arXiv subjects

Michele Peruzzi

Publications and source records attributed to Michele Peruzzi.

11 recordsLinked to original sources

arXiv2026

MoSAIC: Multi-Resolution Spatial Regression Analysis of Cellular Colocalizations in Cancer Imaging

Hierarchical multiplex imaging approaches generate spatially resolved single-cell measurements across multiple, spatially organized fields of view (FOVs) within patient tumor specimens, thereby enabling systematic investigation of how the organization of the tumor microenvironment varies along biologically meaningful intratumoral gradients. Existing approaches fail to jointly address this multi-resolution data structure needed to recover true biological signals. We propose MoSAIC: multi-resolution spatial regression analysis of cell colocalizations, a hierarchical Bayesian spatial regression model designed for multi-resolution spatial data. MoSAIC decomposes the joint variation into three model components: (i) global tumor-gradient effects, (ii) patient-specific effects to capture inter-patient variability, and (iii) Gaussian process models to account for spatial dependence between FOVs within each patient tumor tissue. Simulations demonstrate MoSAIC has improved prediction and model fit compared to existing spatial and non-spatial model alternatives. Our method is motivated by and applied to a renal cell carcinoma multiplex imaging cohort to investigate immune-tumor colocalization patterns across the epithelial-to-mesenchymal transition (EMT) gradient. MoSAIC identifies increased macrophage-tumor colocalization and decreased cytotoxic T-tumor colocalization progressing across the increasing EMT gradient, consistent with EMT-associated immune suppression and spatially varying immune engagement. Overall, MoSAIC provides an interpretable, multi-resolution framework for quantifying spatial tumor-gradient effects in cancer imaging studies. Software is available on GitHub at jcaldous/MoSAIC.

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arXiv2026

Partial correlation networks of Gaussian processes

In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where multivariate analysis defaults to modeling unconditional cross-covariance structure, even when direct relationships remain of scientific interest. We address this gap by establishing a novel characterization of process-level partial correlation for multivariate Gaussian processes that recovers a direct link with Gaussian graphical models. Our analysis proceeds through a class of stationary multivariate processes, termed spectrally inside-out, in which a precision matrix modulates the strength of conditional dependence and yields necessary and sufficient conditions for conditional independence. Within this class, partial cross-correlation functions factorize into a process-level partial correlation coefficient and an attenuation term independent of cross-process parameters. The spectrally inside-out class includes the separable coregionalization model, a process convolution construction, and the parsimonious multivariate Mat\'ern, for which such a characterization was previously thought unavailable. We further show that a nonstationary inside-out model satisfies the same factorization and admits the same necessary and sufficient conditions. Our results clarify the limitations of existing approaches: linear coregionalization models encode conditional independence through the zero pattern of the inverse factor loading matrix and do not result in interpretable partial cross-correlation functions. Low-rank spatial factor models lack a meaningful graphical characterization. Methods that enforce network structure through auxiliary graphical layers only characterize presence or absence of graph edges. We illustrate our results through synthetic and real data.

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arXiv2025

Joint Modeling of Spatial Dependencies Across Multiple Subjects in Multiplexed Tissue Imaging

The tumor microenvironment (TME) is a spatially heterogeneous ecosystem where cellular interactions shape tumor progression and response to therapy. Multiplexed imaging technologies enable high-resolution spatial characterization of the TME, yet statistical methods for analyzing multi-subject spatial tissue data remain limited. We propose a Bayesian hierarchical model for inferring spatial dependencies in multiplexed imaging datasets across multiple subjects. Our model represents the TME as a multivariate log-Gaussian Cox process, where spatial intensity functions of different cell types are governed by a latent multivariate Gaussian process. By pooling information across subjects, we estimate spatial correlation functions that capture within-type and cross-type dependencies, enabling interpretable inference about disease-specific cellular organization. We validate our method using simulations, demonstrating robustness to latent factor specification and spatial resolution. We apply our approach to two multiplexed imaging datasets: pancreatic cancer and colorectal cancer, revealing distinct spatial organization patterns across disease subtypes and highlighting tumor-immune interactions that differentiate immune-permissive and immune-exclusive microenvironments. These findings provide insight into mechanisms of immune evasion and may inform novel therapeutic strategies. Our approach offers a principled framework for modeling spatial dependencies in multi-subject data, with broader applicability to spatially resolved omics and imaging studies. An R package, available online, implements our methods.

