Yen-Chi Chen

Asymptotic theory for density ridges

The large sample theory of estimators for density modes is well understood. In this paper we consider density ridges, which are a higher-dimensional extension of modes. Modes correspond to zero-dimensional, local high-density regions in point clouds. Density ridges correspond to

Nonparametric modal regression

s

Density Level Sets: Asymptotics, Inference, and Visualization

-dimensional, local high-density regions in point clouds. We establish three main results. First we show that under appropriate regularity conditions, the local variation of the estimated ridge can be approximated by an empirical process. Second, we show that the distribution of the estimated ridge converges to a Gaussian process. Third, we establish that the bootstrap leads to valid confidence sets for density ridges.

A comprehensive approach to mode clustering

Modal regression estimates the local modes of the distribution of

Cosmic web reconstruction through density ridges: method and algorithm

Y

Investigating galaxy-filament alignments in hydrodynamic simulations using density ridges

given

GraphCom: A multidimensional measure of graphic complexity applied to 131 written languages

X=x

Statistical Inference using the Morse-Smale Complex

, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of

Cosmic web reconstruction through density ridges: catalogue

Y

A tutorial on kernel density estimation and recent advances

and