Papers

Common psychiatric and brain disorders are highly heritable and affected by a number of genetic risk factors, yet the mechanism by which these genetic factors contribute to the disorders through alterations in brain structure and function remain poorly understood. Contemporary imaging genetic studies integrate genetic and neuroimaging data to investigate how genetic variation contributes to brain disorders via intermediate neuroimaging endophenotypes. However, the large number of potential exposures (genes) and mediators (neuroimaging features) pose new challenges to the traditional mediation analysis. In this paper, we propose a novel multi-exposure-to-multi-mediator mediation model that integrates genetic, neuroimaging and phenotypic data to investigate the "geneneuroimaging-brain disorder" mediation pathway. Our method jointly reduces the dimensions of exposures and mediators into low-dimensional aggregators where the mediation effect is maximized. We further introduce sparsity into the loadings to improve the interpretability. To target the bi-convex optimization problem, we implement an efficient alternating direction method of multipliers algorithm with block coordinate updates. We provide theoretical guarantees for the convergence of our algorithm and establish the asymptotic properties of the resulting estimators. Through extensive simulations, we demonstrate that our method outperforms other competing methods in recovering true loadings and true mediation proportions across a wide range of signal strengths, noise levels, and correlation structures. We further illustrate the utility of the method through a mediation analysis that integrates genetic, brain functional connectivity and smoking behavior data from UK Biobank, and identifies critical genes that impact nicotine dependence via changing the functional connectivity in specific brain regions.

We prove the first margin-based generalization bound for voting classifiers, that is asymptotically tight in the tradeoff between the size of the hypothesis set, the margin, the fraction of training points with the given margin, the number of training samples and the failure probability.

In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prove a 1st and 2nd-order weak approximation properties, and we compute their linear error terms explicitly, under certain regularity conditions. In Ch. 4 we instantiate our results for SGD, working out the example of linear regression explicitly. We use this example to compare the linear error terms of gradient flow and two commonly used 1st-order SMEs for SGD in Ch. 5. In the second part of the thesis we introduce and study a novel diffusion approximation for SGD without replacement (SGDo) in the finite-data setting. In Ch. 6 we motivate and define the notion of an epoched Brownian motion (EBM). We argue that Young differential equations (YDEs) driven by EBMs serve as continuous-time models for SGDo for any shuffling scheme whose induced permutations converge to a det. permuton. Further, we prove a.s. convergence for these YDEs in the strongly convex setting. Moreover, we compute an upper asymptotic bound on the convergence rate which is as sharp as, or better than previous results for SGDo. In Ch. 7 we study scaling limits of families of random walks (RW) that share the same increments up to a random permutation. We show weak convergence under the assumption that the sequence of permutations converges to a det. (higher-dimensional) permuton. This permuton determines the covariance function of the limiting Gaussian process. Conversely, we show that every Gaussian process with a covariance function determined by a permuton in this way arises as a weak scaling limit of families of RW with shared increments. Finally, we apply our weak convergence theory to show that EBMs arise as scaling limits of RW with finitely many distinct increments.

Online advertising aims to increase user engagement and maximize revenue, but users respond heterogeneously to ad exposure. Some users purchase only when exposed to ads, while others purchase regardless of exposure, and still others never purchase. This heterogeneity can be characterized by latent response types, commonly referred to as principal strata, defined by users' joint potential outcomes under exposure and non-exposure. However, users' true strata are unobserved, making direct analysis infeasible. In this article, instead of learning the true strata, we propose a novel approach that learns users' pseudo-strata by leveraging information from an outcome (revenue) observed after the response (purchase). We construct pseudo-strata to classify users and introduce misclassification rewards to quantify the expected revenue gain of pseudo-strata-based policies relative to true strata. Within a Bayesian classification framework, we learn the pseudo-strata by optimizing the expected revenue. To implement these procedures, we introduce identification assumptions and estimation methods, and establish their large-sample properties. Simulation studies show that the proposed method achieves more accurate strata classification and substantially higher revenue than baselines. We further illustrate the method using a large-scale industrial dataset from the Criteo Predictive Search Platform.

The traditional WMW null hypothesis $H_0: F = G$ is erroneously too broad. WMW actually tests narrower $H_0: AUC = 0.5$. Asymptotic distribution of the standardized $U$ statistic (i.e., the empirical AUC) under the correct $H_0$ is derived along with finite sample bias corrections. The traditional alternative hypothesis of stochastic dominance is too narrow. WMW is consistent against $H_1: AUC \neq 0.5$, as established by Van Dantzig in 1951.

