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08/30/2022
Embedding Functional Data: Multidimensional Scaling and Manifold Learning
We adapt concepts, methodology, and theory originally developed in the a...
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07/15/2022
Fitting a Multi-modal Density by Dynamic Programming
We consider the problem of fitting a probability density function when i...
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07/14/2022
Supervising Embedding Algorithms Using the Stress
While classical scaling, just like principal component analysis, is para...
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02/18/2022
Clustering by Hill-Climbing: Consistency Results
We consider several hill-climbing approaches to clustering as formulated...
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11/19/2021
An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree
Two important nonparametric approaches to clustering emerged in the 1970...
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09/17/2021
Level Sets or Gradient Lines? A Unifying View of Modal Clustering
The paper establishes a strong correspondence, if not an equivalence, be...
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06/26/2021
Extending the Patra-Sen Approach to Estimating the Background Component in a Two-Component Mixture Model
Patra and Sen (2016) consider a two-component mixture model, where one c...
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05/07/2021
From Graph Centrality to Data Depth
Given a sample of points in a Euclidean space, we can define a notion of...
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04/16/2021
Estimation of the Global Mode of a Density: Minimaxity, Adaptation, and Computational Complexity
We consider the estimation of the global mode of a density under some de...
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12/14/2020
Template Matching with Ranks
We consider the problem of matching a template to a noisy signal. Motiva...
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11/25/2020
Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Setting
We start by considering the problem of estimating intrinsic distances on...
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10/19/2020
On the Consistency of Metric and Non-Metric K-medoids
We establish the consistency of K-medoids in the context of metric space...
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09/09/2020
Template Matching and Change Point Detection by M-estimation
We consider the fundamental problem of matching a template to a signal. ...
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09/07/2020
Anomaly Detection in Stationary Settings: A Permutation-Based Higher Criticism Approach
Anomaly detection when observing a large number of data streams is essen...
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07/09/2020
K-Means and Gaussian Mixture Modeling with a Separation Constraint
We consider the problem of clustering with K-means and Gaussian mixture ...
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06/20/2019
A Multiscale Scan Statistic for Adaptive Submatrix Localization
We consider the problem of localizing a submatrix with larger-than-usual...
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11/17/2018
Detection of Sparse Positive Dependence
In a bivariate setting, we consider the problem of detecting a sparse co...
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10/22/2018
Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning
One of the common tasks in unsupervised learning is dimensionality reduc...
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08/02/2018
A Scan Procedure for Multiple Testing
In a multiple testing framework, we propose a method that identifies the...
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07/27/2018
The Sparse Variance Contamination Model
We consider a Gaussian contamination (i.e., mixture) model where the con...
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04/27/2018
On the Estimation of Latent Distances Using Graph Distances
We are given the adjacency matrix of a geometric graph and the task of r...
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02/23/2018
Detection of Sparse Mixtures: Higher Criticism and Scan Statistic
We consider the problem of detecting a sparse mixture as studied by Ings...
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11/30/2017
RANSAC Algorithms for Subspace Recovery and Subspace Clustering
We consider the RANSAC algorithm in the context of subspace recovery and...
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06/28/2017
Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation
We study shortest paths and their distances on a subset of a Euclidean s...
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02/23/2016
A Simple Approach to Sparse Clustering
Consider the problem of sparse clustering, where it is assumed that only...
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02/18/2016
A Nonparametric Framework for Quantifying Generative Inference on Neuromorphic Systems
Restricted Boltzmann Machines and Deep Belief Networks have been success...
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08/13/2013
Community Detection in Sparse Random Networks
We consider the problem of detecting a tight community in a sparse rando...
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02/28/2013
Community Detection in Random Networks
We formalize the problem of detecting a community in a network into test...
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01/09/2013
Spectral Clustering Based on Local PCA
We propose a spectral clustering method based on local principal compone...
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08/31/2012
On the convergence of maximum variance unfolding
Maximum Variance Unfolding is one of the main methods for (nonlinear) di...
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08/31/2012
A two-stage denoising filter: the preprocessed Yaroslavsky filter
This paper describes a simple image noise removal method which combines ...
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12/19/2011
Oracle inequalities and minimax rates for non-local means and related adaptive kernel-based methods
This paper describes a novel theoretical characterization of the perform...
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01/08/2010
Spectral clustering based on local linear approximations
In the context of clustering, we assume a generative model where each cl...
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09/12/2009
