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Andrew Warren

Publications and source records attributed to Andrew Warren.

At least 19 recordsLinked to original sources
arXiv2026

Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality

Efficiently and robustly analyzing shape data is critical across many scientific disciplines. While chirality is a fundamental property in numerous applications - most notably in molecular science - existing shape analysis metrics fail to distinguish between a shape and its mirror image. To address this gap, we introduce a multilinear generalization of the Gromov-Wasserstein objective. Under mild assumptions, this objective yields a distance between shapes, represented as probability distributions quotiented by a symmetry group $G$. In particular, for $G = SO(d)$, we introduce the Chiral Gromov-Wasserstein ($\mathrm{CGW}$) distance, sensitive to chirality. We establish robustness properties for the multilinear Gromov-Wasserstein distances and develop efficient algorithms to compute them, reformulating the underlying optimization problem by projecting couplings onto a low-dimensional space. We derive algorithms for both local and approximate global solutions, yielding a fully polynomial-time approximation scheme for these problems. We validate the framework through numerical experiments that demonstrate the effectiveness of $\mathrm{CGW}$ as a shape metric for chiral objects.

math.OC↗
arXiv2026

EpiFlow: A framework for improving the utility of wastewater signals for disease forecasting

Wastewater-based surveillance is an effective tool for disease monitoring and can provide early warning of outbreaks. Although wastewater viral loads (WVL) correlate with disease burden, their utility for improving real-time forecasting remains under investigation. During the early phases of an epidemic, many indicators can effectively monitor disease spread, but their reliability may decline because of reporting fatigue and low prevalence. Hospital burden can vary substantially even during low-prevalence periods, making accurate forecasting of burden indicators essential for minimizing disease impacts. In this paper, we present principled approaches for processing wastewater data, characterizing its relationship with burden indicators, and generating real-time forecasts. We assess the predictability of WVL using entropy measures. We analyze the relationship between WVL and burden indicators using causality tests that capture temporal dynamics and the leading-indicator behavior of WVL. We incorporate these insights into a time-varying forecasting model that accounts for the evolving relationship between the signals. We also evaluate the effects of delays in WVL reporting through simulations. We test the utility of our methods by forecasting COVID-19 hospital admissions across Virginia and its health regions during periods of varying disease prevalence. Incorporating WVL improves forecast accuracy relative to baseline models, particularly during critical epidemic phases, and results in a 20 percentage point improvement in forecast coverage. Our results demonstrate that WVL signals can improve infectious disease forecasting even under conditions of low prevalence or delayed reporting.

cs.LG↗
arXiv2025

STARK denoises spatial transcriptomics images via adaptive regularization

We present an approach to denoising spatial transcriptomics images that is particularly effective for uncovering cell identities in the regime of ultra-low sequencing depths, and also allows for interpolation of gene expression. The method -- Spatial Transcriptomics via Adaptive Regularization and Kernels (STARK) -- augments kernel ridge regression with an incrementally adaptive graph Laplacian regularizer. In each iteration, we (1) perform kernel ridge regression with a fixed graph to update the image, and (2) update the graph based on the new image. The kernel ridge regression step involves reducing the infinite dimensional problem on a space of images to finite dimensions via a modified representer theorem. Starting with a purely spatial graph, and updating it as we improve our image makes the graph more robust to noise in low sequencing depth regimes. We show that the aforementioned approach optimizes a block-convex objective through an alternating minimization scheme wherein the sub-problems have closed form expressions that are easily computed. This perspective allows us to prove convergence of the iterates to a stationary point of this non-convex objective. Statistically, such stationary points converge to the ground truth with rate $\mathcal{O}(R^{-1/2})$ where $R$ is the number of reads. In numerical experiments on real spatial transcriptomics data, the denoising performance of STARK, evaluated in terms of label transfer accuracy, shows consistent improvement over the competing methods tested.

stat.ML↗
arXiv2025

Principal Curves In Metric Spaces And The Space Of Probability Measures

We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a curve in Wasserstein space. Our framework enables new experimental procedures for collecting high-density time-courses of developing populations of cells: time-points can be processed in parallel (making it easier to collect more time-points). However, then the time of collection is unknown, and must be recovered by solving a seriation problem (or one-dimensional manifold learning problem). We propose an estimator based on Wasserstein principal curves, and prove it is consistent for recovering a curve of probability measures in Wasserstein space from empirical samples. This consistency theorem is obtained via a series of results regarding principal curves in compact metric spaces. In particular, we establish the validity of certain numerical discretization schemes for principal curves, which is a new result even in the Euclidean setting.