We extend the convergence analysis of AdaSLS and AdaSPS in [Jiang and Stich, 2024] to the nonconvex setting, presenting a unified convergence analysis of stochastic gradient descent with adaptive Armijo line-search (AdaSLS) and Polyak stepsize (AdaSPS) for nonconvex optimization. Our contributions include: (1) an $\mathcal{O}(1/\sqrt{T})$ convergence rate for general nonconvex smooth functions, (2) an $\mathcal{O}(1/T)$ rate under quasar-convexity and interpolation, and (3) an $\mathcal{O}(1/T)$ rate under the strong growth condition for general nonconvex functions.

Cognitive diagnosis models (CDMs) are restricted latent class models widely used to measure attributes of interest in diagnostic assessments across education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs (PM-CDMs) are an important extension of CDMs. They model individuals' status for each attribute as continuous to measure partial mastery levels, thereby relaxing the restrictive discrete-attribute assumption of classical CDMs. As a result, PM-CDMs often yield better fits to real-world data and more refined measurements of the substantive attributes of interest. However, these models inherit strong parametric assumptions from traditional CDMs about item response functions and thus still face a significant risk of model misspecification. This paper proposes a generalized additive PM-CDM (GaPM-CDM) that substantially relaxes the parametric assumptions of PM-CDMs. This proposal leverages model parsimony and interpretability by modeling each item response function as a mixture of nonparametric monotone functions of attributes. A method for estimating GaPM-CDM is developed that combines the marginal maximum likelihood estimator with a sieve approximation of the nonparametric functions. The new model is applicable in both confirmatory and exploratory settings, depending on whether prior knowledge of the relationship between observed variables and attributes is available. The proposed method is evaluated and compared with PM-CDMs through extensive simulation studies and further applied to two measurement problems from educational testing and healthcare research, respectively.

This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based on the expectation-maximization algorithm, which exploits the structure of the recursive model. In particular, we derive closed-form update formulas when the scaling factor is modeled as a parametric linear predictor. This approach is compared with the fully coupled likelihood maximization of the classical non-recursive formulation introduced by Kennedy and O'Hagan. A series of benchmark experiments, covering applications of increasing complexity, highlights the performance of both approaches. The results demonstrate that the proposed recursive strategy significantly reduces training time, especially when large low-fidelity datasets are available, while maintaining competitive predictive accuracy and uncertainty estimation.

Bayesian additive regression trees (BART) is a popular Bayesian ensemble model used in regression and classification analysis. Under this modeling framework, the regression function is approximated by an ensemble of decision trees, interpreted as weak learners. In this work, we propose a generalization of the BART model that has two main features: first, it automatically selects the number of decision trees using the given data; second, the model allows clusters of observations to have different regression functions since each data point can only use a selection of weak learners, instead of all of them. This model generalization is accomplished by including a binary weight matrix in the conditional distribution of the response variable, which activates only a specific subset of decision trees for each observation. Such a matrix is endowed with an Indian Buffet process prior, and sampled within the MCMC sampler, together with the other BART parameters. We then compare the Infinite BART model with the classic one on simulated and real datasets. Specifically, we provide examples illustrating variable importance, partial dependence and causal estimation.

We study the spatio-temporal features of extremal sub-daily precipitation data over the Piave river basin in northeast Italy using a rich database of observed hourly rainfall. Empirical evidence suggests that both the marginal and dependence structures for extreme precipitation in the area exhibit seasonal patterns, and spatial dependence appears to weaken as events become more extreme. We investigate factors affecting the marginal distributions, the spatial dependence and the interplay between them. Capturing these features is essential to provide a realistic description of extreme precipitation processes in order to better estimate their associated risks. With this aim, we identify various climatic covariates at different spatio-temporal scales and explore their usefulness. We go beyond existing literature by investigating and comparing the performance of recently proposed covariate-dependent models for both the marginal and dependence structures of extremes. Furthermore, a flexible max-id model, which encompasses both asymptotic dependence and independence, is used to learn about the spatio-temporal variability of rainfall processes at extreme levels. We find that modelling non-stationarity only at the marginal level does not fully capture the variability of precipitation extremes, and that it is important to also capture the seasonal variation of extremal dependence.

