# Bayesian statistical learning using density operators

arXiv: https://arxiv.org/abs/2212.14715 · HTML: https://mlsanity.com/paper/2212.14715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 28 Dec 2022.

## Builds on (most cited first, 4 of 4)

- [Quantum-inspired Multimodal Fusion for Video Sentiment Analysis](https://mlsanity.com/paper/2103.10572/) (2021)
- [Supervised Learning with Quantum Measurements](https://mlsanity.com/paper/2004.01227/) (2020)
- [Pattern recognition on the quantum Bloch sphere](https://mlsanity.com/paper/1603.00173/) (2016)
- [Binary Classifier Inspired by Quantum Theory](https://mlsanity.com/paper/1903.01167/) (2019)

## Abstract (arXiv)

This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show that such representation allows to formulate the statistical Bayesian learning problem in different coordinate systems on the sample space. We further show that such representation allows to learn projections of density operators using a kernel trick. In particular, the study highlights that decomposing wave functions rather than probability densities, as it is done in kernel embedding, allows to preserve the nature of probability operators. Results are illustrated with a simple example using discrete orthogonal wavelet transform of density operators.