# Confidence interval estimation of mixed oil length with conditional diffusion model

arXiv: https://arxiv.org/abs/2406.18603 · HTML: https://mlsanity.com/paper/2406.18603/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 19 Jun 2024.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Gradient Boosted Binary Histogram Ensemble for Large-scale Regression](https://mlsanity.com/paper/2106.01986/) (2021)

## Abstract (arXiv)

Accurately estimating the mixed oil length plays a big role in the economic benefit for oil pipeline network. While various proposed methods have tried to predict the mixed oil length, they often exhibit an extremely high probability (around 50%) of underestimating it. This is attributed to their failure to consider the statistical variability inherent in the estimated length of mixed oil. To address such issues, we propose to use the conditional diffusion model to learn the distribution of the mixed oil length given pipeline features. Subsequently, we design a confidence interval estimation for the length of the mixed oil based on the pseudo-samples generated by the learned diffusion model. To our knowledge, we are the first to present an estimation scheme for confidence interval of the oil-mixing length that considers statistical variability, thereby reducing the possibility of underestimating it. When employing the upper bound of the interval as a reference for excluding the mixed oil, the probability of underestimation can be as minimal as 5%, a substantial reduction compared to 50%. Furthermore, utilizing the mean of the generated pseudo samples as the estimator for the mixed oil length enhances prediction accuracy by at least 10% compared to commonly used methods.