We propose an adaptive Sequential Probability Ratio Test (SPRT) which allocates a finite number of applications to the less effective treatment. In the classical SPRT framework, patients are assigned to the two competing treatments one by one until the stopping criterion, based on breaching the boundary values which are pre-determined using the Type-I and Type-II error probabilities, is met. This ensures the control of errors at the cost of ethical efficiency as the exposure to the less effective treatment is large. We begin with proposing an adaptive sequential framework for testing two simple hypotheses that analytically ensures finite exposure to the less effective treatment. Our proposed procedure employs a likelihood ratio driven adaptive allocation rule, dynamically concentrating sampling effort on the superior population while preserving asymptotic efficiency (in terms of average sample number), comparable to the classical SPRT. We derive an explicit closed-form expression for the expected number of allocations to the inferior treatment. Extensive simulation studies and real data analyses substantiate the theoretical results, evincing a significant reduction in inferior allocations compared to the classical SPRT. The proposed design thus offers a balanced method between statistical precision and ethical responsibility, aligning inferential reliability with patient safety.

Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of experimental units are a prominent example. In plant breeding, the amount of seed available for the treatments to be tested may be so limited that only one experimental unit per treatment can be accommodated. In such settings, augmented designs become an interesting option, where a small set of treatments, for which sufficient seed is available, are replicated across the rectangular layout so that row and column effects, as well as the error variance can be estimated. Here, we consider the use of an auxiliary design, also known as a contraction, to generate an augmented row-column design. We make use of the fact that the efficiency factors of the contraction and the associated augmented design are closely interlinked. A major advantage of this approach is that an efficient contraction can be found by computer search at much higher computational speed than is required for direct search for an efficient augmented design. Two examples are used to illustrate the proposed method.

Traditional statistical approaches primarily model associations between variables, however many scientific and practical questions require causal methods instead. These methods typically rely on assumptions about an underlying structure and are often represented by a Directed Acyclic Graph (DAG). While causal structures can be learned for single-level data, hierarchical or multi-level settings, where units (e.g., plants, students or patients) are nested within groups (e.g., environments, schools or hospitals), lack suitable methods. This article addresses such settings. These multi-level structures frequently arise in fields such as agriculture, where plants grow within different environments. Building on nonlinear structural causal models, or additive noise models, we propose an approach that facilitates causal structure learning for hierarchical causal models with additive unobserved group-level effects and group-specific causal functions. We also propose a simulation-based manner to compute hard interventions for the estimated causal model. In a simulation study, we show that the proposed method is able to identify the underlying hierarchical causal mechanism. A winter-wheat example is used to showcase how the proposed method can be used in practice and how to interpret its results.

We are extending Popularity Bias Memorization theorem from arXiv:archive/2404.12008 in several directions. We extend it to arbitrary degree distributions and also prove both upper and lower estimates for the alignment with top-k singular hyperspace.

Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in multivariate analysis and related applications. This paper investigates both the exact and asymptotic distributions of the square root of a standard Wishart matrix. We first derive the exact distribution of the square root matrix. Then, by leveraging the Bartlett decomposition, we establish the joint asymptotic normality of the upper-triangular entries of the square root matrix. The resulting limiting distribution resembles that of a scaled Gaussian Wigner ensemble. Additionally, we quantify the rate of convergence using the 1-Wasserstein distance. To validate our theoretical findings, we conduct extensive Monte Carlo simulations, which demonstrate rapid convergence even with relatively low degrees of freedom. These results offer refined insights into the asymptotic behavior of random matrix functionals.

This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under independence or conservative control under specific one-sided dependence structures, but its validity for correlated two-sided tests has remained an open question. We introduce the notion of positive left-tail dependence under the null (PLTDN), extending classical dependence assumptions to two-sided settings, and show that it ensures valid FDR control for BH-type procedures. Building on this framework, we propose a family of generalized shifted BH (GSBH) methods that incorporate correlation information through simple p-value adjustments. Simulation results demonstrate reliable FDR control and improved power across a range of dependence structures, while an application to an HIV gene expression dataset illustrates the practical effectiveness of the proposed approach.

Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where a single algorithm can simultaneously attain $\mathcal{O}(\sqrt{T})$ regret for convex functions, $\mathcal{O}(d \log T)$ for exp-concave functions, and $\mathcal{O}(\log T)$ for strongly convex functions, where $T$ is the number of rounds and $d$ is the dimension of the feasible domain. However, these methods still lack problem-dependent adaptivity. In particular, no universal method provides regret bounds that scale with the gradient variation $V_T$, a key quantity that plays a crucial role in applications such as stochastic optimization and fast-rate convergence in games. In this work, we introduce UniGrad, a novel approach that achieves both universality and adaptivity, with two distinct realizations: UniGrad.Correct and UniGrad.Bregman. Both methods achieve universal regret guarantees that adapt to gradient variation, simultaneously attaining $\mathcal{O}(\log V_T)$ regret for strongly convex functions and $\mathcal{O}(d \log V_T)$ regret for exp-concave functions. For convex functions, the regret bounds differ: UniGrad.Correct achieves an $\mathcal{O}(\sqrt{V_T \log V_T})$ bound while preserving the RVU property that is crucial for fast convergence in online games, whereas UniGrad.Bregman achieves the optimal $\mathcal{O}(\sqrt{V_T})$ regret bound through a novel design. Both methods employ a meta algorithm with $\mathcal{O}(\log T)$ base learners, which naturally requires $\mathcal{O}(\log T)$ gradient queries per round. To enhance computational efficiency, we introduce UniGrad++, which retains the regret while reducing the gradient query to just $1$ per round via surrogate optimization. We further provide various implications.

We consider the problem of Adaptive Neyman Allocation for the class of AIPW estimators for estimating the average treatment effect in a design-based setting, where potential outcomes and covariates are deterministic. As each subject arrives, an adaptive procedure must select both a treatment assignment probability and a pair of linear predictors to be used in the AIPW estimator. Our goal is to construct an adaptive procedure that minimizes the Neyman Regret, which is the difference between the variance of the adaptive procedure and an oracle variance which uses the optimal non-adaptive choice of assignment probabilities and linear predictors. While previous work has drawn fruitful connections between Neyman Regret and online convex optimization for the Horvitz–Thompson estimator, one of the central challenges for the AIPW estimator is that the underlying optimization is non-convex. In this paper, we propose Sigmoid-FTRL, an adaptive experimental design which addresses the non-convexity via simultaneous minimization of two convex regrets. We prove that under standard regularity conditions, the Neyman Regret of Sigmoid-FTRL converges at a $\sqrt{d/T}$ rate, where $d$ is the dimension of the covariates and $T$ is the number of subjects in the experiment. We establish that this $T$ dependence is optimal by proving a $T^{-1/2}$ lower bound on the Neyman Regret for any adaptive design under our regularity conditions. Finally, we establish a central limit theorem and a consistently conservative variance estimator which facilitate the construction of asymptotically valid Wald-type confidence intervals.

This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients is carried out through controlled decoherence rather than nonlinear thresholding. Phase damping and ancilla-driven constructions realize this behavior coherently and show that statistical adaptivity and quantum unitarity can be combined within a single circuit model. The same physical mechanisms that reduce quantum coherence, such as dephasing and amplitude damping, are repurposed as programmable resources for noise suppression. Practical demonstrations implemented with Qiskit illustrate how circuits and channels emulate coefficientwise attenuation, and all examples are provided as Jupyter notebooks in the companion GitHub repository. Encoding schemes for amplitude, phase, and hybrid representations are examined in relation to transform coherence and measurement feasibility, and realizations suited to current noisy intermediate-scale quantum devices are discussed. The work provides a conceptual and experimental link between wavelet-based statistical inference and quantum information processing, and shows how engineered decoherence can act as an operational surrogate for classical shrinkage.

Decision trees remain central for tabular prediction but struggle with (i) capturing spatial dependence and (ii) producing locally stable (robust) explanations. We present SX-GeoTree, a self-explaining geospatial regression tree that integrates three coupled objectives during recursive splitting: impurity reduction (MSE), spatial residual control (global Moran's I), and explanation robustness via modularity maximization on a consensus similarity network formed from (a) geographically weighted regression (GWR) coefficient distances (stimulus-response similarity) and (b) SHAP attribution distances (explanatory similarity). We recast local Lipschitz continuity of feature attributions as a network community preservation problem, enabling scalable enforcement of spatially coherent explanations without per-sample neighborhood searches. Experiments on two exemplar tasks (county-level GDP in Fujian, n=83; point-wise housing prices in Seattle, n=21,613) show SX-GeoTree maintains competitive predictive accuracy (within 0.01 $R^{2}$ of decision trees) while improving residual spatial evenness and doubling attribution consensus (modularity: Fujian 0.19 vs 0.09; Seattle 0.10 vs 0.05). Ablation confirms Moran's I and modularity terms are complementary; removing either degrades both spatial residual structure and explanation stability. The framework demonstrates how spatial similarity - extended beyond geometric proximity through GWR-derived local relationships - can be embedded in interpretable models, advancing trustworthy geospatial machine learning and offering a transferable template for domain-aware explainability.

