# Noise Regularization for Conditional Density Estimation

## TL;DR

This paper introduces a noise regularization technique for neural network-based conditional density estimation, improving model generalization and outperforming existing methods across multiple datasets.

## Contribution

A novel, model-agnostic noise regularization method for CDE that enhances generalization and is proven to be asymptotically consistent.

## Key findings

- Noise regularization outperforms other regularization methods.
- Method is effective across seven datasets and three CDE models.
- Neural CDE becomes preferable over non- and semi-parametric approaches.

## Abstract

Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum likelihood objective. Due to the inherent structure of such models, classical regularization approaches in the parameter space are rendered ineffective. To address this issue, we develop a model-agnostic noise regularization method for CDE that adds random perturbations to the data during training. We demonstrate that the proposed approach corresponds to a smoothness regularization and prove its asymptotic consistency. In our experiments, noise regularization significantly and consistently outperforms other regularization methods across seven data sets and three CDE models. The effectiveness of noise regularization makes neural network based CDE the preferable method over previous non- and semi-parametric approaches, even when training data is scarce.