# Positive unlabeled learning with tensor networks

arXiv: https://arxiv.org/abs/2211.14085 · HTML: https://mlsanity.com/paper/2211.14085/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Anomaly Detection with Tensor Networks](https://mlsanity.com/paper/2006.02516/) (2020)
- [Generative Tensor Network Classification Model for Supervised Machine Learning](https://mlsanity.com/paper/1903.10742/) (2019)
- [Patch-based Medical Image Segmentation using Matrix Product State Tensor Networks](https://mlsanity.com/paper/2109.07138/) (2021)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Generating Relevant Counter-Examples from a Positive Unlabeled Dataset for Image Classification](https://mlsanity.com/paper/1910.01968/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Matrix Product State Model for Simultaneous Classification and Generation](https://mlsanity.com/paper/2406.17441/) (2024)
- [Using matrix-product states for time-series machine learning](https://mlsanity.com/paper/2412.15826/) (2024)
- [SMT-AD: a scalable quantum-inspired anomaly detection approach](https://mlsanity.com/paper/2604.06265/) (2026)

## Abstract (arXiv)

Positive unlabeled learning is a binary classification problem with positive and unlabeled data. It is common in domains where negative labels are costly or impossible to obtain, e.g., medicine and personalized advertising. Most approaches to positive unlabeled learning apply to specific data types (e.g., images, categorical data) and can not generate new positive and negative samples. This work introduces a feature-space distance-based tensor network approach to the positive unlabeled learning problem. The presented method is not domain specific and significantly improves the state-of-the-art results on the MNIST image and 15 categorical/mixed datasets. The trained tensor network model is also a generative model and enables the generation of new positive and negative instances.