Dimensionality reduction

Gene

Quantum mechanics

Transformation (genetics)

Algorithm

Gaussian

Engineering

Deep neural networks

Aerospace engineering

Pure mathematics

Biology

Statistics

Materials science

Curse of dimensionality

Systems engineering

Dimension (graph theory)

Operating system

Range (aeronautics)

Biochemistry

Computer science

Geology

Paleontology

Estimation

Physics

Generative grammar

Pattern recognition (psychology)

Mathematics

Estimator

Artificial intelligence

Series (stratigraphy)

Composite material

Probability density function

Chemistry

Density estimation

Artificial neural network

Space (punctuation)

Machine learning

Proceedings of the National Academy of Sciences

Significance Density estimation is among the most fundamental problems in statistics. It is notoriously difficult to estimate the density of high-dimensional data due to the “curse of dimensionality.” Here, we introduce a new general-purpose density estimator based on deep generative neural networks. By modeling data normally distributed around a manifold of reduced dimension, we show how the power of bidirectional generative neural networks (e.g., cycleGAN) can be exploited for explicit evaluation of the data density. Simulation and real data experiments suggest that our method is effective in a wide range of problems. This approach should be helpful in many applications where an accurate density estimator is needed.

Density estimation using deep generative neural networks