93 citations · 294 across the 27 of their papers we have counts for
28 papers
First-order asymptotic expansions for spectral convergence of compact self-adjoint operators on general spectral subsets, with application to kernel Gram matrices
Eunseong Bae, Wolfgang Polonik
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space, and derive the first-order asymptotic expansions for their eigenvalues, eigenvect…
Kernel smoothing on manifolds
Eunseong Bae, Wolfgang Polonik
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and…
Common Drivers in Sparsely Interacting Hawkes Processes
Alexander Kreiss, Alexander Fuchs-Kreiss, Enno Mammen +1
We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it a…
Gaussian and Bootstrap Approximation for Matching-based Average Treatment Effect Estimators
Zhaoyang Shi, Chinmoy Bhattacharjee, Krishnakumar Balasubramanian +1
We establish Gaussian approximation bounds for covariate and rank-matching-based Average Treatment Effect (ATE) estimators. By analyzing these estimators through the lens of stabil…
Multivariate Gaussian Approximation for Random Forest via Region-based Stabilization
Zhaoyang Shi, Chinmoy Bhattacharjee, Krishnakumar Balasubramanian +1
We derive Gaussian approximation bounds for -Potential Nearest Neighbor (-PNN) based random forest predictions based on a set of training points given by a Poisson process un…
Nonsmooth Nonparametric Regression via Fractional Laplacian Eigenmaps
Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplac…
Adaptive and non-adaptive minimax rates for weighted Laplacian-eigenmap based nonparametric regression
Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
We show both adaptive and non-adaptive minimax rates of convergence for a family of weighted Laplacian-Eigenmap based nonparametric regression methods, when the true regression fun…
A Flexible Approach for Normal Approximation of Geometric and Topological Statistics
Zhaoyang Shi, Krishnakumar Balasubramanian, Wolfgang Polonik
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score fu…
Antimodes and Graphical Anomaly Exploration via Adaptive Depth Quantile Functions
Gabriel Chandler, Wolfgang Polonik
This work proposes and investigates a novel method for anomaly detection and shows it to be competitive in a variety of Euclidean and non-Euclidean situations. It is based on an ex…
Topologically penalized regression on manifolds
Olympio Hacquard, Krishnakumar Balasubramanian, Gilles Blanchard +2
We study a regression problem on a compact manifold M. In order to take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis…
Algorithms for ridge estimation with convergence guarantees
Wanli Qiao, Wolfgang Polonik
The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose…
Testing For Global Covariate Effects in Dynamic Interaction Event Networks
Alexander Kreiss, Enno Mammen, Wolfgang Polonik
In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the net…
On approximation theorems for the Euler characteristic with applications to the bootstrap
Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Cech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the…
Bootstrapping Persistent Betti Numbers and Other Stabilizing Statistics
Benjamin Roycraft, Johannes Krebs, Wolfgang Polonik
The present contribution investigates multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. Existing limit t…
High Order Adjusted Block-wise Empirical Likelihood For Weakly Dependent Data
Guangxing Wang, Wolfgang Polonik
It is well known that the empirical likelihood ratio confidence region suffers finite sample under-coverage issue, and this severely hampers its application in statistical inferenc…
Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry
Wanli Qiao, Wolfgang Polonik
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizont…
On the asymptotic normality of persistent Betti numbers
Johannes Krebs, Wolfgang Polonik
Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis. Many tools in persistent homology rely on the properties of persistent Be…
Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with application
Gabriel Chandler, Wolfgang Polonik
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature funct…
On the choice of weight functions for linear representations of persistence diagrams
Vincent Divol, Wolfgang Polonik
Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly…
Neighborhood selection with application to social networks
Nana Wang, Wolfgang Polonik
The topic of this paper is modeling and analyzing dependence in stochastic social networks. Using a latent variable block model allows the analysis of dependence between blocks via…
Nonparametric inference for continuous-time event counting and link-based dynamic network models
Alexander Kreiß, Enno Mammen, Wolfgang Polonik
A flexible approach for modeling both dynamic event counting and dynamic link-based networks based on counting processes is proposed, and estimation in these models is studied. We…
Autism Spectrum Disorder Classification using Graph Kernels on Multidimensional Time Series
Rushil Anirudh, Jayaraman J. Thiagarajan, Irene Kim +1
We present an approach to model time series data from resting state fMRI for autism spectrum disorder (ASD) severity classification. We propose to adopt kernel machines and employ…
Theoretical Analysis of Nonparametric Filament Estimation
Wanli Qiao, Wolfgang Polonik
This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density . Points on the filament are considered as local extrem…
Extrema of locally stationary Gaussian fields on growing manifolds
Wanli Qiao, Wolfgang Polonik
We consider a class of non-homogeneous, continuous, centered Gaussian random fields where denotes a rescaled smooth manifo…