Publications (52)
PT-MMD: A Novel Statistical Framework for the Evaluation of Generative Systems
Alexander Potapov, Ian Colbert, Ken Kreutz-Delgado +2
Stochastic-sampling-based Generative Neural Networks, such as Restricted Boltzmann Machines and Generative Adversarial Networks, are now used for applications such as denoising, im…
Using Causal Inference to Explore Government Policy Impact on Computer Usage
Mingjia Zhu, Lechuan Wang, Julien Sebot +3
We explore the causal relationship between COVID-19 lockdown policies and changes in personal computer usage. In particular, we examine how lockdown policies affected average daily…
Classification Logit Two-sample Testing by Neural Networks
Xiuyuan Cheng, Alexander Cloninger
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem.…
A Note on Markov Normalized Magnetic Eigenmaps
Alexander Cloninger
We note that building a magnetic Laplacian from the Markov transition matrix, rather than the graph adjacency matrix, yields several benefits for the magnetic eigenmaps algorithm.…
Function Driven Diffusion for Personalized Counterfactual Inference
Alexander Cloninger
We consider the problem of constructing diffusion operators high dimensional data to address counterfactual functions , such as individualized treatment effectiveness. We pr…
Kernel distance measures for time series, random fields and other structured data
Srinjoy Das, Hrushikesh Mhaskar, Alexander Cloninger
This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure…
Spectral Echolocation via the Wave Embedding
Alexander Cloninger, Stefan Steinerberger
Spectral embedding uses eigenfunctions of the discrete Laplacian on a weighted graph to obtain coordinates for an embedding of an abstract data set into Euclidean space. We propose…
Bounding the Error From Reference Set Kernel Maximum Mean Discrepancy
Alexander Cloninger
In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is qu…
Training Guarantees of Neural Network Classification Two-Sample Tests by Kernel Analysis
Varun Khurana, Xiuyuan Cheng, Alexander Cloninger
We construct and analyze a neural network two-sample test to determine whether two datasets came from the same distribution (null hypothesis) or not (alternative hypothesis). We pe…
Natural Graph Wavelet Packet Dictionaries
Alexander Cloninger, Haotian Li, Naoki Saito
We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eig…
Variational Diffusion Autoencoders with Random Walk Sampling
Henry Li, Ofir Lindenbaum, Xiuyuan Cheng +1
Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to app…
Coresets for Estimating Means and Mean Square Error with Limited Greedy Samples
Saeed Vahidian, Baharan Mirzasoleiman, Alexander Cloninger
In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We int…
LDLE: Low Distortion Local Eigenmaps
Dhruv Kohli, Alexander Cloninger, Gal Mishne
We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers t…
Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights
Zhaiming Shen, Alex Havrilla, Rongjie Lai +2
Transformers serve as the foundational architecture for large language and video generation models, such as GPT, BERT, SORA and their successors. Empirical studies have demonstrate…
Point Cloud Classification via Deep Set Linearized Optimal Transport
Scott Mahan, Caroline Moosmüller, Alexander Cloninger
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an space. This embedding preserves spe…
Bigeometric Organization of Deep Nets
Alexander Cloninger, Ronald R. Coifman, Nicholas Downing +1
In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of th…
Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
Dhruv Kohli, Sawyer J. Robertson, Gal Mishne +1
Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis. The standard approach, Local Principal Component Analysis (LPCA), struggles in…
On a Generalization of Wasserstein Distance and the Beckmann Problem to Connection Graphs
Sawyer Robertson, Dhruv Kohli, Gal Mishne +1
We propose a model of optimal parallel transport between vector fields on a connection graph, which consists of a weighted graph along with a map from its edges to an orthogonal gr…
Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors
Chester Holtz, Gal Mishne, Alexander Cloninger
Probabilistic generative models provide a flexible and systematic framework for learning the underlying geometry of data. However, model selection in this setting is challenging, p…
Provable approximation properties for deep neural networks
Uri Shaham, Alexander Cloninger, Ronald R. Coifman
We discuss approximation of functions using deep neural nets. Given a function on a -dimensional manifold , we construct a sparsely-connected depth-4…
On Suprema of Autoconvolutions with an Application to Sidon sets
Alexander Cloninger, Stefan Steinerberger
Let be a nonnegative function supported on . We show $$ \sup_{x \in \mathbb{R}}{\int_{\mathbb{R}}{f(t)f(x-t)dt}} \geq 1.28\left(\int_{-1/4}^{1/4}{f(x)dx} \right)^2…
Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds
Jun Linwu, Varun Khurana, Nicholas Karris +1
The pyLOT library offers a Python implementation of linearized optimal transport (LOT) techniques and methods to use in downstream tasks. The pipeline embeds probability distributi…
OTClean: Data Cleaning for Conditional Independence Violations using Optimal Transport
Alireza Pirhadi, Mohammad Hossein Moslemi, Alexander Cloninger +2
Ensuring Conditional Independence (CI) constraints is pivotal for the development of fair and trustworthy machine learning models. In this paper, we introduce \sys, a framework tha…
Random Walks, Conductance, and Resistance for the Connection Graph Laplacian
Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn +3
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective r…
Scalable Graph Coreset Selection via Greedy Sampling
Zhaiming Shen, Alexander Cloninger
The paper introduces a greedy column‑selective algorithm that samples representative nodes from large graphs using only small random subsets of Laplacian columns, avoiding eigendec…
Non-degenerate Rigid Alignment in a Patch Framework
Dhruv Kohli, Gal Mishne, Alexander Cloninger
