Guy Wolf

Core Academic Member

wolfguy@mila.quebec

Canada CIFAR AI Chair

Associate Professor, Université de Montréal, Department of Mathematics and Statistics

Concordia University

CHUM - Montreal University Hospital Center

Website

Google Scholar

Biography

Guy Wolf is an associate professor in the Department of Mathematics and Statistics at Université de Montréal.

His research interests lie at the intersection of machine learning, data science and applied mathematics. He is particularly interested in data mining methods that use manifold learning and deep geometric learning, as well as applications for the exploratory analysis of biomedical data.

Wolf’s research focuses on exploratory data analysis and its applications in bioinformatics. His approaches are multidisciplinary and bring together machine learning, signal processing and applied math tools. His recent work has used a combination of diffusion geometries and deep learning to find emergent patterns, dynamics, and structure in big high dimensional- data (e.g., in single-cell genomics and proteomics).

Current Students

Adrien Aumon

PhD - Université de Montréal

adrien.aumon@mila.quebec

Albert Orozco Camacho

PhD - Concordia University

Principal supervisor :

Amine Natik

PhD - Université de Montréal

Principal supervisor :

Guillaume Lajoie

natikami@mila.quebec

Charles-Etienne Joseph

Master's Research - Université de Montréal

Principal supervisor :

Eugene Belilovsky

charles-etienne.joseph@mila.quebec

Github

Will Hua

Master's Research - McGill University

Principal supervisor :

Doina Precup

chenqing.hua@mila.quebec

Donald Shenaj

Collaborating researcher - Concordia University

Principal supervisor :

Eugene Belilovsky

donald.shenaj@mila.quebec

Independent visiting researcher

edouard.oyallon@mila.quebec

Postdoctorate - Concordia University

Principal supervisor :

Eugene Belilovsky

geraldin.nanfack@mila.quebec

Guillaume Huguet

PhD - Université de Montréal

guillaume.huguet@mila.quebec

Github

Google Scholar

Hasti Nafisi

Master's Research - Université de Montréal

Co-supervisor :

Yashar Hezaveh

hasti.nafisi@mila.quebec

Jake Kovalic

Collaborating researcher - Yale

jake.kovalic@mila.quebec

Github

Frederik Wenkel

PhD - Université de Montréal

frederik.wenkel@mila.quebec

PhD - Université de Montréal

lydia.mezrag@mila.quebec

Mehrbod Paria

Master's Research - Concordia University

Principal supervisor :

Eugene Belilovsky

paria.mehrbod@mila.quebec

Muawiz Chaudhary

Collaborating Alumni

muawiz.chaudhary@mila.quebec

Github

Google Scholar

Myriam Lizotte

PhD - Université de Montréal

myriam.lizotte@mila.quebec

Nader Asadi

Collaborating Alumni

Principal supervisor :

Eugene Belilovsky

nader.asadi@mila.quebec

Collaborating researcher - Université de Montréal

Co-supervisor :

Eugene Belilovsky

pedro.vianna@mila.quebec

Github

Google Scholar

Ria Arora

Master's Research - Université de Montréal

Co-supervisor :

Liam Paull

ria.arora@mila.quebec

Github

Sacha Morin

PhD - Université de Montréal

Co-supervisor :

Liam Paull

sacha.morin@mila.quebec

Semih Cantürk

PhD - Université de Montréal

semih.canturk@mila.quebec

Website

Github

Google Scholar

Shuang Ni

PhD - Université de Montréal

shuang.ni@mila.quebec

Website

Github

Siddharth Viswanath

Collaborating researcher - Yale

siddarth.viswanath@mila.quebec

Stefan Horoi

PhD - Université de Montréal

stefan.horoi@mila.quebec

Postdoctorate - Université de Montréal

letournv@mila.quebec

Vivian White

Research Intern - Western Washington University

Principal supervisor :

Guillaume Lajoie

vivian.white@mila.quebec

Github

Zhang Yanlei

Postdoctorate - Université de Montréal

yanlei.zhang@mila.quebec

Website

Google Scholar

Publications

Geometry Regularized Autoencoders

Andres F. Duque Correa

Sacha Morin

Guy Wolf

Kevin R. Moon

A fundamental task in data exploration is to extract low dimensional representations that capture intrinsic geometry in data, especially for… (see more) faithfully visualizing data in two or three dimensions. Common approaches use kernel methods for manifold learning. However, these methods typically only provide an embedding of the input data and cannot extend naturally to new data points. Autoencoders have also become popular for representation learning. While they naturally compute feature extractors that are extendable to new data and invertible (i.e., reconstructing original features from latent representation), they often fail at representing the intrinsic data geometry compared to kernel-based manifold learning. We present a new method for integrating both approaches by incorporating a geometric regularization term in the bottleneck of the autoencoder. This regularization encourages the learned latent representation to follow the intrinsic data geometry, similar to manifold learning algorithms, while still enabling faithful extension to new data and preserving invertibility. We compare our approach to autoencoder models for manifold learning to provide qualitative and quantitative evidence of our advantages in preserving intrinsic structure, out of sample extension, and reconstruction. Our method is easily implemented for big-data applications, whereas other methods are limited in this regard.

