Alexander Tong

Bayesian Dynamic Causal Discovery

Jason Hartford

Learning the causal structure of observable variables is a central focus for scientific discovery. Bayesian causal discovery methods tackle … (voir plus)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.

2022-11-29

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

openreview.net

Embedding Signals on 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… (voir plus)s in many domains. Further, in many cases the target entities for analysis are actually signals on such graphs. We propose to compare and organize such datasets of graph signals by using an earth mover’s distance (EMD) with a geodesic cost over the underlying graph. Typically, EMD is computed by optimizing over the cost of transporting one probability distribution to another over an underlying metric space. However, this is inefficient when computing the EMD between many signals. Here, we propose an unbalanced graph EMD that efficiently embeds the unbalanced EMD on an underlying graph into an L(1) space, whose metric we call unbalanced diffusion earth mover’s distance (UDEMD). Next, we show how this gives distances between graph signals that are robust to noise. Finally, we apply this to organizing patients based on clinical notes, embedding cells modeled as signals on a gene graph, and organizing genes modeled as signals over a large cell graph. In each case, we show that UDEMD-based embeddings find accurate distances that are highly efficient compared to other methods.

2022-05-22

ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (publié)

doi.org

Embedding Signals on 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… (voir plus)s in many domains. Further, in many cases the target entities for analysis are actually signals on such graphs. We propose to compare and organize such datasets of graph signals by using an earth mover's distance (EMD) with a geodesic cost over the underlying graph. Typically, EMD is computed by optimizing over the cost of transporting one probability distribution to another over an underlying metric space. However, this is inefficient when computing the EMD between many signals. Here, we propose an unbalanced graph EMD that efficiently embeds the unbalanced EMD on an underlying graph into an

2022-04-26

IEEE International Conference on Acoustics, Speech and Signal Processing (publié)

doi.org

arxiv.org

Embedding Signals on 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… (voir plus)s in many domains. Further, in many cases the target entities for analysis are actually signals on such graphs. We propose to compare and organize such datasets of graph signals by using an earth mover's distance (EMD) with a geodesic cost over the underlying graph. Typically, EMD is computed by optimizing over the cost of transporting one probability distribution to another over an underlying metric space. However, this is inefficient when computing the EMD between many signals. Here, we propose an unbalanced graph EMD that efficiently embeds the unbalanced EMD on an underlying graph into an

2022-04-26

IEEE International Conference on Acoustics, Speech, and Signal Processing (publié)

doi.org

arxiv.org

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

Manik Kuchroo

Jessie Huang

Patrick Wong

Jean-Christophe Grenier

Dennis Shung

Alexander Tong

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 … (voir 7 de plus)

Charles S. Dela Cruz

Albert I. Ko

F. Perry Wilson

Julie Hussin

Guy Wolf

Akiko Iwasaki

Smita Krishnaswamy

Abstract

The biomedical community is producing increasingly high dimensional datasets, integrated from hundreds of… (voir plus) patient samples, which current computational techniques struggle to explore. To uncover biological meaning from these complex datasets, we present an approach called Multiscale PHATE, which learns abstracted biological features from data that can be directly predictive of disease. Built on a coarse graining process called diffusion condensation, Multiscale PHATE learns a data topology that can be analyzed at coarse levels for high level summarizations of data, as well as at fine levels for detailed representations on subsets. We apply Multiscale PHATE to study the immune response to COVID-19 in 54 million cells from 168 hospitalized patients. Through our analysis of patient samples, we identify CD16-hi,CD66b-lo neutrophil and IFNγ+,GranzymeB+ Th17 cell responses enriched in patients who die. Furthermore, we show that population groupings Multiscale PHATE discovers can be directly fed into a classifier to predict disease outcome. We also use Multiscale PHATE-derived features to construct two different manifolds of patients, one from abstracted flow cytometry features and another directly on patient clinical features, both associating immune subsets and clinical markers with outcome.

2022-02-27

Nature Biotechnology (publié)

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 … (voir plus)learning methods for this task often rely on autoencoder reconstruction error, sometimes in conjunction with other errors. We show that this approach exhibits intrinsic biases that lead to undesirable results. Reconstruction-based methods are sensitive to training-data outliers and simple-to-reconstruct points. Instead, we introduce a new unsupervised Lipschitz anomaly discriminator that does not suffer from these biases. Our anomaly discriminator is trained, similar to the ones used in GANs, 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.

2021-11-27

Journal of Signal Processing Systems (inconnu)

doi.org

arxiv.org

Data-Driven Learning of Geometric Scattering Modules for GNNs

Alexander Tong

Frederick Wenkel

Kincaid MacDonald

Smita Krishnaswamy

Guy Wolf

We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist… (voir plus) of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks.

