# Active Learning for Regression with Aggregated Outputs

arXiv: https://arxiv.org/abs/2210.01329 · HTML: https://mlsanity.com/paper/2210.01329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 54 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Bayesian Batch Active Learning as Sparse Subset Approximation](https://mlsanity.com/paper/1908.02144/) (2019)
- [Learning Algorithms for Active Learning](https://mlsanity.com/paper/1708.00088/) (2017)
- [Learning from Aggregate Observations](https://mlsanity.com/paper/2004.06316/) (2020)
- [Multi-task Learning for Aggregated Data using Gaussian Processes](https://mlsanity.com/paper/1906.09412/) (2019)
- [Variational Learning on Aggregate Outputs with Gaussian Processes](https://mlsanity.com/paper/1805.08463/) (2018)
- [Spatially Aggregated Gaussian Processes with Multivariate Areal Outputs](https://mlsanity.com/paper/1907.08350/) (2019)
- [Refining Coarse-grained Spatial Data using Auxiliary Spatial Data Sets with Various Granularities](https://mlsanity.com/paper/1809.07952/) (2018)
- [Bag-Level Aggregation for Multiple Instance Active Learning in Instance Classification Problems](https://mlsanity.com/paper/1710.02584/) (2017)
- [Collective Diffusion Over Networks: Models and Inference](https://mlsanity.com/paper/1309.6841/) (2013)
- [Generalized Linear Models for Aggregated Data](https://mlsanity.com/paper/1605.04466/) (2016)

## Abstract (arXiv)

Due to the privacy protection or the difficulty of data collection, we cannot observe individual outputs for each instance, but we can observe aggregated outputs that are summed over multiple instances in a set in some real-world applications. To reduce the labeling cost for training regression models for such aggregated data, we propose an active learning method that sequentially selects sets to be labeled to improve the predictive performance with fewer labeled sets. For the selection measurement, the proposed method uses the mutual information, which quantifies the reduction of the uncertainty of the model parameters by observing the aggregated output. With Bayesian linear basis functions for modeling outputs given an input, which include approximated Gaussian processes and neural networks, we can efficiently calculate the mutual information in a closed form. With the experiments using various datasets, we demonstrate that the proposed method achieves better predictive performance with fewer labeled sets than existing methods.