Journal article
Kernel density matrices for probabilistic deep learning
Quantum machine intelligence, v 7(2), 94
01 Dec 2025
Featured in Collection : UN Sustainable Development Goals @ Drexel
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.
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Details
- Title
- Kernel density matrices for probabilistic deep learning
- Creators
- Fabio A. Gonzalez - Universidad Nacional de ColombiaRaul Ramos-Pollan - Universidad de AntioquiaJoseph Gallego (Corresponding Author) - Universidad Nacional de Colombia
- Publication Details
- Quantum machine intelligence, v 7(2), 94
- Publisher
- Springer Nature
- Number of pages
- 15
- Grant note
- Colombia Consortium
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Computer Science
- Web of Science ID
- WOS:001588392800001
- Scopus ID
- 2-s2.0-105018665964
- Other Identifier
- 991022197436104721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Artificial Intelligence
- Quantum Science & Technology