# A New Distributional Ranking Loss With Uncertainty: Illustrated in Relative Depth Estimation

arXiv: https://arxiv.org/abs/2010.07091 · HTML: https://mlsanity.com/paper/2010.07091/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Single Image Depth Estimation: An Overview](https://mlsanity.com/paper/2104.06456/) (2021)
- [Real-time Monocular Depth Estimation with Sparse Supervision on Mobile](https://mlsanity.com/paper/2105.12053/) (2021)
- [RLSEP: Learning Label Ranks for Multi-label Classification](https://mlsanity.com/paper/2212.04022/) (2022)
- [GaussianMLR: Learning Implicit Class Significance via Calibrated Multi-Label Ranking](https://mlsanity.com/paper/2303.03907/) (2023)
- [UniMLR: Modeling Implicit Class Significance for Multi-Label Ranking](https://mlsanity.com/paper/2508.21772/) (2025)

## Abstract (arXiv)

We propose a new approach for the problem of relative depth estimation from a single image. Instead of directly regressing over depth scores, we formulate the problem as estimation of a probability distribution over depth and aim to learn the parameters of the distributions which maximize the likelihood of the given data. To train our model, we propose a new ranking loss, Distributional Loss, which tries to increase the probability of farther pixel's depth being greater than the closer pixel's depth. Our proposed approach allows our model to output confidence in its estimation in the form of standard deviation of the distribution. We achieve state of the art results against a number of baselines while providing confidence in our estimations. Our analysis show that estimated confidence is actually a good indicator of accuracy. We investigate the usage of confidence information in a downstream task of metric depth estimation, to increase its performance.