# Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Mean

arXiv: https://arxiv.org/abs/2301.11862 · HTML: https://mlsanity.com/paper/2301.11862/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 56 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [Attention Bottlenecks for Multimodal Fusion](https://mlsanity.com/paper/2107.00135/) (2021)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactions](https://mlsanity.com/paper/2003.07132/) (2020)
- [BertGCN: Transductive Text Classification by Combining GCN and BERT](https://mlsanity.com/paper/2105.05727/) (2021)
- [Uncertainty in Gradient Boosting via Ensembles](https://mlsanity.com/paper/2006.10562/) (2020)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Balancing Methods for Multi-label Text Classification with Long-Tailed Class Distribution](https://mlsanity.com/paper/2109.04712/) (2021)
- [Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection](https://mlsanity.com/paper/2209.09326/) (2022)
- [Scalable Interpretability via Polynomials](https://mlsanity.com/paper/2205.14108/) (2022)
- [Significance Tests for Neural Networks](https://mlsanity.com/paper/1902.06021/) (2019)
- [Distributional Gradient Boosting Machines](https://mlsanity.com/paper/2204.00778/) (2022)
- [Extending the Neural Additive Model for Survival Analysis with EHR Data](https://mlsanity.com/paper/2211.07814/) (2022)
- [Partially Interpretable Estimators (PIE): Black-Box-Refined Interpretable Machine Learning](https://mlsanity.com/paper/2105.02410/) (2021)
- [Neural Additive Models for Nowcasting](https://mlsanity.com/paper/2205.10020/) (2022)
- [Generalized Groves of Neural Additive Models: Pursuing transparent and accurate machine learning models in finance](https://mlsanity.com/paper/2209.10082/) (2022)

## Built on by (most cited first, 18 of 18)

- [Mambular: A Sequential Model for Tabular Deep Learning](https://mlsanity.com/paper/2408.06291/) (2024)
- [Improving Neural Additive Models with Bayesian Principles](https://mlsanity.com/paper/2305.16905/) (2023)
- [Structural Neural Additive Models: Enhanced Interpretable Machine Learning](https://mlsanity.com/paper/2302.09275/) (2023)
- [Online Distributional Regression](https://mlsanity.com/paper/2407.08750/) (2024)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [Leveraging Graph Neural Networks to Forecast Electricity Consumption](https://mlsanity.com/paper/2408.17366/) (2024)
- [NBMLSS: probabilistic forecasting of electricity prices via Neural Basis Models for Location Scale and Shape](https://mlsanity.com/paper/2411.13921/) (2024)
- [Beyond Black-Box Predictions: Identifying Marginal Feature Effects in Tabular Transformer Networks](https://mlsanity.com/paper/2504.08712/) (2025)
- [Neural Additive Image Model: Interpretation through Interpolation](https://mlsanity.com/paper/2405.02295/) (2024)
- [Graph Neural Networks for Electricity Load Forecasting](https://mlsanity.com/paper/2507.03690/) (2025)
- [Provably Explaining Neural Additive Models](https://mlsanity.com/paper/2602.17530/) (2026)
- [textttfindr: Transparent and Fair Credit Risk Decisions through Semi-Structured Regressions](https://mlsanity.com/paper/2608.24582/) (2026)
- [LucidAtlas: Learning Uncertainty-Aware, Covariate-Disentangled, Individualized Atlas Representations](https://mlsanity.com/paper/2502.08445/) (2025)
- [Explainable Boosting Machine for Predicting Claim Severity and Frequency in Car Insurance](https://mlsanity.com/paper/2503.21321/) (2025)
- [From Distributional to Quantile Neural Basis Models: the case of Electricity Price Forecasting](https://mlsanity.com/paper/2509.14113/) (2025)
- [Bayesian Neural Networks for Functional ANOVA model](https://mlsanity.com/paper/2510.00545/) (2025)
- [EviNAM: Intelligibility and Uncertainty via Evidential Neural Additive Models](https://mlsanity.com/paper/2601.08556/) (2026)
- [Neural Additive Experts: Context-Gated Experts for Controllable Model Additivity](https://mlsanity.com/paper/2602.10585/) (2026)

## Abstract (arXiv)

Deep neural networks (DNNs) have proven to be highly effective in a variety of tasks, making them the go-to method for problems requiring high-level predictive power. Despite this success, the inner workings of DNNs are often not transparent, making them difficult to interpret or understand. This lack of interpretability has led to increased research on inherently interpretable neural networks in recent years. Models such as Neural Additive Models (NAMs) achieve visual interpretability through the combination of classical statistical methods with DNNs. However, these approaches only concentrate on mean response predictions, leaving out other properties of the response distribution of the underlying data. We propose Neural Additive Models for Location Scale and Shape (NAMLSS), a modelling framework that combines the predictive power of classical deep learning models with the inherent advantages of distributional regression while maintaining the interpretability of additive models. The code is available at the following link: https://github.com/AnFreTh/NAMpy