Guy Wolf

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

Ria Arora

Master's Research - Université de Montréal

Co-supervisor :

Liam Paull

Adrien Aumon

PhD - Université de Montréal

Semih Cantürk

PhD - Université de Montréal

Collaborating Alumni

Enrique Fita Sanmartin

Collaborating Alumni - Université de Montréal

Stefan Horoi

PhD - Université de Montréal

Will Hua

Collaborating Alumni - McGill University

Xiaolong Huang

Master's Research - Concordia University

Principal supervisor :

Eugene Belilovsky

Guillaume Huguet

PhD - Université de Montréal

Paul Janson

PhD - Concordia University

Principal supervisor :

Charles-Etienne Joseph

Master's Research - Université de Montréal

Principal supervisor :

Eugene Belilovsky

M. Elyes Kanoun

Research Intern - Université de Montréal

Vincent Létourneau

Collaborating Alumni - Université de Montréal

Myriam Lizotte

PhD - Université de Montréal

Philippe Martin

PhD - Université de Montréal

Co-supervisor :

Paul François

Paria Mehrbod

Master's Research - Concordia University

Principal supervisor :

Eugene Belilovsky

Lydia Mezrag

PhD - Université de Montréal

Kevin Moon

Independent visiting researcher

Sacha Morin

PhD - Université de Montréal

Co-supervisor :

Postdoctorate - Concordia University

Principal supervisor :

Shuang Ni

PhD - Université de Montréal

Albert Orozco Camacho

PhD - Concordia University

Principal supervisor :

Master's Research - Université de Montréal

Matthew Scicluna

PhD - Université de Montréal

Principal supervisor :

Master's Research - Université de Montréal

Pedro Vianna

Collaborating researcher - Université de Montréal

Co-supervisor :

PhD - Université de Montréal

Postdoctorate - Université de Montréal

Stephanie Zandee

Collaborating researcher - McGill University (assistant professor)

Exploring the COVID-19 Interferon Paradox with Dimensionality Reduction and Clustering

Blog Posts

Graph and representation of working methodology, and graph of data on deaths 60 days after onset of symptoms.

February 19, 2025

Sacha Morin

Elsa Brunet-Ratnasingham

Guy Wolf

Read the article

Publications

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)

Graph Fourier MMD for signals on data graphs

Samuel Leone

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

Improving and generalizing flow-based generative models with minibatch optimal transport

Yanlei Zhang

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their si… (see more)mulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schr\"odinger bridge inference.

2023-02-01

ArXiv (preprint)

Improving and generalizing flow-based generative models with minibatch optimal transport

Yanlei Zhang

2023-02-01

ArXiv (preprint)

Improving and generalizing flow-based generative models with minibatch optimal transport

Yanlei Zhang

2023-02-01

ArXiv (preprint)

Improving and generalizing flow-based generative models with minibatch optimal transport

Yanlei Zhang

2023-02-01

ArXiv (preprint)

Reliability of CKA as a Similarity Measure in Deep Learning

MohammadReza Davari

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)

openreview.net

Conditional Flow Matching: Simulation-Free Dynamic Optimal Transport

Yanlei Zhang

Continuous normalizing ﬂows (CNFs) are an attractive generative modeling technique, but they have thus far been held back by limitations i… (see more)n their simulation-based maximum likelihood training. In this paper, we introduce a new technique called conditional ﬂow matching (CFM), a simulation-free training objective for CNFs. CFM features a stable regression objective like that used to train the stochastic ﬂow in diffusion models but enjoys the efﬁcient inference of deterministic ﬂow models. In contrast to both diffusion models and prior CNF training algorithms, our CFM objec-tive does not require the source distribution to be Gaussian or require evaluation of its density. Based on this new objective, we also introduce optimal transport CFM (OT-CFM), which creates simpler ﬂows that are more stable to train and lead to faster inference, as evaluated in our experiments. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks such as inferring single cell dynamics, unsupervised image translation, and Schr ¨ odinger bridge inference. Code is available at https://github.com/atong01/ conditional-flow-matching .

2023-01-01

arXiv.org (preprint)

Conditional Flow Matching: Simulation-Free Dynamic Optimal Transport

Yanlei Zhang

2023-01-01

arXiv.org (preprint)

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)