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

Sabeur Aridhi

Independent visiting researcher - University of Lorraine

Ria Arora

Master's Research - Université de Montréal

Co-supervisor :

Liam Paull

Nader Asadi

Collaborating Alumni

Principal supervisor :

PhD - Université de Montréal

Semih Cantürk

PhD - Université de Montréal

semihcanturk00@gmail.com

Collaborating Alumni

Collaborating researcher - Western Washington University (faculty; assistant prof))

Co-supervisor :

PhD - Université de Montréal

Will Hua

Master's Research - McGill University

Principal supervisor :

Doina Precup

Guillaume Huguet

PhD - Université de Montréal

Charles-Etienne Joseph

Master's Research - Université de Montréal

Principal supervisor :

Jake Kovalic

Collaborating researcher - Yale

Smita Krishnaswamy Krishnaswamy

Independent visiting researcher - Yale University

Postdoctorate - Université de Montréal

Myriam Lizotte

PhD - Université de Montréal

Lydia Mezrag

PhD - Université de Montréal

Sacha Morin

PhD - Université de Montréal

Co-supervisor :

Liam Paull

Hasti Nafisi

Master's Research - Université de Montréal

Co-supervisor :

Yashar Hezaveh

Geraldin Nanfack

Postdoctorate - Concordia University

Principal supervisor :

Amine Natik

PhD - Université de Montréal

Principal supervisor :

Guillaume Lajoie

Shuang Ni

PhD - Université de Montréal

Albert Orozco Camacho

PhD - Concordia University

Principal supervisor :

Independent visiting researcher

Master's Research - Concordia University

Principal supervisor :

Thomas Sabourin

Master's Research - Université de Montréal

Donald Shenaj

Collaborating researcher - Concordia University

Principal supervisor :

Collaborating researcher - Université de Montréal

Co-supervisor :

Collaborating researcher - Yale

Frederik Wenkel

PhD - Université de Montréal

Research Intern - Western Washington University

Principal supervisor :

Guillaume Lajoie

Zhang Yanlei

Postdoctorate - Université de Montréal

Publications

The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges

Sitao Luan

Chenqing Hua

Qincheng Lu

Liheng Ma

Lirong Wu

Xinyu Wang

Minkai Xu

Xiao-Wen Chang

Doina Precup

Rex Ying

Stan Z. Li

Jian Tang

Stefanie Jegelka

Homophily principle, \ie{} nodes with the same labels or similar attributes are more likely to be connected, has been commonly believed to b… (see more)e the main reason for the superiority of Graph Neural Networks (GNNs) over traditional Neural Networks (NNs) on graph-structured data, especially on node-level tasks. However, recent work has identified a non-trivial set of datasets where GNN's performance compared to the NN's is not satisfactory. Heterophily, i.e. low homophily, has been considered the main cause of this empirical observation. People have begun to revisit and re-evaluate most existing graph models, including graph transformer and its variants, in the heterophily scenario across various kinds of graphs, e.g. heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely related to the heterophily problem. In the past few years, considerable effort has been devoted to studying and addressing the heterophily issue. In this survey, we provide a comprehensive review of the latest progress on heterophilic graph learning, including an extensive summary of benchmark datasets and evaluation of homophily metrics on synthetic graphs, meticulous classification of the most updated supervised and unsupervised learning methods, thorough digestion of the theoretical analysis on homophily/heterophily, and broad exploration of the heterophily-related applications. Notably, through detailed experiments, we are the first to categorize benchmark heterophilic datasets into three sub-categories: malignant, benign and ambiguous heterophily. Malignant and ambiguous datasets are identified as the real challenging datasets to test the effectiveness of new models on the heterophily challenge. Finally, we propose several challenges and future directions for heterophilic graph representation learning.