math.ST↗
arXiv2024

Gradient flow structure for some nonlocal diffusion equations

We study ``nonlocal diffusion equations'' of the form \[ \partial_{t}\frac{d\rho_{t}}{d\pi}(x)+\int_{X}\left(\frac{d\rho_{t}}{d\pi}(x)-\frac{d\rho_{t}}{d\pi}(y)\right)\eta(x,y)d\pi(y)=0\qquad(\dagger) \] where $X$ is either $\mathbb{R}^{d}$ or $\mathbb{T}^{d}$, $\pi$ is a probability distribution on $X$, and $\eta(x,y)$ is a ``transition kernel'' which may be singular as $x\rightarrow y$. For a suitable notion of weak solutions which we discuss below, we show that solutions to these nonlocal diffusion equations can be interpreted as gradient flows of the relative entropy with respect to a certain nonlocal Wasserstein-type metric defined in terms of $\eta$ and $\pi$. These ``nonlocal Wasserstein metrics'' endow the space of probability measures on $X$ with a formal Riemannian structure, thereby providing for us a nonlocal analogue of the \emph{Otto calculus} originally developed in the context of the 2-Wasserstein metric. The class of equations $(\dagger)$ includes a family of ``nonlocal Fokker-Planck equations'', which are thus identified as nonlocal Wasserstein gradient flows of the relative entropy, analogously with the usual Fokker-Planck equation and the $W_{2}$ metric. The gradient flow structure we provide allows us to deduce: existence and uniqueness of solutions to ($\dagger$) in a suitable class of weak solutions; stability of solutions in the sense of evolutionary $\Gamma$-convergence, with respect to perturbations of initial condition, reference measure $\pi$, and transition kernel $\eta$; sufficient conditions for exponential convergence to equilibrium, in terms of a nonlocal analogue of the log-Sobolev inequality; as well as the consistency of a finite-volume-type spatial discretization scheme in the $\mathbb{T}^{d}$ case.

math.AP↗
arXiv2024

A High-Resolution, US-scale Digital Similar of Interacting Livestock, Wild Birds, and Human Ecosystems with Applications to Multi-host Epidemic Spread

One Health issues, such as the spread of highly pathogenic avian influenza~(HPAI), present significant challenges at the human-animal-environmental interface. Recent H5N1 outbreaks underscore the need for comprehensive modeling efforts that capture the complex interactions between various entities in these interconnected ecosystems. To support such efforts, we develop a methodology to construct a synthetic spatiotemporal gridded dataset of livestock production and processing, human population, and wild birds for the contiguous United States, called a \emph{digital similar}. This representation is a result of fusing diverse datasets using statistical and optimization techniques, followed by extensive verification and validation. The livestock component includes farm-level representations of four major livestock types -- cattle, poultry, swine, and sheep -- including further categorization into subtypes such as dairy cows, beef cows, chickens, turkeys, ducks, etc. Weekly abundance data for wild bird species identified in the transmission of avian influenza are included. Gridded distributions of the human population, along with demographic and occupational features, capture the placement of agricultural workers and the general population. We demonstrate how the digital similar can be applied to evaluate spillover risk to dairy cows and poultry from wild bird population, then validate these results using historical H5N1 incidences. The resulting subtype-specific spatiotemporal risk maps identify hotspots of high risk from H5N1 infected wild bird population to dairy cattle and poultry operations, thus guiding surveillance efforts.

cs.CE↗
arXiv2024

Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE from data is a challenging task, especially if individual trajectories are not observable. Motivated by burgeoning research in single-cell datasets, we present the first comprehensive approach for jointly identifying the drift and diffusion of an SDE from its temporal marginals. Assuming linear drift and additive diffusion, we show that non-identifiability can only arise if the initial distribution possesses generalized rotational symmetries. We further prove that even if this condition holds, the drift and diffusion can almost always be recovered from the marginals. Additionally, we show that the causal graph of any SDE with additive diffusion can be recovered from the identified SDE parameters. To complement this theory, we adapt entropy-regularized optimal transport to handle anisotropic diffusion, and introduce APPEX (Alternating Projection Parameter Estimation from $X_0$), an iterative algorithm designed to estimate the drift, diffusion, and causal graph of an additive noise SDE, solely from temporal marginals. We show that APPEX iteratively decreases Kullback-Leibler divergence to the true solution, and demonstrate its effectiveness on simulated data from linear additive noise SDEs.

stat.ML↗
arXiv2024

Statistical inference of convex order by Wasserstein projection

Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a statistical point of view. This article addresses this gap by introducing a simple statistical test for convex order based on the Wasserstein projection distance. This projection distance not only encodes whether two distributions are indeed in convex order, but also quantifies the deviation from the desired convex order and produces an optimal convex order approximation. Lipschitz stability of the backward and forward Wasserstein projection distance is proved, which leads to elegant consistency and concentration results of the estimator we employ as our test statistic. Combining these with state of the art results regarding the convergence rate of empirical distributions, we also derive upper bounds for the $p$-value and type I error of our test statistic, as well as upper bounds on the type II error for an appropriate class of strict alternatives. With proper choices of families of distributions, we further attain that the power of the proposed test increases to one as the number of samples grows to infinity. Lastly, we provide an efficient numerical scheme for our test statistic, by way of an entropic Frank-Wolfe algorithm. Experiments based on synthetic data sets illuminate the success of our approach.

