arXiv subjects

Arkaprava Roy

Publications and source records attributed to Arkaprava Roy.

At least 19 recordsLinked to original sources

arXiv2026

An Additive MLP-GNN Framework for Characterizing Chemical and Structural Contributions to Aqueous Solubility

Aqueous solubility is a key property in early-stage drug discovery, but most predictive models merge physicochemical descriptors and molecular graph information into a single representation, obscuring whether a prediction is driven by global chemistry, molecular structure, or both. We present an additive deep-learning framework that keeps these two sources of information separate throughout training: physicochemical descriptors are encoded by a multilayer perceptron (the chemical branch) and molecular graph topology by a graph neural network (the structural branch), with the two outputs combined only at the prediction stage through an additive model with an optional multiplicative interaction. This design provides a direct decomposition of chemical and structural components that can be examined separately after training. Furthermore, pretraining on the larger AqSolDB dataset and fine-tuning on the smaller BigSolDB2 dataset substantially improve accuracy and reduce run-to-run variations, indicating generalizability of the learned features from the data-rich settings. We further interpret the fitted model using best linear projections of the branch outputs, molecule-level embedding summaries across solubility classes, and atom-level GNNExplainer masks aggregated over functional groups. These analyses show that the chemical branch aligns with familiar physicochemical descriptors, while the structural branch captures graph-topological and functional-group patterns associated with solubility. Across both datasets, the framework attains competitive predictive performance while making the distinct roles of chemical and structural information more transparent.

stat.ML↗

arXiv2026

Conformity-Based Bayesian Projective Prediction

We propose a general robust prediction framework, termed conformity-based projective prediction (CPP), that integrates Bayesian predictive modeling with ideas from conformity-based conformal prediction. Rather than assessing conformity through residual-based scores, the CPP criterion defines conformity distributionally: a candidate value for a future response is considered conforming to the extent that its inclusion in the data leaves the leave-one-out predictive distributions of the observed responses undisturbed. The framework requires only that the leave-one-out and swapped predictive distributions are available in closed form and that the swapped predictive mean is differentiable in the candidate value. Under these conditions, we establish a general bounded-influence proposition and a general local convexity lemma, and prove that CPP dominates any plug-in predictor with unbounded influence in asymptotic variance under $\epsilon$-contamination models. When the posterior mean is linear in the observations -- as in Gaussian linear models, basis-expansion regression, and Gaussian process regression -- the swapped predictive mean is affine in the candidate value, yielding closed-form or one-dimensional optimization solutions and an efficient rank-two computational update; all general theoretical results specialize to explicit corollaries in this setting. Simulation experiments and two data analyses under the Gaussian linear model illustrate the finite-sample advantages of the proposed method, confirming the theoretical predictions across contamination levels, sample sizes, and predictor dimensions.

stat.ME↗

arXiv2026

Linked-Tucker Factorized Individualized Regression for Paired Multivariate Categorical Outcomes

We propose a joint individualized hurdle-ordinal regression model for paired zero-inflated ordinal outcomes with subject-specific, spatially varying, and time-varying covariate effects, motivated by the Iowa Fluoride Study (IFS). The two outcomes, dental caries and dental fluorosis, are measured repeatedly across ages at fine spatial resolution, yielding nested longitudinal data with substantial zero inflation, ordinality, and heterogeneity across individuals and locations. For each outcome, a hurdle component models disease presence, while a proportional-odds component models severity among positive observations. To parsimoniously represent the high-dimensional coefficient arrays, we introduce a linked Tucker tensor factorization. Shared subject-mode factors induce dependence between the caries and fluorosis coefficient tensors, while separate spatial factors accommodate the distinct measurement grids of tooth surfaces and tooth zones. A horseshoe prior on the core tensor elements encourages sparsity, and posterior computation is performed using the No-U-Turn Sampler in NumPyro. Population-level effect summaries are obtained by projecting individualized posterior linear predictors onto the design space, and Wasserstein barycenters aggregate these summaries across tooth locations and anatomical classes. Applied to the IFS, the model reveals spatially heterogeneous associations between early-life fluoride and dietary exposures and both outcomes. Fluoride exposure is associated with increased odds and severity of fluorosis, while soda intake consistently increases caries risk. These associations differ between presence and severity components and vary across tooth locations, ages, and subpopulations defined by prior caries status, highlighting the importance of the joint hurdle-ordinal framework for disentangling disease occurrence from disease progression in multilevel dental data.