2024-07-12

ArXiv (preprint)

Graph Positional and Structural Encoder

Renming Liu

Semih Cantürk

Olivier Lapointe-Gagné

Vincent Létourneau

Dominique Beaini

Ladislav Rampášek

Positional and structural encodings (PSE) enable better identifiability of nodes within a graph, as in general graphs lack a canonical node … (see more)ordering. This renders PSEs essential tools for empowering modern GNNs, and in particular graph Transformers. However, designing PSEs that work optimally for a variety of graph prediction tasks is a challenging and unsolved problem. Here, we present the graph positional and structural encoder (GPSE), a first-ever attempt to train a graph encoder that captures rich PSE representations for augmenting any GNN. GPSE can effectively learn a common latent representation for multiple PSEs, and is highly transferable. The encoder trained on a particular graph dataset can be used effectively on datasets drawn from significantly different distributions and even modalities. We show that across a wide range of benchmarks, GPSE-enhanced models can significantly improve the performance in certain tasks, while performing on par with those that employ explicitly computed PSEs in other cases. Our results pave the way for the development of large pre-trained models for extracting graph positional and structural information and highlight their potential as a viable alternative to explicitly computed PSEs as well as to existing self-supervised pre-training approaches.

2024-07-08

Proceedings of the 41st International Conference on Machine Learning (published)

Harmony in Diversity: Merging Neural Networks with Canonical Correlation Analysis

Stefan Horoi

Albert Manuel Orozco Camacho

2024-07-08

Proceedings of the 41st International Conference on Machine Learning (published)

Geometry-Aware Generative Autoencoders for Metric Learning and Generative Modeling on Data Manifolds

Xingzhi Sun

Danqi Liao

Kincaid MacDonald

Yanlei Zhang

Guillaume Huguet

Ian Adelstein

Tim G. J. Rudner

Smita Krishnaswamy

Non-linear dimensionality reduction methods have proven successful at learning low-dimensional representations of high-dimensional point clo… (see more)uds on or near data manifolds. However, existing methods are not easily extensible—that is, for large datasets, it is prohibitively expensive to add new points to these embeddings. As a result, it is very difficult to use existing embeddings generatively, to sample new points on and along these manifolds. In this paper, we propose GAGA (geometry-aware generative autoencoders) a framework which merges the power of generative deep learning with non-linear manifold learning by: 1) learning generalizable geometry-aware neural network embeddings based on non-linear dimensionality reduction methods like PHATE and diffusion maps, 2) deriving a non-euclidean pullback metric on the embedded space to generate points faithfully along manifold geodesics, and 3) learning a flow on the manifold that allows us to transport populations. We provide illustration on easily-interpretable synthetic datasets and showcase results on simulated and real single cell datasets. In particular, we show that the geodesic-based generation can be especially important for scientific datasets where the manifold represents a state space and geodesics can represent dynamics of entities over this space.

2024-06-17

ICML.cc/2024/Workshop/GRaM (published)

Simulating federated learning for steatosis detection using ultrasound images

Yue Qi

Pedro Vianna

Alexandre Cadrin-Chênevert

Katleen Blanchet

Emmanuel Montagnon

Louis-Antoine Mullie

Guy Cloutier

Michael Chassé

An Tang

2024-06-10

Scientific Reports (published)

Enhancing Supervised Visualization through Autoencoder and Random Forest Proximities for Out-of-Sample Extension

Shuang Ni

Adrien Aumon

Kevin R. Moon

Jake S. Rhodes

The value of supervised dimensionality reduction lies in its ability to uncover meaningful connections between data features and labels. Com… (see more)mon dimensionality reduction methods embed a set of fixed, latent points, but are not capable of generalizing to an unseen test set. In this paper, we provide an out-of-sample extension method for the random forest-based supervised dimensionality reduction method, RF-PHATE, combining information learned from the random forest model with the function-learning capabilities of autoencoders. Through quantitative assessment of various autoencoder architectures, we identify that networks that reconstruct random forest proximities are more robust for the embedding extension problem. Furthermore, by leveraging proximity-based prototypes, we achieve a 40% reduction in training time without compromising extension quality. Our method does not require label information for out-of-sample points, thus serving as a semi-supervised method, and can achieve consistent quality using only 10% of the training data.

