# An Interpretable Neural Network for Parameter Inference

arXiv: https://arxiv.org/abs/2106.05536 · HTML: https://mlsanity.com/paper/2106.05536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 82 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Scaleable input gradient regularization for adversarial robustness](https://mlsanity.com/paper/1905.11468/) (2019)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [Local Linear Forests](https://mlsanity.com/paper/1807.11408/) (2018)
- [Significance Tests for Neural Networks](https://mlsanity.com/paper/1902.06021/) (2019)
- [Discovering Nonlinear Relations with Minimum Predictive Information Regularization](https://mlsanity.com/paper/2001.01885/) (2020)
- [Symmetric Variational Autoencoder and Connections to Adversarial Learning](https://mlsanity.com/paper/1709.01846/) (2017)
- [An Interpretable and Sparse Neural Network Model for Nonlinear Granger Causality Discovery](https://mlsanity.com/paper/1711.08160/) (2017)
- [From interpretability to inference: an estimation framework for universal approximators](https://mlsanity.com/paper/1903.04209/) (2019)

## Abstract (arXiv)

Adoption of deep neural networks in fields such as economics or finance has been constrained by the lack of interpretability of model outcomes. This paper proposes a generative neural network architecture - the parameter encoder neural network (PENN) - capable of estimating local posterior distributions for the parameters of a regression model. The parameters fully explain predictions in terms of the inputs and permit visualization, interpretation and inference in the presence of complex heterogeneous effects and feature dependencies. The use of Bayesian inference techniques offers an intuitive mechanism to regularize local parameter estimates towards a stable solution, and to reduce noise-fitting in settings of limited data availability. The proposed neural network is particularly well-suited to applications in economics and finance, where parameter inference plays an important role. An application to an asset pricing problem demonstrates how the PENN can be used to explore nonlinear risk dynamics in financial markets, and to compare empirical nonlinear effects to behavior posited by financial theory.