# Regression with Sensor Data Containing Incomplete Observations

arXiv: https://arxiv.org/abs/2304.13415 · HTML: https://mlsanity.com/paper/2304.13415/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 75 references that are in the map.
- First posted on arXiv 26 Apr 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model](https://mlsanity.com/paper/1706.03458/) (2017)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Processing of missing data by neural networks](https://mlsanity.com/paper/1805.07405/) (2018)
- [Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance](https://mlsanity.com/paper/1805.10407/) (2018)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [Estimating the class prior and posterior from noisy positives and unlabeled data](https://mlsanity.com/paper/1606.08561/) (2016)
- [Learning from Positive and Unlabeled Data with Arbitrary Positive Shift](https://mlsanity.com/paper/2002.10261/) (2020)
- [Federated Learning with Positive and Unlabeled Data](https://mlsanity.com/paper/2106.10904/) (2021)
- [Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimization](https://mlsanity.com/paper/2210.08461/) (2022)
- [Refining Coarse-grained Spatial Data using Auxiliary Spatial Data Sets with Various Granularities](https://mlsanity.com/paper/1809.07952/) (2018)
- [Learning Classifiers on Positive and Unlabeled Data with Policy Gradient](https://mlsanity.com/paper/1910.06535/) (2019)

## Abstract (arXiv)

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the sensor made an incomplete observation. This leads to a bias toward lower values in labels and the resultant learning because labels may have lower values due to incomplete observations, even if the actual magnitude of the phenomenon was high. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models incomplete observations corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased as if it were learned from uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.