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Alexander Tong

alexander.tong@mila.quebec
Postdoctorate - Université de Montréal
Supervisor
Yoshua Bengio

Publications

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 … (see 6 more)
Rahul M. Dhodapkar
Matthew Hirn
Bastian Rieck
Guy Wolf
Smita Krishnaswamy
Brian P. Hafler
2023-05-05
Nature Communications (published)
doi.org
Neural FIM for learning Fisher Information Metrics from point cloud data
Oluwadamilola Fasina
Guillaume Huguet
Alexander Tong
Yanlei Zhang
Guy Wolf
Maximilian Nickel
Ian Adelstein
Smita Krishnaswamy
Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the under… (see more)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)
doi.org
openreview.net
Graph Fourier MMD for signals on data graphs
Samuel Leone
Alexander Tong
Guillaume Huguet
Guy Wolf
Smita Krishnaswamy
While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little at… (see more)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)
openreview.net
openreview.net
Conditional Flow Matching: Simulation-Free Dynamic Optimal Transport
Alexander Tong
Nikolay Malkin
Guillaume Huguet
Yanlei Zhang
Jarrid Rector-Brooks
Kilian FATRAS
Guy Wolf
Yoshua Bengio
2023-01-01
arXiv.org (preprint)
doi.org
DynGFN: Bayesian Dynamic Causal Discovery using Generative Flow Networks
Lazar Atanackovic
Alexander Tong
Jason Hartford
Leo Jingyu Lee
Bo Wang
Yoshua Bengio
Learning the causal structure of observable variables is a central focus for scientific discovery. Bayesian causal discovery methods tackle… (see more) this problem by learning a posterior over the set of admissible graphs given our priors and observations. Existing methods primarily consider observations from static systems and assume the underlying causal structure takes the form of a directed acyclic graph (DAG). In settings with dynamic feedback mechanisms that regulate the trajectories of individual variables, this acyclicity assumption fails unless we account for time. We focus on learning Bayesian posteriors over cyclic graphs and treat causal discovery as a problem of sparse identification of a dynamical sys-tem. This imposes a natural temporal causal order between variables and captures cyclic feedback loops through time. Under this lens, we propose a new framework for Bayesian causal discovery for dynamical systems and present a novel generative flow network architecture (DynGFN) tailored for this task. Our results indicate that DynGFN learns posteriors that better encapsulate the distributions over admissible cyclic causal structures compared to counterpart state-of-the-art approaches.
2023-01-01
arXiv.org (preprint)
doi.org
GEODESIC SINKHORN FOR FAST AND ACCURATE OPTIMAL TRANSPORT ON MANIFOLDS
Guillaume Huguet
Alexander Tong
María Ramos Zapatero
Christopher J. Tape
Guy Wolf
Smita Krishnaswamy
Efficient computation of optimal transport distance between distributions is of growing importance in data science. Sinkhorn-based methods a… (see more)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) (published)
doi.org
arxiv.org
A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction
Guillaume Huguet
Alexander Tong
Edward De Brouwer
Yanlei Zhang
Guy Wolf
Ian Adelstein
Smita Krishnaswamy
openreview.net
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 … (see 10 more)
John Fournier
Shelli Farhadian
Charles S. Dela Cruz
Albert I. Ko
Matthew Hirn
F. Perry Wilson
Julie Hussin
Guy Wolf
Akiko Iwasaki
Smita Krishnaswamy
2022-02-28
Nature Biotechnology (published)
doi.org
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 … (see 10 more)
John Byrne Fournier
Shelli F. Farhadian
C. D. Dela Cruz
A. Ko
Matthew Hirn
F. Wilson
Julie Hussin
Guy Wolf
Akiko Iwasaki
Smita Krishnaswamy
2022-02-28
Nature Biotechnology (published)
doi.org
Fixing Bias in Reconstruction-based Anomaly Detection with Lipschitz Discriminators
Alexander Tong
Guy Wolf
Smita Krishnaswamy
Anomaly detection is of great interest in fields where abnormalities need to be identified and corrected (e.g., medicine and finance). Deep … (see more)learning methods for this task often rely on autoencoder reconstruction error, sometimes in conjunction with other penalties. We show that this approach exhibits intrinsic biases that lead to undesirable results. Reconstruction-based methods can sometimes show low error on simple-to-reconstruct points that are not part of the training data, for example the all black image. Instead, we introduce a new unsupervised Lipschitz anomaly discriminator (LAD) that does not suffer from these biases. Our anomaly discriminator is trained, similar to the discriminator of a GAN, to detect the difference between the training data and corruptions of the training data. We show that this procedure successfully detects unseen anomalies with guarantees on those that have a certain Wasserstein distance from the data or corrupted training set. These additions allow us to show improved performance on MNIST, CIFAR10, and health record data. Further, LAD does not require decoding back to the original data space, which makes anomaly detection possible in domains where it is difficult to define a decoder, such as in irregular graph structured data. Empirically, we show this framework leads to improved performance on image, health record, and graph data.
2021-11-28
Journal of Signal Processing Systems (published)
doi.org
Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance
Alexander Tong
Guillaume Huguet
Dennis L. Shung
Amine Natik
Manik Kuchroo
Guillaume Lajoie
Guy Wolf
Smita Krishnaswamy
In modern relational machine learning it is common to encounter large graphs that arise via interactions or similarities between observation… (see more)s in many domains. Further
2021-01-01
arXiv.org (preprint)
dblp.uni-trier.de
Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance
Alexander Tong
Guillaume Huguet
Dennis Shung
Amine Natik
Manik Kuchroo
Guillaume Lajoie
Guy Wolf
Smita Krishnaswamy
In modern relational machine learning it is common to encounter large graphs that arise via interactions or similarities between observation… (see more)s in many domains. Further
2021-01-01
arXiv.org (preprint)
dblp.uni-trier.de