Abhirup Datta

Wentao Zhan, Abhirup Datta

Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a covariance model, encoding the spatial dependence. We relax the strong assumption of linearity and propose embedding neural networks directly within the traditional geostatistical models to accommodate non-linear mean functions while retaining all other advantages including use of Gaussian Processes to explicitly model the spatial covariance, enabling inference on the covariate effect through the mean and on the spatial dependence through the covariance, and offering predictions at new locations via kriging. We propose NN-GLS, a new neural network estimation algorithm for the non-linear mean in GP models that explicitly accounts for the spatial covariance through generalized least squares (GLS), the same loss used in the linear case. We show that NN-GLS admits a representation as a special type of graph neural network (GNN). This connection facilitates use of standard neural network computational techniques for irregular geospatial data, enabling novel and scalable mini-batching, backpropagation, and kriging schemes. Theoretically, we show that NN-GLS will be consistent for irregularly observed spatially correlated data processes. We also provide a finite sample concentration rate, which quantifies the need to accurately model the spatial covariance in neural networks for dependent data. To our knowledge, these are the first large-sample results for any neural network algorithm for irregular spatial data. We demonstrate the methodology through simulated and real datasets.

Jiafang Song, Sandipan Pramanik, Abhirup Datta

In many scientific applications, uncertainty of estimates from an earlier (upstream) analysis needs to be propagated in subsequent (downstream) Bayesian analysis, without feedback. Cutting feedback methods, also termed cut-Bayes, achieve this by constructing a cut-posterior distribution that prevents backward information flow. Cutting feedback like nested MCMC is computationally challenging while variational inference (VI) cut-Bayes methods need two variational approximations and require access to the upstream data and model. In this manuscript we propose, NeVI-Cut, a provably accurate and modular neural network-based variational inference method for cutting feedback. We directly utilize samples from the upstream analysis without requiring access to the upstream data or model. This simultaneously preserves modularity of analysis and reduces approximation errors by avoiding a variational approximation for the upstream model. We then use normalizing flows to specify the conditional variational family for the downstream parameters and estimate the conditional cut-posterior as a variational solution of Monte Carlo average loss over all the upstream samples. We provide theoretical guarantees on the NeVI-Cut estimate to approximate any cut-posterior. Our results are in a fixed-data regime and provide convergence rates of the actual variational solution, quantifying how richness of the neural architecture and the complexity of the target cut-posterior dictate the approximation quality. In the process, we establish new results on uniform Kullback-Leibler approximation rates of conditional normalizing flows. Simulation studies and two real-world analyses illustrate how NeVI-Cut achieves significant computational gains over traditional cutting feedback methods and is considerably more accurate than parametric variational cut approaches.

Yiqun T. Chen, Tyler H. McCormick, Li Liu et al.

Verbal autopsy (VA) is a critical tool for estimating causes of death in resource-limited settings where medical certification is unavailable. This study presents LA-VA, a proof-of-concept pipeline that combines Large Language Models (LLMs) with traditional algorithmic approaches and embedding-based classification for improved cause-of-death prediction. Using the Population Health Metrics Research Consortium (PHMRC) dataset across three age categories (Adult: 7,580; Child: 1,960; Neonate: 2,438), we evaluate multiple approaches: GPT-5 predictions, LCVA baseline, text embeddings, and meta-learner ensembles. Our results demonstrate that GPT-5 achieves the highest individual performance with average test site accuracies of 48.6% (Adult), 50.5% (Child), and 53.5% (Neonate), outperforming traditional statistical machine learning baselines by 5-10%. Our findings suggest that simple off-the-shelf LLM-assisted approaches could substantially improve verbal autopsy accuracy, with important implications for global health surveillance in low-resource settings.

Arkajyoti Saha, Sumanta Basu, Abhirup Datta

Random forest (RF) is one of the most popular methods for estimating regression functions. The local nature of the RF algorithm, based on intra-node means and variances, is ideal when errors are i.i.d. For dependent error processes like time series and spatial settings where data in all the nodes will be correlated, operating locally ignores this dependence. Also, RF will involve resampling of correlated data, violating the principles of bootstrap. Theoretically, consistency of RF has been established for i.i.d. errors, but little is known about the case of dependent errors. We propose RF-GLS, a novel extension of RF for dependent error processes in the same way Generalized Least Squares (GLS) fundamentally extends Ordinary Least Squares (OLS) for linear models under dependence. The key to this extension is the equivalent representation of the local decision-making in a regression tree as a global OLS optimization which is then replaced with a GLS loss to create a GLS-style regression tree. This also synergistically addresses the resampling issue, as the use of GLS loss amounts to resampling uncorrelated contrasts (pre-whitened data) instead of the correlated data. For spatial settings, RF-GLS can be used in conjunction with Gaussian Process correlated errors to generate kriging predictions at new locations. RF becomes a special case of RF-GLS with an identity working covariance matrix. We establish consistency of RF-GLS under beta- (absolutely regular) mixing error processes and show that this general result subsumes important cases like autoregressive time series and spatial Matern Gaussian Processes. As a byproduct, we also establish consistency of RF for beta-mixing processes, which to our knowledge, is the first such result for RF under dependence. We empirically demonstrate the improvement achieved by RF-GLS over RF for both estimation and prediction under dependence.