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arXiv2024

Inside-out cross-covariance for spatial multivariate data

As the spatial features of multivariate data are increasingly central in researchers' applied problems, there is a growing demand for novel spatially-aware methods that are flexible, easily interpretable, and scalable to large data. We develop inside-out cross-covariance (IOX) models for multivariate spatial likelihood-based inference. IOX leads to valid cross-covariance matrix functions which we interpret as inducing spatial dependence on independent replicates of a correlated random vector. The resulting sample cross-covariance matrices are "inside-out" relative to the ubiquitous linear model of coregionalization (LMC). However, unlike LMCs, our methods offer direct marginal inference, easy prior elicitation of covariance parameters, the ability to model outcomes with unequal smoothness, and flexible dimension reduction. As a covariance model for a q-variate Gaussian process, IOX leads to scalable models for noisy vector data as well as flexible latent models. For large n cases, IOX complements Vecchia approximations and related process-based methods based on sparse graphical models. We demonstrate superior performance of IOX on synthetic datasets as well as on colorectal cancer proteomics data. An R package implementing the proposed methods is available at github.com/mkln/spiox.

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arXiv2022

Radial Neighbors for Provably Accurate Scalable Approximations of Gaussian Processes

In geostatistical problems with massive sample size, Gaussian processes can be approximated using sparse directed acyclic graphs to achieve scalable $O(n)$ computational complexity. In these models, data at each location are typically assumed conditionally dependent on a small set of parents which usually include a subset of the nearest neighbors. These methodologies often exhibit excellent empirical performance, but the lack of theoretical validation leads to unclear guidance in specifying the underlying graphical model and sensitivity to graph choice. We address these issues by introducing radial neighbors Gaussian processes (RadGP), a class of Gaussian processes based on directed acyclic graphs in which directed edges connect every location to all of its neighbors within a predetermined radius. We prove that any radial neighbors Gaussian process can accurately approximate the corresponding unrestricted Gaussian process in Wasserstein-2 distance, with an error rate determined by the approximation radius, the spatial covariance function, and the spatial dispersion of samples. We offer further empirical validation of our approach via applications on simulated and real world data showing excellent performance in both prior and posterior approximations to the original Gaussian process.

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arXiv2022

Spatial meshing for general Bayesian multivariate models

Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial dependence is encoded as a latent Gaussian process (GP) in the increasingly common large scale data settings on which we focus. The scenario worsens in non-Gaussian models because the reduced analytical tractability leads to additional hurdles to computational efficiency. In this article, we introduce Bayesian models of spatially referenced data in which the likelihood or the latent process (or both) are not Gaussian. First, we exploit the advantages of spatial processes built via directed acyclic graphs, in which case the spatial nodes enter the Bayesian hierarchy and lead to posterior sampling via routine Markov chain Monte Carlo (MCMC) methods. Second, motivated by the possible inefficiencies of popular gradient-based sampling approaches in the multivariate contexts on which we focus, we introduce the simplified manifold preconditioner adaptation (SiMPA) algorithm which uses second order information about the target but avoids expensive matrix operations. We demostrate the performance and efficiency improvements of our methods relative to alternatives in extensive synthetic and real world remote sensing and community ecology applications with large scale data at up to hundreds of thousands of spatial locations and up to tens of outcomes. Software for the proposed methods is part of R package 'meshed', available on CRAN.

