Alexander Tong

Conditional Flow Matching: Simulation-Free Dynamic Optimal Transport

Yanlei Zhang

2023-01-01

arXiv.org (preprint)

DynGFN: Bayesian Dynamic Causal Discovery using Generative Flow Networks

Lazar Atanackovic

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)

GEODESIC SINKHORN FOR FAST AND ACCURATE OPTIMAL TRANSPORT ON MANIFOLDS

Guillaume Huguet

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… (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)

arxiv.org

A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction

Guillaume Huguet

Edward De Brouwer

Yanlei Zhang

Ian Adelstein

openreview.net

Bayesian Dynamic Causal Discovery

Lazar Atanackovic

Jason Hartford

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 that are equally likely 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 treat causal discovery in the unrolled causal graph as a problem of sparse identification of a dynamical system. 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 (Dyn-GFN) tailored for this task. Dyn-GFN imposes an edge-wise sparse prior to sequentially build a k -sparse causal graph. Through evaluation on temporal data, our results show that the posterior learned with Dyn-GFN yields improved Bayes coverage of admissible causal structures relative to state of the art Bayesian causal discovery methods.

2022-11-30

NeurIPS.cc/2022/Workshop/CDS (poster)

openreview.net

Multiscale PHATE identifies multimodal signatures of COVID-19

Manik Kuchroo

Je-chun Huang

Patrick Wong

Jean-Christophe Grenier

Dennis Shung

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

Akiko Iwasaki

2022-02-28

Nature Biotechnology (published)

Multiscale PHATE identifies multimodal signatures of COVID-19

Manik Kuchroo

Je-chun Huang

Patrick W. Wong

Jean-Christophe Grenier

Dennis L. Shung

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

Akiko Iwasaki

2022-02-28

Nature Biotechnology (published)

Fixing Bias in Reconstruction-based Anomaly Detection with Lipschitz Discriminators

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)

Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance

Dennis Shung

Manik Kuchroo

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

Dennis L. Shung

Manik Kuchroo

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

Multiscale PHATE Exploration of SARS-CoV-2 Data Reveals Multimodal Signatures of Disease

Manik Kuchroo

Jessie Huang

Patrick Wong

Jean-Christophe Grenier

Dennis Shung

Carolina Lucas

Jon Klein

Daniel B. Burkhardt

Scott Gigante

Abhinav Godavarthi

Benjamin Israelow

Tianyang Mao

Ji Eun Oh

Julio Silva

Takehiro Takahashi

Camila D. Odio

Arnau Casanovas-Massana

John Fournier

Shelli Farhadian … (see 7 more)

Charles S. Dela Cruz

Albert I. Ko

F. Perry Wilson

Julie Hussin

Akiko Iwasaki

2020-11-17

bioRxiv (preprint)