stat.ME↗

arXiv2026

Sparse Reduced-rank Regression Methods for Spatially Misaligned Data with Application to Spatial Transcriptomics

Understanding the spatiotemporal dynamics of disease progression in relation to transcriptomic profiles provides key insights into complex conditions such as Alzheimer's disease. To enable such investigations, STARmap PLUS technology offers joint profiling of high-resolution spatial transcriptomics and protein detection within the same tissue section. Detailed visual and clustering-based analyses of STARmap PLUS data by Zeng et al. (2023) provided important insights into molecular and cellular changes associated with Alzheimer's disease pathology. Motivated by this work, we develop a kernel-weighted sparse reduced-rank regression framework that estimates associations between plaque size and neighboring cell-level transcriptomic profiles while enabling gene selection and borrowing strength across genes, cell types, and disease stages. The proposed approach is implemented in a fully automated manner with data-driven specification of key model components. Through simulation studies, we demonstrate the robustness of the proposed method and its superiority across a range of simulation scenarios. Applied to Alzheimer's disease data, the proposed framework uncovers biologically meaningful associations, highlighting its potential for advancing the understanding of disease mechanisms.

stat.AP↗

arXiv2025

Bayesian Graphical High-Dimensional Time Series Models for Detecting Structural Changes

We study the structural changes in multivariate time-series by estimating and comparing stationary graphs for macroeconomic time series before and after an economic crisis such as the Great Recession. Building on a latent time series framework called Orthogonally-rotated Univariate Time-series (OUT), we propose a shared-parameter framework-the spOUT autoregressive model (spOUTAR)-that jointly models two related multivariate time series and enables coherent Bayesian estimation of their corresponding stationary precision matrices. This framework provides a principled mechanism to detect and quantify which conditional relationships among the variables changed, or formed following the crisis. Specifically, we study the impact of the Great Recession (December 2007-June 2009) that substantially disrupted global and national economies, prompting long-lasting shifts in macroeconomic indicators and their interrelationships. While many studies document its economic consequences, far less is known about how the underlying conditional dependency structure among economic variables changed as economies moved from pre-crisis stability through the shock and back to normalcy. Using the proposed approach to analyze U.S. and OECD macroeconomic data, we demonstrate that spOUTAR effectively captures recession-induced changes in stationary graphical structure, offering a flexible and interpretable tool for studying structural shifts in economic systems.

stat.ME↗

arXiv2025

Graphical Model-based Inference on Persistent Homology

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use across domains such as computer vision and neuroscience. Most statistical treatments, however, use homology primarily as a feature extractor, relying on statistical distance-based tests or simple time-to-event models for inferential tasks. While these approaches can detect global differences, they rarely localize the source of those differences. We address this gap by taking a graphical model-based approach: we associate each vertex with a population latent position in a conic space and model each bar's key events (birth and death times) using an exponential distribution, whose rate is a transformation of the latent positions according to an event occurring on the graph. The low-dimensional bars have simple graph-event representations, such as the formation of a minimum spanning tree or the triangulation of a loop, and thus enjoy tractable likelihoods. Taking a Bayesian approach, we infer latent positions and enable model extensions such as hierarchical models that allow borrowing strength across groups. Applications to a neuroimaging study of Alzheimer's disease demonstrate that our method localizes sources of difference and provides interpretable, model-based analyses of topological structure in complex data. The code is provided and maintained at https://github.com/zitian-wu/graphPH.

