Smita Krishnaswamy

Maximilian Nickel

Ian Adelstein

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the under… (voir plus)lying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM’s utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

2023-07-03

Proceedings of the 40th International Conference on Machine Learning (publié)

Graph Fourier MMD for Signals on Graphs

Samuel Leone

Aarthi Venkat

Guillaume Huguet

Alexander Tong

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little at… (voir plus)tention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes the difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization.

2023-05-21

SampTA/2023/Conference (publié)

Single-cell analysis reveals inflammatory interactions driving macular degeneration

Manik Kuchroo

Marcello DiStasio

Eric Song

Eda Calapkulu

Le Zhang

Maryam Ige

Amar H. Sheth

Abdelilah Majdoubi

Madhvi Menon

Alexander Tong

Abhinav Godavarthi

Yu Xing

Scott Gigante

Holly Steach

Jessie Huang

Je-chun Huang

Guillaume Huguet

Janhavi Narain

Kisung You

George Mourgkos … (voir 6 de plus)

Rahul M. Dhodapkar

Matthew Hirn

Bastian Rieck

Brian P. Hafler

2023-05-05

Nature Communications (publié)

Neural FIM for learning Fisher Information Metrics from point cloud data

Oluwadamilola Fasina

Guillaume Huguet

Alexander Tong

Yanlei Zhang

Maximilian Nickel

Ian Adelstein

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the under… (voir plus)lying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

2023-04-24

ICML.cc/2023/Conference (poster)

Multi-view manifold learning of human brain state trajectories

Erica Lindsey Busch

Je-chun Huang

Andrew Benz

Tom Wallenstein

Guillaume Lajoie

Nicholas Turk-Browne

2023-03-27

Nature Computational Science (publié)

Graph Fourier MMD for signals on data graphs

Samuel Leone

Alexander Tong

Guillaume Huguet

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little at… (voir plus)tention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel a distance between distributions, or non-negative signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called {\em gene localization score} which helps select genes for cellular state space characterization.

2023-02-01

ICLR.cc/2023/Conference (rejected)

GEODESIC SINKHORN FOR FAST AND ACCURATE OPTIMAL TRANSPORT ON MANIFOLDS

Guillaume Huguet

Alexander Tong

María Ramos Zapatero

Christopher J. Tape

Efficient computation of optimal transport distance between distributions is of growing importance in data science. Sinkhorn-based methods a… (voir plus)re currently the state-of-the-art for such computations, but require O(n2) computations. In addition, Sinkhorn-based methods commonly use an Euclidean ground distance between datapoints. However, with the prevalence of manifold structured scientific data, it is often desirable to consider geodesic ground distance. Here, we tackle both issues by proposing Geodesic Sinkhorn—based on diffusing a heat kernel on a manifold graph. Notably, Geodesic Sinkhorn requires only O(n log n) computation, as we approximate the heat kernel with Chebyshev polynomials based on the sparse graph Laplacian. We apply our method to the computation of barycenters of several distributions of high dimensional single cell data from patient samples undergoing chemotherapy. In particular, we define the barycentric distance as the distance between two such barycenters. Using this definition, we identify an optimal transport distance and path associated with the effect of treatment on cellular data.

2023-01-01

2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP) (publié)

arxiv.org

A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction

Guillaume Huguet

Alexander Tong

Edward De Brouwer

Yanlei Zhang

Ian Adelstein

Inferring Dynamic Regulatory Interaction Graphs From Time Series Data With Perturbations

Dhananjay Bhaskar

Daniel Sumner Magruder

Edward De Brouwer

Matheo Morales

Aarthi Venkat

Frederik Wenkel

2023-01-01

LoG (publié)

Learning Shared Neural Manifolds from Multi-Subject FMRI Data

Jessie Huang

Je-chun Huang

Erica Lindsey Busch

Tom Wallenstein

Michal Gerasimiuk

Andrew Benz

Guillaume Lajoie

Nicholas Turk-Browne

Functional magnetic resonance imaging (fMRI) data is collected in millions of noisy, redundant dimensions. To understand how different brain… (voir plus)s process the same stimulus, we aim to denoise the fMRI signal via a meaningful embedding space that captures the data's intrinsic structure as shared across brains. We assume that stimulus-driven responses share latent features common across subjects that are jointly discoverable. Previous approaches to this problem have relied on linear methods like principal component analysis and shared response modeling. We propose a neural network called MRMD-AE (manifold-regularized multiple- decoder, autoencoder) that learns a common embedding from multi-subject fMRI data while retaining the ability to decode individual responses. Our latent common space represents an extensible manifold (where untrained data can be mapped) and improves classification accuracy of stimulus features of unseen timepoints, as well as cross-subject translation of fMRI signals.

2022-08-22

2022 IEEE 32nd International Workshop on Machine Learning for Signal Processing (MLSP) (publié)

Multiscale PHATE identifies multimodal signatures of COVID-19

Manik Kuchroo

Je-chun Huang

Patrick Wong

Jean-Christophe Grenier

Dennis Shung

Alexander Tong

Carolina Lucas

Jon Klein

Daniel B. Burkhardt

Scott Gigante

Abhinav Godavarthi

Bastian Rieck

Benjamin Israelow

Michael Simonov

Tianyang Mao

Ji Eun Oh

Julio Silva

Takehiro Takahashi

Camila D. Odio

Arnau Casanovas-Massana … (voir 10 de plus)

John Fournier

Shelli Farhadian

Charles S. Dela Cruz

Albert I. Ko

Matthew Hirn

F. Perry Wilson

Julie Hussin

Akiko Iwasaki

2022-02-28

Nature Biotechnology (publié)

Multiscale PHATE identifies multimodal signatures of COVID-19

Manik Kuchroo

Je-chun Huang

Patrick W. Wong

Jean-Christophe Grenier

Dennis L. Shung

Alexander Tong

C. Lucas

J. Klein

Daniel B. Burkhardt

Scott Gigante

Abhinav Godavarthi

Bastian Rieck

Benjamin Israelow

Michael Simonov

Tianyang Mao

Ji Eun Oh

Julio Silva

Takehiro Takahashi

C. Odio

Arnau Casanovas‐massana … (voir 10 de plus)

John Byrne Fournier

Shelli F. Farhadian

C. D. Dela Cruz

A. Ko

Matthew Hirn

F. Wilson

Julie Hussin

Akiko Iwasaki

2022-02-28

Nature Biotechnology (published)