arXiv subjects

Alexander Tong

Publications and source records attributed to Alexander Tong.

61 records · Page 4Linked to original sources

arXiv2022

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

In modern relational machine learning it is common to encounter large graphs that arise via interactions or similarities between observations 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.

cs.LG↗

arXiv2022

Multimodal Data Visualization and Denoising with Integrated Diffusion

We propose a method called integrated diffusion for combining multimodal datasets, or data gathered via several different measurements on the 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.

cs.LG↗

arXiv2021

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

A major challenge in embedding or visualizing clinical patient data is the heterogeneity of variable types including continuous lab values, 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.

cs.LG↗

arXiv2021

Diffusion Earth Mover's Distance and Distribution Embeddings

We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover'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 $\tilde{O}(n)$ time and is more accurate than similarly fast algorithms such as tree-based EMDs. We also show Diffusion EMD is fully differentiable, making it amenable to future uses in gradient-descent frameworks such as deep neural networks. Finally, we demonstrate an application of Diffusion EMD to single cell data collected from 210 COVID-19 patient samples at Yale New Haven Hospital. Here, Diffusion EMD can derive distances between patients on the manifold of cells at least two orders of magnitude faster than equally accurate methods. This distance matrix between patients can be embedded into a higher level patient manifold which uncovers structure and heterogeneity in patients. More generally, Diffusion EMD is applicable to all datasets that are massively collected in parallel in many medical and biological systems.

cs.LG↗

arXiv2020

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 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.

cs.LG↗

arXiv2020

TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model continuous dynamics and non-linear paths that entities can take in these systems. To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present TrajectoryNet, which controls the continuous paths taken between distributions to produce dynamic optimal transport. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

stat.ML↗

arXiv2020

Interpretable Neuron Structuring with Graph Spectral Regularization

While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on the primary task. Taking inspiration from spatial organization and localization of neuron activations in biological networks, we use a graph Laplacian penalty to structure the activations within a layer. This penalty encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data via co-activations of a hidden layer of the neural network. We show numerous uses for this additional structure including cluster indication and visualization in biological and image data sets.

cs.LG↗