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arXiv2021

Bag of DAGs: Inferring Directional Dependence in Spatiotemporal Processes

We propose a class of nonstationary processes to characterize space- and time-varying directional associations in point-referenced data. We are motivated by spatiotemporal modeling of air pollutants in which local wind patterns are key determinants of the pollutant spread, but information regarding prevailing wind directions may be missing or unreliable. We propose to map a discrete set of wind directions to edges in a sparse directed acyclic graph (DAG), accounting for uncertainty in directional correlation patterns across a domain. The resulting Bag of DAGs processes (BAGs) lead to interpretable nonstationarity and scalability for large data due to sparsity of DAGs in the bag. We outline Bayesian hierarchical models using BAGs and illustrate inferential and performance gains of our methods compared to other state-of-the-art alternatives. We analyze fine particulate matter using high-resolution data from low-cost air quality sensors in California during the 2020 wildfire season. An R package is available on GitHub.

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arXiv2021

Gridding and Parameter Expansion for Scalable Latent Gaussian Models of Spatial Multivariate Data

Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms for posterior sampling of the latent process, but these may exhibit pathological behavior in estimating covariance parameters. In this article, we introduce gridding and parameter expansion methods to improve the practical performance of MCMC algorithms in terms of effective sample size per unit time (ESS/s). Gridding is a model-based strategy that reduces the number of expensive operations necessary during MCMC on irregularly spaced data. Parameter expansion reduces dependence in posterior samples in spatial regression for high resolution data. These two strategies lead to computational gains in the big data settings on which we focus. We consider popular constructions of univariate spatial processes based on Mat\'ern covariance functions and multivariate coregionalization models for Gaussian outcomes in extensive analyses of synthetic datasets comparing with alternative methods. We demonstrate effectiveness of our proposed methods in a forestry application using remotely sensed data from NASA's Goddard LiDAR, Hyper-Spectral, and Thermal imager (G-LiHT).

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arXiv2020

Spatial Multivariate Trees for Big Data Bayesian Regression

High resolution geospatial data are challenging because standard geostatistical models based on Gaussian processes are known to not scale to large data sizes. While progress has been made towards methods that can be computed more efficiently, considerably less attention has been devoted to big data methods that allow the description of complex relationships between several outcomes recorded at high resolutions by different sensors. Our Bayesian multivariate regression models based on spatial multivariate trees (SpamTrees) achieve scalability via conditional independence assumptions on latent random effects following a treed directed acyclic graph. Information-theoretic arguments and considerations on computational efficiency guide the construction of the tree and the related efficient sampling algorithms in imbalanced multivariate settings. In addition to simulated data examples, we illustrate SpamTrees using a large climate data set which combines satellite data with land-based station data. Source code is available at https://github.com/mkln/spamtree

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arXiv2020

Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the regions in the partition using a sparsity-inducing directed acyclic graph (DAG). We extend the model over the DAG to a well-defined spatial process, which we call the Meshed Gaussian Process (MGP). A major contribution is the development of a MGPs on tessellated domains, accompanied by a Gibbs sampler for the efficient recovery of spatial random effects. In particular, the cubic MGP (Q-MGP) can harness high-performance computing resources by executing all large-scale operations in parallel within the Gibbs sampler, improving mixing and computing time compared to sequential updating schemes. Unlike some existing models for large spatial data, a Q-MGP facilitates massive caching of expensive matrix operations, making it particularly apt in dealing with spatiotemporal remote-sensing data. We compare Q-MGPs with large synthetic and real world data against state-of-the-art methods. We also illustrate using Normalized Difference Vegetation Index (NDVI) data from the Serengeti park region to recover latent multivariate spatiotemporal random effects at millions of locations. The source code is available at https://github.com/mkln/meshgp.

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arXiv2018

Bayesian Modular and Multiscale Regression

We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed as an additive expansion of coarse to fine step functions. Our Modular and Multiscale (M&M) methodology provides multiscale decomposition of high-dimensional data arising from very fine measurements. Unlike more complex methods for functional predictors, our approach provides easy interpretation of the results. Additionally, it provides a quantification of uncertainty on the data resolution, solving a common problem researchers encounter with simple models on down-sampled data. We show that our modular and multiscale posterior has an empirical Bayes interpretation, with a simple limiting distribution in large samples. An efficient sampling algorithm is developed for posterior computation, and the methods are illustrated through simulation studies and an application to brain image classification. Source code is available as an R package at https://github.com/mkln/bmms.

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