The topology of probability distributions on manifolds

Complexity of random smooth functions on the high-dimensional sphere

(2013) Antonio Auffinger et al.   ANNALS OF PROBABILITY

Rotation and scale space random fields and the Gaussian kinematic formula

(2013) Robert J. Adler et al.   ANNALS OF STATISTICS

Limit theorems for Betti numbers of random simplicial complexes

(2013) Matthew Kahle et al.   Homology Homotopy and Applications

Min-Type Morse Theory for Configuration Spaces of Hard Spheres

(2013) Yuliy Baryshnikov et al.   INTERNATIONAL MATHEMATICS RESEARCH NOTICES

Nonlinear manifold representations for functional data

(2012) Dong Chen et al.   ANNALS OF STATISTICS

EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY

(2012) OMER BOBROWSKI et al.   Journal of Topology and Analysis

Spectral clustering and the high-dimensional stochastic blockmodel

(2011) Karl Rohe et al.   ANNALS OF STATISTICS

Random Geometric Complexes

(2011) Matthew Kahle   DISCRETE & COMPUTATIONAL GEOMETRY

A Topological View of Unsupervised Learning from Noisy Data

(2011) P. Niyogi et al.   SIAM JOURNAL ON COMPUTING

Regression on manifolds: Estimation of the exterior derivative

(2010) Anil Aswani et al.   ANNALS OF STATISTICS

Learning gradients on manifolds

(2010) Sayan Mukherjee et al.   BERNOULLI

On the path density of a gradient field

(2009) Christopher R. Genovese et al.   ANNALS OF STATISTICS

A Sampling Theory for Compact Sets in Euclidean Space

(2009) Frédéric Chazal et al.   DISCRETE & COMPUTATIONAL GEOMETRY

Tilted Euler characteristic densities for Central Limit random fields, with application to “bubbles”

(2008) N. Chamandy et al.   ANNALS OF STATISTICS

Random fields of multivariate test statistics, with applications to shape analysis

(2008) J. E. Taylor et al.   ANNALS OF STATISTICS

Topology of random clique complexes

(2008) Matthew Kahle   DISCRETE MATHEMATICS