2021-10-24

PubMed Central (accepté)

doi.org

arxiv.org

Multimodal Data Visualization and Denoising with Integrated Diffusion

Manik Kuchroo

Abhinav Godavarthi

Alexander Tong

Guy Wolf

Smita Krishnaswamy

We propose a method called integrated diffusion for combining multimodal datasets, or data gathered via several different measurements on th… (voir plus)e same system, to create a joint data diffusion operator. As real world data suffers from both local and global noise, we introduce mechanisms to optimally calculate a diffusion operator that reflects the combined information from both modalities. We show the utility of this joint operator in data denoising, visualization and clustering, performing better than other methods to integrate and analyze multimodal data. We apply our method to multi-omic data generated from blood cells, measuring both gene expression and chromatin accessibility. Our approach better visualizes the geometry of the joint data, captures known cross-modality associations and identifies known cellular populations. More generally, integrated diffusion is broadly applicable to multimodal datasets generated in many medical and biological systems.

2021-10-24

PubMed Central (accepté)

doi.org

arxiv.org

Diffusion Earth Mover's Distance and Distribution Embeddings

Alexander Tong

Guillaume Huguet

Amine Natik

Kincaid MacDonald

Manik Kuchroo

Ronald R. Coifman

Guy Wolf

Smita Krishnaswamy

We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mo… (voir plus)ver's Distance (EMD). We model the datasets as distributions supported on common data graph that is derived from the affinity matrix computed on the combined data. In such cases where the graph is a discretization of an underlying Riemannian closed manifold, we prove that Diffusion EMD is topologically equivalent to the standard EMD with a geodesic ground distance. Diffusion EMD can be computed in

2021-07-19

International Conference on Machine Learning (Spotlight)

doi.org

proceedings.mlr.press

Finding Archetypal Spaces Using Neural Networks

David van Dijk

Daniel B. Burkhardt

Matthew Amodio

Alexander Tong

Guy Wolf

Smita Krishnaswamy

Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or a… (voir plus)rchetypes. These archetypes represent extrema of a data space in which there is a trade-off between features, such as in biology where different combinations of traits provide optimal fitness for different environments. Existing methods for archetypal analysis work well when a linear relationship exists between the feature space and the archetypal space. However, such methods are not applicable to systems where the feature space is generated non-linearly from the combination of archetypes, such as in biological systems or image transformations. Here, we propose a reformulation of the problem such that the goal is to learn a non-linear transformation of the data into a latent archetypal space. To solve this problem, we introduce Archetypal Analysis network (AAnet), which is a deep neural network framework for learning and generating from a latent archetypal representation of data. We demonstrate state-of-the-art recovery of ground-truth archetypes in non-linear data domains, show AAnet can generate from data geometry rather than from data density, and use AAnet to identify biologically meaningful archetypes in single-cell gene expression data.

2020-12-31

IEEE International Conference on Big Data (inconnu)

doi.org

arxiv.org

MURAL: An Unsupervised Random Forest-Based Embedding for Electronic Health Record Data

Michal Gerasimiuk

Dennis Shung

Alexander Tong

Adrian Stanley

Michael Schultz

Jeffrey Ngu

Loren Laine

Guy Wolf

Smita Krishnaswamy

A major challenge in embedding or visualizing clinical patient data is the heterogeneity of variable types including continuous lab values, … (voir plus)categorical diagnostic codes, as well as missing or incomplete data. In particular, in EHR data, some variables are {\em missing not at random (MNAR)} but deliberately not collected and thus are a source of information. For example, lab tests may be deemed necessary for some patients on the basis of suspected diagnosis, but not for others. Here we present the MURAL forest -- an unsupervised random forest for representing data with disparate variable types (e.g., categorical, continuous, MNAR). MURAL forests consist of a set of decision trees where node-splitting variables are chosen at random, such that the marginal entropy of all other variables is minimized by the split. This allows us to also split on MNAR variables and discrete variables in a way that is consistent with the continuous variables. The end goal is to learn the MURAL embedding of patients using average tree distances between those patients. These distances can be fed to nonlinear dimensionality reduction method like PHATE to derive visualizable embeddings. While such methods are ubiquitous in continuous-valued datasets (like single cell RNA-sequencing) they have not been used extensively in mixed variable data. We showcase the use of our method on one artificial and two clinical datasets. We show that using our approach, we can visualize and classify data more accurately than competing approaches. Finally, we show that MURAL can also be used to compare cohorts of patients via the recently proposed tree-sliced Wasserstein distances.

2020-12-31

IEEE International Conference on Big Data (inconnu)

doi.org

arxiv.org

Topological Analysis of Single-Cell Hierarchy Reveals Inflammatory Glial Landscape of Macular Degeneration

Manik Kuchroo

Marcello DiStasio

Eric Song

Eda Calapkulu

Le Zhang

Maryam Ige

Amar H. Sheth