# Learning from Aggregate Observations

arXiv: https://arxiv.org/abs/2004.06316 · HTML: https://mlsanity.com/paper/2004.06316/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2020.

## Built on by (most cited first, 30 of 30)

- [Deconditional Downscaling with Gaussian Processes](https://mlsanity.com/paper/2105.12909/) (2021)
- [On Learning Latent Models with Multi-Instance Weak Supervision](https://mlsanity.com/paper/2306.13796/) (2023)
- [Learning from Aggregated Data: Curated Bags versus Random Bags](https://mlsanity.com/paper/2305.09557/) (2023)
- [Imprecise Label Learning: A Unified Framework for Learning with Various Imprecise Label Configurations](https://mlsanity.com/paper/2305.12715/) (2023)
- [Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees](https://mlsanity.com/paper/2308.10487/) (2023)
- [A Universal Unbiased Method for Classification from Aggregate Observations](https://mlsanity.com/paper/2306.11343/) (2023)
- [Lessons from the AdKDD'21 Privacy-Preserving ML Challenge](https://mlsanity.com/paper/2201.13123/) (2022)
- [Multitask Weakly Supervised Learning for Origin Destination Travel Time Estimation](https://mlsanity.com/paper/2301.05336/) (2023)
- [Gaussian Process Bandits with Aggregated Feedback](https://mlsanity.com/paper/2112.13029/) (2021)
- [Multi-Scale Graph Learning for Anti-Sparse Downscaling](https://mlsanity.com/paper/2505.01948/) (2025)
- [Learning from Aggregate responses: Instance Level versus Bag Level Loss Functions](https://mlsanity.com/paper/2401.11081/) (2024)
- [Monitoring Vegetation From Space at Extremely Fine Resolutions via Coarsely-Supervised Smooth U-Net](https://mlsanity.com/paper/2207.08022/) (2022)
- [SARN: Structurally-Aware Recurrent Network for Spatio-Temporal Disaggregation](https://mlsanity.com/paper/2306.07292/) (2023)
- [Generating Origin-Destination Matrices in Neural Spatial Interaction Models](https://mlsanity.com/paper/2410.07352/) (2024)
- [On Improving Neurosymbolic Learning by Exploiting the Representation Space](https://mlsanity.com/paper/2602.07973/) (2026)
- [CLAM: Causal Spatial Disaggregation to Infer Local Effects From Coarse Data](https://mlsanity.com/paper/2608.08064/) (2026)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [Non-approximate Inference for Collective Graphical Models on Path Graphs via Discrete Difference of Convex Algorithm](https://mlsanity.com/paper/2102.09191/) (2021)
- [Entropic Herding](https://mlsanity.com/paper/2112.11616/) (2021)
- [AODisaggregation: toward global aerosol vertical profiles](https://mlsanity.com/paper/2205.04296/) (2022)
- [Route to Time and Time to Route: Travel Time Estimation from Sparse Trajectories](https://mlsanity.com/paper/2206.10418/) (2022)
- [Aggregated Multi-output Gaussian Processes with Knowledge Transfer Across Domains](https://mlsanity.com/paper/2206.12141/) (2022)
- [Active Learning for Regression with Aggregated Outputs](https://mlsanity.com/paper/2210.01329/) (2022)
- [Learning from aggregated data with a maximum entropy model](https://mlsanity.com/paper/2210.02450/) (2022)
- [Learning Robust Diffusion Models from Imprecise Supervision](https://mlsanity.com/paper/2510.03016/) (2025)
- [FastBUS: A Fast Bayesian Framework for Unified Weakly-Supervised Learning](https://mlsanity.com/paper/2603.00517/) (2026)
- [Learning from Label Proportions with Dual-proportion Constraints](https://mlsanity.com/paper/2603.21153/) (2026)
- [Risk-Consistent Multiclass Learning from Random Label-Subset Membership Queries](https://mlsanity.com/paper/2605.07413/) (2026)
- [Learning Collective Dynamics with Differentiable Gaussian Representations](https://mlsanity.com/paper/2609.28405/) (2026)
- [Puffin: Probabilistic Learning of Spatial Detail From Coarse Observations](https://mlsanity.com/paper/2610.11914/) (2026)

## Abstract (arXiv)

We study the problem of learning from aggregate observations where supervision signals are given to sets of instances instead of individual instances, while the goal is still to predict labels of unseen individuals. A well-known example is multiple instance learning (MIL). In this paper, we extend MIL beyond binary classification to other problems such as multiclass classification and regression. We present a general probabilistic framework that accommodates a variety of aggregate observations, e.g., pairwise similarity/triplet comparison for classification and mean/difference/rank observation for regression. Simple maximum likelihood solutions can be applied to various differentiable models such as deep neural networks and gradient boosting machines. Moreover, we develop the concept of consistency up to an equivalence relation to characterize our estimator and show that it has nice convergence properties under mild assumptions. Experiments on three problem settings -- classification via triplet comparison and regression via mean/rank observation indicate the effectiveness of the proposed method.