stat.ME↗

arXiv2025

Imaging Genetics Analysis of Alzheimer's Disease

Alzheimer's disease (AD) is a progressive neurodegenerative disorder characterized by cognitive decline, structural brain changes, and genetic predispositions. This study leverages machine-learning and statistical techniques to investigate the mechanistic relationships between cognitive function, genetic markers, and neuroimaging biomarkers in AD progression. Using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), we perform both low-dimensional and high-dimensional analyses to identify key predictors of disease states, including cognitively normal (CN), mild cognitive impairment (MCI), and AD. Our low-dimensional approach utilizes multiple linear and ordinal logistic regression to examine the influence of cognitive scores, cerebrospinal fluid (CSF) biomarkers, and demographic factors on disease classification. The results highlight significant associations between Mini-Mental State Examination (MMSE), Clinical Dementia Rating Sum of Boxes (CDRSB), and phosphorylated tau levels in predicting cognitive decline. The high-dimensional analysis employs Sure Independence Screening (SIS) and LASSO regression to reduce dimensionality and identify genetic markers correlated with cognitive impairment and white matter integrity. Genes such as CLIC1, NAB2, and TGFBR1 emerge as significant predictors across multiple analyses, linking genetic expression to neurodegeneration. Additionally, imaging genetic analysis reveals shared genetic influences across brain hemispheres and the corpus callosum, suggesting distinct genetic contributions to white matter degradation. These findings enhance our understanding of AD pathology by integrating cognitive, genetic, and imaging data. Future research should explore longitudinal analyses and potential gene-environment interactions to further elucidate the biological mechanisms underlying AD progression.

stat.AP↗

arXiv2025

Nonparametric Bayesian Multi-Treatment Mixture Cure Survival Model with Application in Pediatric Oncology

Heterogeneous treatment effect estimation is critical in oncology, particularly in multi-arm trials with overlapping therapeutic components and long-term survivors. These shared mechanisms pose a central challenge to identifying causal effects in precision medicine. We propose a novel covariate-dependent nonparametric Bayesian multi-treatment cure survival model that jointly accounts for common structures among treatments and cure fractions. Through latent link functions, our model leverages sharing among treatments through a flexible modeling approach, enabling individualized survival inference. We adopt a Bayesian route for inference and implement an efficient MCMC algorithm for approximating the posterior. Simulation studies demonstrate the method's robustness and superiority in various specification scenarios. Finally, application to the AALL0434 trial reveals clinically meaningful differences in survival across methotrexate-based regimens and their associations with different covariates, underscoring its practical utility for learning treatment effects in real-world pediatric oncology data.

stat.ME↗

arXiv2025

Bayesian Semiparametric Orthogonal Tucker Factorized Mixed Models for Multi-dimensional Longitudinal Functional Data

We introduce a novel longitudinal mixed model for analyzing complex multidimensional functional data, addressing challenges such as high-resolution, structural complexities, and computational demands. Our approach integrates dimension reduction techniques, including basis function representation and Tucker tensor decomposition, to model complex functional (e.g., spatial and temporal) variations, group differences, and individual heterogeneity while drastically reducing model dimensions. The model accommodates multiplicative random effects whose marginalization yields a novel Tucker-decomposed covariance-tensor framework. To ensure scalability, we employ semi-orthogonal mode matrices implemented via a novel graph-Laplacian-based smoothness prior with low-rank approximation, leading to an efficient posterior sampling method. A cumulative shrinkage strategy promotes sparsity and enables semiautomated rank selection. We establish theoretical guarantees for posterior convergence and demonstrate the method's effectiveness through simulations, showing significant improvements over existing techniques. Applying the method to Alzheimer's Disease Neuroimaging Initiative (ADNI) neuroimaging data reveals novel insights into local brain changes associated with disease progression, highlighting the method's practical utility for studying cognitive decline and neurodegenerative conditions.

stat.ME↗

arXiv2025

Bayesian Inference for High-dimensional Time Series with a Stationary Directed Acyclic Graphical Structure

In multivariate time series analysis, understanding the underlying causal relationships among variables is often of interest for various applications. Directed acyclic graphs (DAGs) provide a powerful framework for representing causal dependencies. This paper proposes a novel Bayesian approach for modeling multivariate time series where conditional independencies and causal structure are encoded by a DAG. The proposed model allows structural properties such as stationarity to be easily accommodated. Given the application, we further extend the model for matrix-variate time series. We take a Bayesian approach to inference, and a ``immersion-posterior'' based efficient computational algorithm is developed. The posterior convergence properties of the proposed method are established along with two identifiability results for the unrestricted structural equation models. The utility of the proposed method is demonstrated through simulation studies and real data analysis.

stat.ME↗

arXiv2024

Relational Graph in Vector Autoregression: A Case Study on the Effect of the Great Recession on Connectivity of Economic Indicators