2023-06-01

IEEE Transactions on Pattern Analysis and Machine Intelligence (published)

doi.org

Identifying Critical Neurons in ANN Architectures using Mixed Integer Programming

Mostafa ElAraby

Guy Wolf

Margarida Carvalho

2023-05-23

Integration of Constraint Programming, Artificial Intelligence, and Operations Research (published)

doi.org

arxiv.org

Data Imputation with an Autoencoder and MAGIC

Devin Eddington

Andres Felipe Duque Correa

Guy Wolf

Kevin R. Moon

Missing data is a common problem in many applications. Imputing missing values is a challenging task, as the imputations need to be accurate… (see more) and robust to avoid introducing bias in downstream analysis. In this paper, we propose an ensemble method that combines the strengths of a manifold learning-based imputation method called MAGIC and an autoencoder deep learning model. We call our method Deep MAGIC. Deep MAGIC is trained on a linear combination of the mean squared error of the original data and the mean squared error of the MAGIC-imputed data. Experimental results on three benchmark datasets show that Deep MAGIC outperforms several state-of-the-art imputation methods, demonstrating its effectiveness and robustness in handling large amounts of missing data.

2023-05-21

SampTA/2023/Conference (published)

doi.org

openreview.net

Graph Fourier MMD for Signals on Graphs

Samuel Leone

Aarthi Venkat

Guillaume Huguet

Alexander Tong

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 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 (published)

doi.org

openreview.net

Manifold Alignment with Label Information

Andres F. Duque Correa

Myriam Lizotte

Guy Wolf

Kevin R. Moon

Multi-domain data is becoming increasingly common and presents both challenges and opportunities in the data science community. The integrat… (see more)ion of distinct data-views can be used for exploratory data analysis, and benefit downstream analysis including machine learning related tasks. With this in mind, we present a novel manifold alignment method called MALI (Manifold alignment with label information) that learns a correspondence between two distinct domains. MALI belongs to a middle ground between the more commonly addressed semi-supervised manifold alignment, where some known correspondences between the two domains are assumed to be known beforehand, and the purely unsupervised case, where no information linking both domains is available. To do this, MALI learns the manifold structure in both domains via a diffusion process and then leverages discrete class labels to guide the alignment. MALI recovers a pairing and a common representation that reveals related samples in both domains. We show that MALI outperforms the current state-of-the-art manifold alignment methods across multiple datasets.

2023-05-21

SampTA/2023/Conference (published)

doi.org

openreview.net

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

Multi-view manifold learning of human brain state trajectories

Erica Lindsey Busch

Je-chun Huang

Andrew Benz

Tom Wallenstein

Guillaume Lajoie

Guy Wolf

Smita Krishnaswamy

Nicholas Turk-Browne

2023-03-27

Nature Computational Science (published)

doi.org

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

Reliability of CKA as a Similarity Measure in Deep Learning

MohammadReza Davari

Stefan Horoi

Amine Natik

Guillaume Lajoie

Guy Wolf

Eugene Belilovsky

Comparing learned neural representations in neural networks is a challenging but important problem, which has been approached in different w… (see more)ays. The Centered Kernel Alignment (CKA) similarity metric, particularly its linear variant, has recently become a popular approach and has been widely used to compare representations of a network's different layers, of architecturally similar networks trained differently, or of models with different architectures trained on the same data. A wide variety of claims about similarity and dissimilarity of these various representations have been made using CKA results. In this work we present analysis that formally characterizes CKA sensitivity to a large class of simple transformations, which can naturally occur in the context of modern machine learning. This provides a concrete explanation to CKA sensitivity to outliers, which has been observed in past works, and to transformations that preserve the linear separability of the data, an important generalization attribute. We empirically investigate several weaknesses of the CKA similarity metric, demonstrating situations in which it gives unexpected or counterintuitive results. Finally we study approaches for modifying representations to maintain functional behaviour while changing the CKA value. Our results illustrate that, in many cases, the CKA value can be easily manipulated without substantial changes to the functional behaviour of the models, and call for caution when leveraging activation alignment metrics.

2023-02-01

ICLR.cc/2023/Conference (poster)

doi.org

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

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

AI Research Driven by Real-World Problems

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Student Life and Resources

Guy Wolf

Biography

Current Students

Publications

AI Research Driven by Real-World Problems

AI Policy Compass

Student Life and Resources

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Guy Wolf

Biography

Current Students

Publications