We introduce the Cisco Time Series Model, a univariate zero-shot forecaster. This time series foundation model is the result of a general architectural innovation to a time series model enabling it to accept multiresolution input, applied to a popular decoder-only time series model (TimesFM). The resulting multiresolution decoder-only model is trained on over 300B unique data points, with more than half coming from the observability domain. Quantitative and qualitative evaluations demonstrate that the resulting model achieves superior performance on observability datasets while retaining very similar performance on a standard general-purpose forecasting benchmark (GIFT-Eval), and suggest that the multiresolution structure enables the model to make more accurate predictions on long context input.

This paper investigates how institutional learning and regional spillovers shape volatility dynamics in ASEAN equity markets. Using daily data for Indonesia, Malaysia, the Philippines, and Thailand from 2010 to 2024, we construct a high-frequency institutional learning index via a MIDAS-EPU approach. Unlike existing studies that treat institutional quality as a static background characteristic, this paper models institutions as a dynamic mechanism that reacts to policy shocks, information pressure, and crisis events. Building on this perspective, we introduce two new volatility frameworks: the Institutional Response Dynamics Model (IRDM), which embeds crisis memory, policy shocks, and information flows; and the Network-Integrated IRDM (N-IRDM), which incorporates dynamic-correlation and institutional-similarity networks to capture cross-market transmission. Empirical results show that institutional learning amplifies short-run sensitivity to shocks yet accelerates post-crisis normalization. Crisis-memory terms explain prolonged volatility clustering, while network interactions improve tail behavior and short-horizon forecasts. Robustness checks using placebo and lagged networks indicate that spillovers reflect a strong regional common factor rather than dependence on specific correlation topologies. Diebold-Mariano and ENCNEW tests confirm that the N-IRDM significantly outperforms baseline GARCH benchmarks. The findings highlight a dual role of institutions and offer policy insights on transparency enhancement, macroprudential communication, and coordinated regional governance.

Identifying key driver genes governing biological processes such as development and disease progression remains a challenge. While existing methods can reconstruct cellular trajectories or infer static gene regulatory networks (GRNs), they often fail to quantify time-resolved regulatory effects within specific temporal windows. Here, we present Time-varying Network Driver Estimation (TNDE), a computational framework quantifying dynamic gene driver effects from single-cell snapshot data under a linear Markov assumption. TNDE leverages a shared graph attention encoder to preserve the local topological structure of the data. Furthermore, by incorporating partial optimal transport, TNDE accounts for unmatched cells arising from proliferation or apoptosis, thereby enabling trajectory alignment in non-equilibrium processes. Benchmarking on simulated datasets demonstrates that TNDE outperforms existing baseline methods across diverse complex regulatory scenarios. Applied to mouse erythropoiesis data, TNDE identifies stage-specific driver genes, the functional relevance of which is corroborated by biological validation. TNDE offers an effective quantitative tool for dissecting dynamic regulatory mechanisms underlying complex biological processes.

We present a case study for the calibration of Low-cost air-quality (LCAQ) CO sensors from one of the largest multi-site-multi-season-multi-sensor-multi-pollutant mobile air-quality monitoring network deployments in India. LCAQ sensors have been shown to play a critical role in the establishment of dense, expansive air-quality monitoring networks and combating elevated pollution levels. The calibration of LCAQ sensors against regulatory-grade monitors is an expensive, laborious and time-consuming process, especially when a large number of sensors are to be deployed in a geographically diverse layout. In this work, we present the RESPIRE technique to calibrate LCAQ sensors to detect ambient CO (Carbon Monoxide) levels. RESPIRE offers specific advantages over baseline calibration methods popular in literature, such as improved prediction in cross-site, cross-season, and cross-sensor settings. RESPIRE offers a training algorithm that is provably resistant to outliers and an explainable model with the ability to flag instances of model overfitting. Empirical results are presented based on data collected during an extensive deployment spanning four sites, two seasons and six sensor packages. RESPIRE code is available at https://github.com/purushottamkar/respire.

We investigate complex-valued Variational AutoEncoders (CVAE) for radar Out-Of-Distribution (OOD) detection in complex radar environments. We proposed several detection metrics: the reconstruction error of CVAE (CVAE-MSE), the latent-based scores (Mahalanobis, Kullback-Leibler divergence (KLD)), and compared their performance against the classical ANMF-Tyler detector (ANMF-FP). The performance of all these detectors is analyzed on synthetic and experimental radar data, showing the advantages and the weaknesses of each detector.

