2.1k citations · 2.4k across the 35 of their papers we have counts for
15 papers · 1 filter
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…
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…
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 featur…
Nonclosedness of Sets of Neural Networks in Sobolev Spaces
Scott Mahan, Emily King, Alex Cloninger
We examine the closedness of sets of realized neural networks of a fixed architecture in Sobolev spaces. For an exactly -times differentiable activation function , we constru…
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.…
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…
Defending against Adversarial Images using Basis Functions Transformations
Uri Shaham, James Garritano, Yutaro Yamada +5
We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images. Speci…
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…
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…
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…
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…
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…
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…
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…