Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Abstract

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 106 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

Random forest Algorithm for the Classification of Spectral Data of Astronomical Objects

“…From the wide range of astronomical datasets generated by scientists throughout the centuries, we have chosen three of them due to the interest shown by researchers. The prestige of these three datasets is reflected in the quantity and quality of scientific articles published in high-impact journals over the last lustrum [23][24][25][26][27][28][29]. The objective of these datasets is to classify stars, galaxies, and quasars based on their spectral characteristics, so the patterns of each dataset are divided into three classes: stars, galaxies, and quasars.…”

Probability Density Estimation through Nonparametric Adaptive Partitioning and Stitching

“…Most importantly, NMEM can self-detect poor solutions and can be applied to censored windows with much better performance characteristics. Recently, NMEM was leveraged by iteratively building tensor products of univariate conditional probabilities to obtain fast and accurate multivariate density estimation [32]. Therefore, improving univariate probability density estimation performance will have a direct impact on the multivariate case as well.…”