# Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization

arXiv: https://arxiv.org/abs/2311.01900 · HTML: https://mlsanity.com/paper/2311.01900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Optimal Bounds between f-Divergences and Integral Probability Metrics](https://mlsanity.com/paper/2006.05973/) (2020)
- [Practical and Consistent Estimation of f-Divergences](https://mlsanity.com/paper/1905.11112/) (2019)
- [Training Neural Networks for Likelihood/Density Ratio Estimation](https://mlsanity.com/paper/1911.00405/) (2019)

## Built on by (most cited first, 1 of 1)

- [Collaborative non-parametric two-sample testing](https://mlsanity.com/paper/2402.05715/) (2024)

## Abstract (arXiv)

Quantifying the difference between two probability density functions, p and q, using available data, is a fundamental problem in Statistics and Machine Learning. A usual approach for addressing this problem is the likelihood-ratio estimation (LRE) between p and q, which -- to our best knowledge -- has been investigated mainly for the offline case. This paper contributes by introducing a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations (xt ~ p, x't ~ q) are observed over time. The non-parametric nature of our approach has the advantage of being agnostic to the forms of p and q. Moreover, we capitalize on the recent advances in Kernel Methods and functional minimization to develop an estimator that can be efficiently updated online. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.