Under a high-dimensional vector autoregressive (VAR) model, we propose a way of efficiently estimating both the stationary graph structure between the nodal time series and their temporal dynamics. The framework is then used to make inferences on the change in interdependencies between several economic indicators due to the impact of the Great Recession, the financial crisis that lasted from 2007 through 2009. There are several key advantages of the proposed framework; (1) it develops a reparametrized VAR likelihood that can be used in general high-dimensional VAR problems, (2) it strictly maintains causality of the estimated process, making inference on stationary features more meaningful and (3) it is computationally efficient due to the reduced rank structure of the parameterization. We apply the methodology to the seasonally adjusted quarterly economic indicators available in the FRED-QD database of the Federal Reserve. The analysis essentially confirms much of the prevailing knowledge about the impact of the Great Recession on different economic indicators. At the same time, it provides deeper insight into the nature and extent of the impact on the interplay of the different indicators. We also contribute to the theory of Bayesian VAR by showing the consistency of the posterior under sparse priors for the parameters of the reduced rank formulation of the VAR process.

stat.ME↗

arXiv2024

Consistency of Graphical Model-based Clustering: Robust Clustering using Bayesian Spanning Forest

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to inconsistent clustering results. Graphical model-based clustering adopts a different strategy, specifying the likelihood by treating data as dependently generated from a disjoint union of component graphs. Recent work on Bayesian spanning forests addresses graph uncertainty by using the integrated posterior of the node partition, marginalized over the latent edge distribution, to produce probabilistic clustering estimates. Despite strong empirical performance, theoretical guarantees such as consistency remain unclear, particularly when the true data-generating process deviates from the assumed graphical model. This article establishes a positive asymptotic result: when data are generated from an unknown collection of component distributions and a mild asymptotic separation condition holds with probability tending to one (without requiring complete support separation), the posterior concentrates on the true partition, thereby yielding consistent clustering estimates, including the number of clusters. Our results hold whether the number of clusters is fixed or increases with sample size. Additionally, we derive an upper bound on the expected misclassification rate. These results highlight graphical models as a robust alternative to mixture models in clustering.

math.ST↗

arXiv2024

Bayesian Learning of Relational Graph in Semiparametric High-dimensional Time Series

Time series data arising in many applications nowadays are high-dimensional. A large number of parameters describe features of these time series. We propose a novel approach to modeling a high-dimensional time series through several independent univariate time series, which are then orthogonally rotated and sparsely linearly transformed. With this approach, any specified intrinsic relations among component time series given by a graphical structure can be maintained at all time snapshots. We call the resulting process an Orthogonally-rotated Univariate Time series (OUT). Key structural properties of time series such as stationarity and causality can be easily accommodated in the OUT model. For Bayesian inference, we put suitable prior distributions on the spectral densities of the independent latent times series, the orthogonal rotation matrix, and the common precision matrix of the component times series at every time point. A likelihood is constructed using the Whittle approximation for univariate latent time series. An efficient Markov Chain Monte Carlo (MCMC) algorithm is developed for posterior computation. We study the convergence of the pseudo-posterior distribution based on the Whittle likelihood for the model's parameters upon developing a new general posterior convergence theorem for pseudo-posteriors. We find that the posterior contraction rate for independent observations essentially prevails in the OUT model under very mild conditions on the temporal dependence described in terms of the smoothness of the corresponding spectral densities. Through a simulation study, we compare the accuracy of estimating the parameters and identifying the graphical structure with other approaches. We apply the proposed methodology to analyze a dataset on different industrial components of the US gross domestic product between 2010 and 2019 and predict future observations.

stat.ME↗

arXiv2024

Individualized Multi-Treatment Response Curves Estimation using RBF-net with Shared Neurons

Heterogeneous treatment effect estimation is an important problem in precision medicine. Specific interests lie in identifying the differential effect of different treatments based on some external covariates. We propose a novel non-parametric treatment effect estimation method in a multi-treatment setting. Our non-parametric modeling of the response curves relies on radial basis function (RBF)-nets with shared hidden neurons. Our model thus facilitates modeling commonality among the treatment outcomes. The estimation and inference schemes are developed under a Bayesian framework using thresholded best linear projections and implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of the analysis. The numerical performance of the method is demonstrated through simulation experiments. Applying our proposed method to MIMIC data, we obtain several interesting findings related to the impact of different treatment strategies on the length of ICU stay and 12-hour SOFA score for sepsis patients who are home-discharged.