stat.ME↗
arXiv2024

Wastewater-based Epidemiology for COVID-19 Surveillance and Beyond: A Survey

The pandemic of COVID-19 has imposed tremendous pressure on public health systems and social economic ecosystems over the past years. To alleviate its social impact, it is important to proactively track the prevalence of COVID-19 within communities. The traditional way to estimate the disease prevalence is to estimate from reported clinical test data or surveys. However, the coverage of clinical tests is often limited and the tests can be labor-intensive, requires reliable and timely results, and consistent diagnostic and reporting criteria. Recent studies revealed that patients who are diagnosed with COVID-19 often undergo fecal shedding of SARS-CoV-2 virus into wastewater, which makes wastewater-based epidemiology for COVID-19 surveillance a promising approach to complement traditional clinical testing. In this paper, we survey the existing literature regarding wastewater-based epidemiology for COVID-19 surveillance and summarize the current advances in the area. Specifically, we have covered the key aspects of wastewater sampling, sample testing, and presented a comprehensive and organized summary of wastewater data analytical methods. Finally, we provide the open challenges on current wastewater-based COVID-19 surveillance studies, aiming to encourage new ideas to advance the development of effective wastewater-based surveillance systems for general infectious diseases.

stat.AP↗
arXiv2023

Ultralimits of Wasserstein spaces and metric measure spaces with Ricci curvature bounded from below

We investigate the stability of the Wasserstein distance, a metric structure on the space of probability measures arising from the theory of optimal transport, under metric ultralimits. We first show that if $(X_{i},d_{i})_{i\in\mathbb{N}}$ is a sequence of metric spaces with metric ultralimit $(\hat{X},\hat{d})$, then the p-Wasserstein space $(\mathcal{P}_{p}(\hat{X}),W_{p})$ embeds isometrically in a canonical fashion into the metric ultralimit of the sequence of p-Wasserstein spaces $(\mathcal{P}_{p}(X_{i}),W_{p})$. Second, using a notion of ultralimit of metric measure spaces modeled on the one introduced by Elek, we use the machinery of ultralimits of Wasserstein spaces to prove that an ultralimit of CD(K,$\infty$) spaces is a CD(K,$\infty$) space. This provides a new proof that the CD(K,$\infty$) property is stable under pointed measured Gromov convergence. Along the way, we establish some basic results on how the Loeb measure construction interacts with Wasserstein distances as well as integral functionals, which may be of independent interest.

math.MG↗
arXiv2022

Nonlocal Wasserstein Distance: Metric and Asymptotic Properties

The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of probability measures, where paths are solutions of the continuity equation and the action is the kinetic energy. Here we consider a fundamental modification of the framework where the paths are solutions of nonlocal (jump) continuity equations and the action is a nonlocal kinetic energy. The resulting nonlocal Wasserstein distances are relevant to fractional diffusions and Wasserstein distances on graphs. We characterize the basic properties of the distance and obtain sharp conditions on the (jump) kernel specifying the nonlocal transport that determine whether the topology metrized is the weak or the strong topology. A key result of the paper are the quantitative comparisons between the nonlocal and local Wasserstein distance.

math.AP↗
arXiv2021

Wasserstein Conditional Independence Testing

We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting multiple $p$-Wasserstein two-sample tests. Under a $p$-Wasserstein Lipschitz assumption on the conditional distributions $\mathcal{L}_{X|Z}$, $\mathcal{L}_{Y|Z}$, and $\mathcal{L}_{(X,Y)|Z}$, we show that it is possible to control the Type I and Type II error of this test, and give examples of explicit finite-sample error bounds in the case where the distribution of $Z$ has compact support.

math.ST↗
arXiv2021

Fluctuation bounds for ergodic averages of amenable groups

We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable groups acting on uniformly convex Banach spaces, we deduce a highly uniform bound on the number of fluctuations of the ergodic average for a class of Følner sequences satisfying an analogue of Lindenstrauss's temperedness condition. Equivalently, we deduce a uniform bound on the number of fluctuations over long distances for arbitrary Følner sequences. As a corollary, these results imply associated bounds for a continuous action of an amenable group on a $σ$-finite $L^{p}$ space with $p\in(1,\infty)$.

math.DS↗
arXiv2020

Efficient Algorithms for Generating Provably Near-Optimal Cluster Descriptors for Explainability

