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.
Highlights
Many data analysis problems, reaching from population analysis to computer vision [6, 28], require estimating continuous models from discrete samples
We introduce a learned, data-driven deep density estimation (DDE) to infer probability density function (PDF) in an accurate and efficient manner, while being independent of domain dimensionality or sample size
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
Summary
Many data analysis problems, reaching from population analysis to computer vision [6, 28], require estimating continuous models from discrete samples. This is the density estimation problem, where, given a sample fxig $ pðxÞ, we would like to estimate the probability density function (PDF) p(x). Our aim is to enable this at high speed and quality with very little assumptions about the data fxig or the PDF p(x). While this is a well-solved problem for PDFs on a 1-dimensional (1D) domain, it becomes increasingly difficult in higher-dimensional domains and implies a strong bias on the estimate. To achieve the task of finding a good and fast estimator for arbitrary
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