An Interpretable Neural Network for Parameter Inference

TL;DR

This paper introduces PENN, an interpretable neural network architecture that estimates local posterior distributions of regression parameters, enhancing understanding and inference in economics and finance applications.

Contribution

The paper presents a novel generative neural network architecture, PENN, that provides interpretable local parameter estimates with Bayesian regularization, suitable for complex economic and financial data.

Findings

PENN effectively visualizes and interprets complex heterogeneous effects.

The model reduces noise in limited data settings through Bayesian regularization.

Application to asset pricing reveals nonlinear risk dynamics.

Abstract

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.