Given a set of overlapping local views (patches) of a dataset, we consider the problem of finding a rigid alignment of the views that minimizes a -norm based alignment error. In…
A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems
Yimeng Zhang, Alexander Cloninger, Bo Li +1
We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for system…
Resistance Distance and Linearized Optimal Transport on Graphs
Sawyer Robertson, Zhengchao Wan, Alexander Cloninger
We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy…
LINSCAN -- A Linearity Based Clustering Algorithm
Andrew Dennehy, Xiaoyu Zou, Shabnam J. Semnani +2
DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverag…
Diffusion Nets
Gal Mishne, Uri Shaham, Alexander Cloninger +1
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold l…
Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders
Stefan C. Schonsheck, Scott Mahan, Timo Klock +2
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect h…
Two-sample Statistics Based on Anisotropic Kernels
Xiuyuan Cheng, Alexander Cloninger, Ronald R. Coifman
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When…
Optimal Transport, Timesteppers, Newton-Krylov Methods and Steady States of Collective Particle Dynamics
Hannes Vandecasteele, Nicholas Karris, Alexander Cloninger +1
Timesteppers constitute a powerful tool in modern computational science and engineering. Although they are typically used to advance the system forward in time, they can also be vi…
Robust Graph-Based Semi-Supervised Learning via -Conductances
Sawyer Jack Robertson, Chester Holtz, Zhengchao Wan +2
We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called -conductance learning…
On the Dual Geometry of Laplacian Eigenfunctions
Alexander Cloninger, Stefan Steinerberger
We discuss the geometry of Laplacian eigenfunctions on compact manifolds and combinatorial graphs . The 'dual' geometry of Laplacian eigenfunctions i…
Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systems
Nicholas Karris, Evangelos A. Nikitopoulos, Ioannis G. Kevrekidis +2
We develop an Euler-type method to predict the evolution of a time-dependent probability measure without explicitly learning an operator that governs its evolution. We use lineariz…
Semi-Supervised Laplace Learning on Stiefel Manifolds
Chester Holtz, Pengwen Chen, Alexander Cloninger +2
Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a non…
Cautious Active Clustering
Alexander Cloninger, Hrushikesh Mhaskar
We consider the problem of classification of points sampled from an unknown probability measure on a Euclidean space. We study the question of querying the class label at a very sm…
StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm
Andreas Oslandsbotn, Zeljko Kereta, Valeriya Naumova +2
Kernel ridge regression (KRR) is a popular scheme for non-linear non-parametric learning. However, existing implementations of KRR require that all the data is stored in the main m…
Outcome Based Matching
Jonathan Bates, Alexander Cloninger
We propose a method to reduce variance in treatment effect estimates in the setting of high-dimensional data. In particular, we introduce an approach for learning a metric to be us…
Supervised learning of sheared distributions using linearized optimal transport
Varun Khurana, Harish Kannan, Alexander Cloninger +1
In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into spaces usi…
Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability
Tongtong Liang, Esha Singh, Rahul Parhi +2
Gradient descent on overparameterized neural networks typically operates at the Edge of Stability (EoS), where the largest Hessian eigenvalue hovers around a step-size-dependent th…
Generalization Below the Edge of Stability: The Role of Data Geometry
Tongtong Liang, Alexander Cloninger, Rahul Parhi +1
Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we t…
Linearized Optimal Transport for Analysis of High-Dimensional Point-Cloud and Single-Cell Data
Tianxiang Wang, Yingtong Ke, Dhananjay Bhaskar +2
Single-cell technologies generate high-dimensional point clouds of cells, enabling detailed characterization of complex patient states and treatment responses. Yet each patient is…
Linearized Wasserstein dimensionality reduction with approximation guarantees
Alexander Cloninger, Keaton Hamm, Varun Khurana +1
We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that ma…
People Mover's Distance: Class level geometry using fast pairwise data adaptive transportation costs
Alexander Cloninger, Brita Roy, Carley Riley +1
We address the problem of defining a network graph on a large collection of classes. Each class is comprised of a collection of data points, sampled in a non i.i.d. way, from some…
Effective resistance in metric spaces
Robi Bhattacharjee, Alexander Cloninger, Yoav Freund +1
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigenvectors of the graph Laplacian. One attractive app…
Sigma-Delta and Distributed Noise-Shaping Quantization Methods for Random Fourier Features
Jinjie Zhang, Harish Kannan, Alexander Cloninger +1
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We…
Robust boundary detection and density estimation using doubly stochastic scaling of the Gaussian kernel
Dhruv Kohli, Jesse He, Chester Holtz +2
This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the pre…
Linear Optimal Transport Embedding: Provable Wasserstein classification for certain rigid transformations and perturbations
Caroline Moosmüller, Alexander Cloninger
Discriminating between distributions is an important problem in a number of scientific fields. This motivated the introduction of Linear Optimal Transportation (LOT), which embeds…
A deep network construction that adapts to intrinsic dimensionality beyond the domain
Alexander Cloninger, Timo Klock
We study the approximation of two-layer compositions via deep networks with ReLU activation, where is a geometrically intuitive, dimensionality reducing feat…
DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network
Jared Katzman, Uri Shaham, Jonathan Bates +3
Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of var…