# Continual Density Ratio Estimation in an Online Setting

arXiv: https://arxiv.org/abs/2103.05276 · HTML: https://mlsanity.com/paper/2103.05276/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 9 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Generative Models from the perspective of Continual Learning](https://mlsanity.com/paper/1812.09111/) (2018)
- [Generative Adversarial Nets from a Density Ratio Estimation Perspective](https://mlsanity.com/paper/1610.02920/) (2016)

## Built on by (most cited first, 2 of 2)

- [Adapting to Continuous Covariate Shift via Online Density Ratio Estimation](https://mlsanity.com/paper/2302.02552/) (2023)
- [Neural Total Variation Distance Estimators for Changepoint Detection in News Data](https://mlsanity.com/paper/2506.18764/) (2025)

## Abstract (arXiv)

In online applications with streaming data, awareness of how far the training or test set has shifted away from the original dataset can be crucial to the performance of the model. However, we may not have access to historical samples in the data stream. To cope with such situations, we propose a novel method, Continual Density Ratio Estimation (CDRE), for estimating density ratios between the initial and current distributions (p/qt) of a data stream in an iterative fashion without the need of storing past samples, where qt is shifting away from p over time t. We demonstrate that CDRE can be more accurate than standard DRE in terms of estimating divergences between distributions, despite not requiring samples from the original distribution. CDRE can be applied in scenarios of online learning, such as importance weighted covariate shift, tracing dataset changes for better decision making. In addition, (CDRE) enables the evaluation of generative models under the setting of continual learning. To the best of our knowledge, there is no existing method that can evaluate generative models in continual learning without storing samples from the original distribution.