Data-driven deep density estimation
This method addresses the need for continuous models from discrete observations in various data analysis tasks, such as population data analysis or 3D scene reconstruction, and is incremental as it builds on deep learning approaches for density estimation.
The paper tackles the problem of density estimation from discrete samples by introducing a data-driven deep density estimation (DDE) method that infers probability density functions accurately and efficiently, independent of domain dimensionality or sample size, without requiring access to the original PDF during estimation.
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.