# Fully Heteroscedastic Count Regression with Deep Double Poisson Networks

arXiv: https://arxiv.org/abs/2406.09262 · HTML: https://mlsanity.com/paper/2406.09262/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 79 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 30 of 34)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Visual Transformers: Token-based Image Representation and Processing for Computer Vision](https://mlsanity.com/paper/2006.03677/) (2020)
- [Drone-based Object Counting by Spatially Regularized Regional Proposal Network](https://mlsanity.com/paper/1707.05972/) (2017)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Uncertainty in the Variational Information Bottleneck](https://mlsanity.com/paper/1807.00906/) (2018)
- [Faithful Heteroscedastic Regression with Neural Networks](https://mlsanity.com/paper/2212.09184/) (2022)
- [A Large-Scale Study of Probabilistic Calibration in Neural Network Regression](https://mlsanity.com/paper/2306.02738/) (2023)
- [People, Penguins and Petri Dishes: Adapting Object Counting Models To New Visual Domains And Object Types Without Forgetting](https://mlsanity.com/paper/1711.05586/) (2017)
- [Hybrid Graph Neural Networks for Crowd Counting](https://mlsanity.com/paper/2002.00092/) (2020)
- [Calibration by Distribution Matching: Trainable Kernel Calibration Metrics](https://mlsanity.com/paper/2310.20211/) (2023)

## Built on by (most cited first, 3 of 3)

- [Generative AI in Transportation Planning: A Survey](https://mlsanity.com/paper/2503.07158/) (2025)
- [Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding](https://mlsanity.com/paper/2605.08446/) (2026)
- [Residual Correlation as a Diagnostic for Joint-Uncertainty Gains from GP Coregionalisation](https://mlsanity.com/paper/2609.30085/) (2026)

## Abstract (arXiv)

Neural networks capable of accurate, input-conditional uncertainty representation are essential for real-world AI systems. Deep ensembles of Gaussian networks have proven highly effective for continuous regression due to their ability to flexibly represent aleatoric uncertainty via unrestricted heteroscedastic variance, which in turn enables accurate epistemic uncertainty estimation. However, no analogous approach exists for count regression, despite many important applications. To address this gap, we propose the Deep Double Poisson Network (DDPN), a novel neural discrete count regression model that outputs the parameters of the Double Poisson distribution, enabling arbitrarily high or low predictive aleatoric uncertainty for count data and improving epistemic uncertainty estimation when ensembled. We formalize and prove that DDPN exhibits robust regression properties similar to heteroscedastic Gaussian models via learnable loss attenuation, and introduce a simple loss modification to control this behavior. Experiments on diverse datasets demonstrate that DDPN outperforms current baselines in accuracy, calibration, and out-of-distribution detection, establishing a new state-of-the-art in deep count regression.