Data-driven deep density estimation

TL;DR

This paper introduces a novel deep learning method for density estimation that accurately infers probability density functions from data without relying on domain-specific priors or large natural datasets.

Contribution

It presents a data-driven deep density estimation approach trained on synthetic PDFs, enabling domain-independent and sample-efficient density inference.

Findings

Accurately infers PDFs from discrete samples

Independent of domain dimensionality and sample size

Generalizes well across various natural PDFs

Abstract

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in 2D sensor readings, or reconstructing scenes from 3D scans. In this paper, we introduce a learned, data-driven deep density estimation (DDE) to infer PDFs in an accurate and efficient manner, while being independent of domain dimensionality or sample size. Furthermore, we do not require access to the original PDF during estimation, neither in parametric form, nor as priors, or in the form of many samples. This is enabled by training an unstructured convolutional neural network on an infinite stream of synthetic PDFs, as unbound amounts of synthetic training data generalize better across a deck of natural PDFs than any natural finite training data will do. Thus, we hope that our publicly available DDE method will be beneficial in many areas of data analysis, where continuous models are to be estimated from discrete observations.