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS 2018] for constructing succinct representations for clusters. Given a set of objects $S$, a partition $π$ of $S$ (into clusters), and a universe $T$ of tags such that each element in $S$ is associated with a subset of tags, the goal is to find a representative set of tags for each cluster such that those sets are pairwise-disjoint and the total size of all the representatives is minimized. Since this problem is NP-hard in general, we develop approximation algorithms with provable performance guarantees for the problem. We also show applications to explain clusters from datasets, including clusters of genomic sequences that represent different threat levels.

cs.DS↗
arXiv2019

Fluctuation bounds for ergodic averages of amenable groups on uniformly convex Banach spaces

We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable groups acting on uniformly convex Banach spaces, we deduce a highly uniform bound on the number of fluctuations of the ergodic average for a class of Følner sequences satisfying an analogue of Lindenstrauss's temperedness condition. Equivalently, we deduce a uniform bound on the number of fluctuations over long distances for arbitrary Følner sequences. As a corollary, these results imply associated bounds for a continuous action of an amenable group on a $σ$-finite $L^{p}$ space with $p\in(1,\infty)$.

math.DS↗
arXiv2017

Using Entropy Estimates for DAG-Based Ontologies

Motivation: Entropy measurements on hierarchical structures have been used in methods for information retrieval and natural language modeling. Here we explore its application to semantic similarity. By finding shared ontology terms, semantic similarity can be established between annotated genes. A common procedure for establishing semantic similarity is to calculate the descriptiveness (information content) of ontology terms and use these values to determine the similarity of annotations. Most often information content is calculated for an ontology term by analyzing its frequency in an annotation corpus. The inherent problems in using these values to model functional similarity motivates our work. Summary: We present a novel calculation for establishing the entropy of a DAG-based ontology, which can be used in an alternative method for establishing the information content of its terms. We also compare our IC metric to two others using semantic and sequence similarity.

cs.CL↗
arXiv2017

An Experimental Platform for Multi-spacecraft Phase-Array Communications

The emergence of small satellites and CubeSats for interplanetary exploration will mean hundreds if not thousands of spacecraft exploring every corner of the solar-system. Current methods for communication and tracking of deep space probes use ground based systems such as the Deep Space Network (DSN). However, the increased communication demand will require radically new methods to ease communication congestion. Networks of communication relay satellites located at strategic locations such as geostationary orbit and Lagrange points are potential solutions. Instead of one large communication relay satellite, we could have scores of small satellites that utilize phase arrays to effectively operate as one large satellite. Excess payload capacity on rockets can be used to warehouse more small satellites in the communication network. The advantage of this network is that even if one or a few of the satellites are damaged or destroyed, the network still operates but with degraded performance. The satellite network would operate in a distributed architecture and some satellites maybe dynamically repurposed to split and communicate with multiple targets at once. The potential for this alternate communication architecture is significant, but this requires development of satellite formation flying and networking technologies. Our research has found neural-network control approaches such as the Artificial Neural Tissue can be effectively used to control multirobot/multi-spacecraft systems and can produce human competitive controllers. We have been developing a laboratory experiment platform called Athena to develop critical spacecraft control algorithms and cognitive communication methods. We briefly report on the development of the platform and our plans to gain insight into communication phase arrays for space.

cs.RO↗
arXiv2017

Guidance, Navigation and Control of Multirobot Systems in Cooperative Cliff Climbing

The application of GNC devices on small robots is a game-changer that enables these robots to be mobile on low-gravity planetary surfaces and small bodies. Use of reaction wheels enables these robots to roll, hop, summersault and rest on precarious/sloped surfaces that would otherwise not be possible with conven-tional wheeled robots. We are extending this technology to enable robots to climb off-world canyons, cliffs and caves. A single robot may slip and fall, however, a multirobot system can work cooperatively by being interlinked using spring-tethers and work much like a team of mountaineers to systematically climb a slope. A multirobot system as we will show in this paper can climb sur-faces not possible with a single robot alone. We consider a team of four robots that are interlinked with tethers in an 'x' configuration. Each robot secures itself to a slope using spiny gripping actuators, and one by one each robot moves up-wards by crawling, rolling or hopping up the slope. If any one of the robots loses grip, slips or falls, the remaining robots will be holding it up as they are anchored. This distributed controls approach to cliff climbing enables the system to reconfigure itself where possible and avoid getting stuck at one hard to reach location. Instead, the risk is distributed and through close cooperation, the robots can identify multiple trajectories to climb a cliff or rugged surface. The benefits can also be realized on milligravity surfaces such as asteroids. Too fast a jump can result in the robot flying off the surface into space. Having multiple robots anchored to the surface keeps the entire system secure. Our work combines dynamics and control simulation to evaluate the feasibility of our approach. The simulation results show a promising pathway towards advanced development of this technology on a team of real robots.

cs.RO↗