2024-06-06

ArXiv (preprint)

Noisy Data Visualization using Functional Data Analysis

Haozhe Chen

Andres Felipe Duque Correa

Kevin R. Moon

Data visualization via dimensionality reduction is an important tool in exploratory data analysis. However, when the data are noisy, many ex… (see more)isting methods fail to capture the underlying structure of the data. The method called Empirical Intrinsic Geometry (EIG) was previously proposed for performing dimensionality reduction on high dimensional dynamical processes while theoretically eliminating all noise. However, implementing EIG in practice requires the construction of high-dimensional histograms, which suffer from the curse of dimensionality. Here we propose a new data visualization method called Functional Information Geometry (FIG) for dynamical processes that adapts the EIG framework while using approaches from functional data analysis to mitigate the curse of dimensionality. We experimentally demonstrate that the resulting method outperforms a variant of EIG designed for visualization in terms of capturing the true structure, hyperparameter robustness, and computational speed. We then use our method to visualize EEG brain measurements of sleep activity.

2024-06-05

ArXiv (preprint)

Towards a General GNN Framework for Combinatorial Optimization

Frederik Wenkel

Semih Cantürk

Michael Perlmutter

2024-05-31

ArXiv (preprint)

AdaFisher: Adaptive Second Order Optimization via Fisher Information

Damien Martins Gomes

Yanlei Zhang

Mahdi S. Hosseini

First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limi… (see more)ted curvature information by employing the diagonal matrix preconditioning of the stochastic gradient during the training. Despite their widespread, second-order optimization algorithms exhibit superior convergence properties compared to their first-order counterparts e.g. Adam and SGD. However, their practicality in training DNNs are still limited due to increased per-iteration computations and suboptimal accuracy compared to the first order methods. We present AdaFisher--an adaptive second-order optimizer that leverages a block-diagonal approximation to the Fisher information matrix for adaptive gradient preconditioning. AdaFisher aims to bridge the gap between enhanced convergence capabilities and computational efficiency in second-order optimization framework for training DNNs. Despite the slow pace of second-order optimizers, we showcase that AdaFisher can be reliably adopted for image classification, language modelling and stand out for its stability and robustness in hyperparameter tuning. We demonstrate that AdaFisher outperforms the SOTA optimizers in terms of both accuracy and convergence speed. Code available from \href{https://github.com/AtlasAnalyticsLab/AdaFisher}{https://github.com/AtlasAnalyticsLab/AdaFisher}

2024-05-26

ArXiv (preprint)

Supervised latent factor modeling isolates cell-type-specific transcriptomic modules that underlie Alzheimer’s disease progression

Liam Hodgson

Yue Li

Yasser Iturria-Medina

Jo Anne Stratton

Smita Krishnaswamy

David A. Bennett

Danilo Bzdok

2024-05-17

Communications Biology (published)

Harmony in Diversity: Merging Neural Networks with Canonical Correlation Analysis

Stefan Horoi

Albert Manuel Orozco Camacho

Ensembling multiple models enhances predictive performance by utilizing the varied learned features of the different models but incurs signi… (see more)ficant computational and storage costs. Model fusion, which combines parameters from multiple models into one, aims to mitigate these costs but faces practical challenges due to the complex, non-convex nature of neural network loss landscapes, where learned minima are often separated by high loss barriers. Recent works have explored using permutations to align network features, reducing the loss barrier in parameter space. However, permutations are restrictive since they assume a one-to-one mapping between the different models' neurons exists. We propose a new model merging algorithm, CCA Merge, which is based on Canonical Correlation Analysis and aims to maximize the correlations between linear combinations of the model features. We show that our method of aligning models leads to better performances than past methods when averaging models trained on the same, or differing data splits. We also extend this analysis into the harder many models setting where more than 2 models are merged, and we find that CCA Merge works significantly better in this setting than past methods.

2024-05-01

ICML.cc/2024/Conference (poster)

Improving and Generalizing Flow-Based Generative Models with Minibatch Optimal Transport

Alexander Tong

Kilian FATRAS

Nikolay Malkin

Guillaume Huguet

Yanlei Zhang

Jarrid Rector-Brooks

Yoshua Bengio

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 \textit{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, OT-CFM is the first method to compute dynamic OT in a simulation-free way. 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 Schrödinger bridge inference.

2024-03-11

TMLR (accepted)