Data-driven deep density estimation

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.

PDFEstimator: An R Package for Density Estimation and Analysis

“…The relative comparison between these three methods shows that estimatePDF, on average, produces more accurate estimates at the expense of increased computational time. These trends generally agree with more comprehensive comparisons between estimatePDF and other nonparametric methods (Puchert et al, 2021). density and bkde are very similar to one another, with density marginally slower and more accurate on average over bkde.…”

“…estimatePDF estimatePDF provides an R interface for nonparametric density estimation based on a novel method providing an alternative to traditional KDE implementations. Details of this approach, based on the principle of maximum entropy (Wu, 1997), were published previously and have been shown to produce more accurate estimates than KDE in most cases (Farmer and Jacobs, 2018;Farmer et al, 2019;Puchert et al, 2021;Farmer and Jacobs, 2022). For optimal performance and flexibility with other applications, this functionality is performed within a set of C++ classes and is not the focus of this paper, but a brief summary is provided for insight into the estimatePDF interface.…”