stat.ME↗

arXiv2023

Nonparametric Modeling of Diffusion MRI Signal in Q-space

This paper describes a novel nonparametric model for modeling diffusion MRI signals in q-space. In q-space, diffusion MRI signal is measured for a sequence of magnetic strengths (b-values) and magnetic gradient directions (b-vectors). We propose a Poly-RBF model, which employs a bidirectional framework with polynomial bases to model the signal along the b-value direction and Gaussian radial bases across the b-vectors. The model can accommodate sparse data on b-values and moderately dense data on b-vectors. The utility of Poly-RBF is inspected for two applications: 1) prediction of the dMRI signal, and 2) harmonization of dMRI data collected under different acquisition protocols with different scanners. Our results indicate that the proposed Poly-RBF model can more accurately predict the unmeasured diffusion signal than its competitors such as the Gaussian process model in {\tt Eddy} of FSL. Applying it to harmonizing the diffusion signal can significantly improve the reproducibility of derived white matter microstructure measures.

stat.AP↗

arXiv2023

Linking stability with molecular geometries of perovskites and lanthanide richness using machine learning methods

Oxide perovskite materials of type ABO3 have a wide range of technological applications, such as catalysts in solid oxide fuel cells and as light-absorbing materials in solar photovoltaics. These materials often exhibit differential structural and electrostatic properties through lanthanide or non-lanthanide derived A- and B- sites. Although, experimental and/or computational verification of these differences are often difficult. In this paper, we thus take a data-driven approach. Specifically, we run three analysis using the dataset Li, Jacobs, and Morgan [2018a] applying advanced machine learning tools to perform nonparametric regressions and also to produce data visualizations using latent factor analysis (LFA) and principal component analysis (PCA). We also implement a nonparametric feature screening step while performing our high dimensional regression analysis, ensuring robustness in our results

cond-mat.mtrl-sci↗

arXiv2023

Conic Sparsity: Estimation of Regression Parameters in Closed Convex Polyhedral Cones

Statistical problems often involve linear equality and inequality constraints on model parameters. Direct estimation of parameters restricted to general polyhedral cones, particularly when one is interested in estimating low dimensional features, may be challenging. We use a dual form parameterization to characterize parameter vectors restricted to lower dimensional faces of polyhedral cones and use the characterization to define a notion of 'sparsity' on such cones. We show that the proposed notion agrees with the usual notion of sparsity in the unrestricted case and prove the validity of the proposed definition as a measure of sparsity. The identifiable parameterization of the lower dimensional faces allows a generalization of popular spike-and-slab priors to a closed convex polyhedral cone. The prior measure utilizes the geometry of the cone by defining a Markov random field over the adjacency graph of the extreme rays of the cone. We describe an efficient way of computing the posterior of the parameters in the restricted case. We illustrate the usefulness of the proposed methodology for imposing linear equality and inequality constraints by using wearables data from the National Health and Nutrition Examination Survey (NHANES) actigraph study where the daily average activity profiles of participants exhibit patterns that seem to obey such constraints.

stat.ME↗

arXiv2022

Spatial von-Mises Fisher Regression for Directional Data

Spatially varying directional data are routinely observed in several modern applications such as meteorology, biology, geophysics, engineering, etc. However, only a few approaches are available for covariate-dependent statistical analysis for such data. To address this gap, we propose a novel generalized linear model to analyze such that using a von Mises Fisher (vMF) distributed error structure. Using a novel link function that relies on the transformation between Cartesian and spherical coordinates, we regress the vMF-distributed directional data on the external covariates. This regression model enables us to quantify the impact of external factors on the observed directional data. Furthermore, we impose the spatial dependence using an autoregressive model, appropriately accounting for the directional dependence in the outcome. This novel specification renders computational efficiency and flexibility. In addition, a comprehensive Bayesian inferential toolbox is thoroughly developed and applied to our analysis. Subsequently, employing our regression model on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, we gain new insights into the relationship between cognitive impairment and the orientations of brain fibers, along with examining empirical efficacy through simulation experiments. The code for implementing our proposed method is available on GitHub: https://github.com/lanzhouBWH/Spatial_VMF_Regression.

stat.AP↗