernel Density Matrices for Probabilistic Deep Learning","arxiv_id":"2305.18204","date":"2023-05-26","proceeding":null,"authors":["Fabio A. González","Raúl Ramos-Pollán","Joseph A. Gallego-Mejia"],"abstract":"This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This work extends the concept of density matrices by allowing them to be defined in a reproducing kernel Hilbert space. This abstraction allows the construction of differentiable models for density estimation, inference, and sampling, and enables their integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. The broad applicability of the framework is illustrated by two examples: an image classification model that can be naturally transformed into a conditional generative model, and a model for learning with label proportions that demonstrates the framework's ability to deal with uncertainty in the training samples. The framework is implemented as a library and is available at: https://github.com/fagonzalezo/kdm.","url_abs":"https://arxiv.org/abs/2305.18204v3","url_pdf":"https://arxiv.org/pdf/2305.18204v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"quantum-kernel-mixtures-for-probabilistic","repo_url":"https://github.com/fagonzalezo/kdm_for_probabilistic_dl_experiments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"quantum-kernel-mixtures-for-probabilistic","repo_url":"https://github.com/fagonzalezo/kdm","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"probabilistic-deep-learning","task_name":"Probabilistic Deep Learning"},{"task_slug":"weakly-supervised-classification","task_name":"Weakly Supervised Classification"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[{"method_slug":null,"method_name":"Library"},{"method_slug":"kdm","method_name":"kdm"}],"datasets_introduced":[],"methods_introduced":[{"slug":"kdm","name":"kdm","full_name":"Kernel Density Matrices"}],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}