arXiv subjects

Aaron Scheffler

Publications and source records attributed to Aaron Scheffler.

6 recordsLinked to original sources

arXiv2026

Uncertainty-Aware Neural Multivariate Geostatistics

We propose Deep Neural Coregionalization, a scalable framework for uncertainty-aware multivariate geostatistics. DNC models multivariate spatial effects through spatially varying latent factors and loadings, assigning deep Gaussian process (DGP) priors to both the factors and the entries of the loading matrix. This joint construction learns shared latent spatial structure together with response-specific, location-dependent mixing weights, enabling flexible nonlinear and space-dependent associations within and across variables. A key contribution is a variational formulation that makes the DGP to deep neural network (DNN) correspondence explicit: maximizing the DGP evidence lower bound (ELBO) is equivalent to training DNNs with weight decay and Monte Carlo (MC) dropout. This yields fast mini-batch stochastic optimization without Markov Chain Monte Carlo (MCMC), while providing principled uncertainty quantification through MC-dropout forward passes as approximate posterior draws, producing calibrated credible surfaces for prediction and spatial effect estimation. Across simulations, DNC is competitive with existing spatial factor models, particularly under strong nonstationarity and complex cross-dependence, while delivering substantial computational gains. In a multivariate environmental case study, DNC captures spatially varying cross-variable interactions, produces interpretable maps of multivariate outcomes, and scales uncertainty quantification to large datasets with orders-of-magnitude reductions in runtime.

stat.ME↗

arXiv2025

Deep Generative Modeling with Spatial and Network Images: An Explainable AI (XAI) Approach

This article addresses the challenge of modeling the amplitude of spatially indexed low frequency fluctuations (ALFF) in resting state functional MRI as a function of cortical structural features and a multi-task coactivation network in the Adolescent Brain Cognitive Development (ABCD) Study. It proposes a generative model that integrates effects of spatially-varying inputs and a network-valued input using deep neural networks to capture complex non-linear and spatial associations with the output. The method models spatial smoothness, accounts for subject heterogeneity and complex associations between network and spatial images at different scales, enables accurate inference of each images effect on the output image, and allows prediction with uncertainty quantification via Monte Carlo dropout, contributing to one of the first Explainable AI (XAI) frameworks for heterogeneous imaging data. The model is highly scalable to high-resolution data without the heavy pre-processing or summarization often required by Bayesian methods. Empirical results demonstrate its strong performance compared to existing statistical and deep learning methods. We applied the XAI model to the ABCD data which revealed associations between cortical features and ALFF throughout the entire brain. Our model performed comparably to existing methods in predictive accuracy but provided superior uncertainty quantification and faster computation, demonstrating its effectiveness for large-scale neuroimaging analysis. Open-source software in Python for XAI is available.

stat.ME↗

arXiv2025

Interpretable Deep Neural Network for Modeling Functional Surrogates

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for analyzing functional outputs with vector-valued inputs. The relationship between the functional output and vector-valued input is modeled as an infinite sequence of unknown functions, each representing the relationship at a specific location within the functional domain. These spatially indexed functions are expressed through a combination of basis functions and their corresponding coefficient functions, both of which are modeled using deep neural networks (DNN). The proposed framework accounts for spatial dependencies across locations, while capturing the relationship between the functional output and scalar predictors. It also integrates a Monte Carlo (MC) dropout strategy to quantify prediction uncertainty, enhancing explainability in the deep neural network architecture. The proposed method enables efficient inference on datasets with approximately 50,000 spatial locations and 20 simulations, achieving results in under 10 minutes using standard hardware. The approach is validated on extensive synthetic datasets and a large-scale simulation from the Sea Lake and Overland Surge from Hurricanes (SLOSH) simulator. An open-source Python package implementing the method is made available.

stat.ME↗

arXiv2024

Multi-object Data Integration in the Study of Primary Progressive Aphasia

This article focuses on a multi-modal imaging data application where structural/anatomical information from gray matter (GM) and brain connectivity information in the form of a brain connectome network from functional magnetic resonance imaging (fMRI) are available for a number of subjects with different degrees of primary progressive aphasia (PPA), a neurodegenerative disorder (ND) measured through a speech rate measure on motor speech loss. The clinical/scientific goal in this study becomes the identification of brain regions of interest significantly related to the speech rate measure to gain insight into ND patterns. Viewing the brain connectome network and GM images as objects, we develop an integrated object response regression framework of network and GM images on the speech rate measure. A novel integrated prior formulation is proposed on network and structural image coefficients in order to exploit network information of the brain connectome while leveraging the interconnections among the two objects. The principled Bayesian framework allows the characterization of uncertainty in ascertaining a region being actively related to the speech rate measure. Our framework yields new insights into the relationship of brain regions associated with PPA, offering a deeper understanding of neuro-degenerative patterns of PPA. The supplementary file adds details about posterior computation and additional empirical results.

q-bio.NC↗

arXiv2024

Integrative Variational Autoencoders for Generative Modeling of an Image Outcome with Multiple Input Images

Understanding relationships across multiple imaging modalities is central to neuroimaging research. We introduce the Integrative Variational Autoencoder (InVA), the first hierarchical VAE framework for image-on-image regression in multimodal neuroimaging. Unlike standard VAEs, which are not designed for predictive integration across modalities, InVA models outcome images as functions of both shared and modality-specific features. This flexible, data-driven approach avoids rigid assumptions of classical tensor regression and outperforms conventional VAEs and nonlinear models such as BART. As a key application, InVA accurately predicts costly PET scans from structural MRI, offering an efficient and powerful tool for multimodal neuroimaging.

eess.IV↗

arXiv2021

Sketching in Bayesian High Dimensional Regression With Big Data Using Gaussian Scale Mixture Priors

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the heavy computational cost that grows in the cubic order of p, with p as the number of features. Although a few recently developed algorithms make the computation efficient in presence of a small to moderately large sample size (with the complexity growing in the cubic order of n), the computation becomes intractable when sample size n is also large. In this article we adopt the data sketching approach to compress the n original samples by a random linear transformation to m<<n samples in p dimensions, and compute Bayesian regression with Gaussian scale mixture prior distributions with the randomly compressed response vector and feature matrix. Our proposed approach yields computational complexity growing in the cubic order of m. Another important motivation for this compression procedure is that it anonymizes the data by revealing little information about the original data in the course of analysis. Our detailed empirical investigation with the Horseshoe prior from the class of Gaussian scale mixture priors shows closely similar inference and a massive reduction in per iteration computation time of the proposed approach compared to the regression with the full sample. One notable contribution of this article is to derive posterior contraction rate for high dimensional predictor coefficient with a general class of shrinkage priors on them under data compression/sketching. In particular, we characterize the dimension of the compressed response vector m as a function of the sample size, number of predictors and sparsity in the regression to guarantee accurate estimation of predictor coefficients asymptotically, even after data compression.

stat.ME↗