The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying dynamics responsible for their emergence. We present an effort to characterize the neural activity from the cortex of a mouse during natural sleep, captured through local field potential measurements. Our approach relies on using a discretized Wilson–Cowan Amari neural field model for neural activity, along with a data assimilation method that allows the Bayesian joint estimation of the state and parameters. We demonstrate the feasibility of our approach on synthetic measurements before applying it to a dataset available in literature. Our findings suggest the potential of our approach to characterize the stimulus received by the cortex from other brain regions, while simultaneously inferring a state that aligns with the observed signal.

Seat belt use remains one of the most effective measures for reducing vehicle occupant fatalities and injuries. Yet, seat-belt compliance across different locales demands far more granular data than traditional, roadside surveys can provide. These surveys are spatially sparse, temporally intermittent, and costly to administer, often providing coarse-grained snapshots insufficient for capturing dynamic behavioral patterns or localized disparities. Telematics data emerges as a transformative alternative, offering continuous, high-resolution driver event records, such as seat belt latch status, across vast geographic areas. This granular and scalable data enables the application of advanced spatiotemporal models that more accurately reflect the complex interactions driving seatbelt use. This study utilizes telematics data to generate county-level seat belt compliance metrics for Iowa in 2022, employing a suite of beta-regression models that incorporate spatial and temporal random effects. The study findings demonstrate that models including both spatial and temporal components outperform those with spatial or temporal effects alone, underscoring the importance of jointly accounting for geographic clustering and temporal dynamics. Among explanatory variables, vehicle miles traveled (VMT) and per capita income emerge as significant predictors of compliance rates. The significant spatial and temporal effects highlight that telematics-based granular data substantially enhances model fit and inference quality. The results demonstrate that integrating granular telematics data within sophisticated spatiotemporal frameworks significantly improves inference, providing policymakers with precise insights for targeted interventions and advancing traffic safety research.

The validation of a data-driven model is the process of assessing the model's ability to generalize to new, unseen data in the population of interest. This paper proposes a set of general rules for model validation. These rules are designed to help practitioners create reliable validation plans and report their results transparently. While no validation scheme is flawless, these rules can help practitioners ensure their strategy is sufficient for practical use, openly discuss any limitations of their validation strategy, and report clear, comparable performance metrics.

Inverse problems are fundamental to science and engineering, where the goal is to infer an underlying signal or state from incomplete or noisy measurements. Recent approaches employ diffusion models as powerful implicit priors for such problems, owing to their ability to capture complex data distributions. However, existing diffusion-based methods for inverse problems often rely on strong approximations of the posterior distribution, require computationally expensive gradient backpropagation through the score network, or are restricted to linear measurement models. In this work, we propose Restart for Posterior Sampling (RePS), a general and efficient framework for solving both linear and non-linear inverse problems using pre-trained diffusion models. RePS builds on the idea of restart-based sampling, previously shown to improve sample quality in unconditional diffusion, and extends it to posterior inference. Our method employs a conditioned ODE applicable to any differentiable measurement model and introduces a simplified restart strategy that contracts accumulated approximation errors during sampling. Unlike some of the prior approaches, RePS avoids backpropagation through the score network, substantially reducing computational cost. We demonstrate that RePS achieves faster convergence and superior reconstruction quality compared to existing diffusion-based baselines across a range of inverse problems, including both linear and non-linear settings.

Early and accurate detection of Alzheimer's disease (AD) is crucial for enabling timely intervention and improving outcomes. However, developing reliable machine learning (ML) models for AD diagnosis is challenging due to limited labeled data, multi-site heterogeneity, and class imbalance. We propose a Transformer-based diagnostic framework that combines diffusion-based synthetic data generation with graph representation learning and transfer learning. A class-conditional denoising diffusion probabilistic model (DDPM) is trained on the real-world NACC dataset to generate a large synthetic cohort that mirrors multimodal clinical and neuroimaging feature distributions while balancing diagnostic classes. Modality-specific Graph Transformer encoders are first pretrained on this synthetic data to learn robust, class-discriminative representations and are then frozen while a neural classifier is trained on embeddings from the original NACC data. We quantify distributional alignment between real and synthetic cohorts using metrics such as Maximum Mean Discrepancy (MMD), Frechet distance, and energy distance, and complement discrimination metrics with calibration and fixed-specificity sensitivity analyses. Empirically, our framework outperforms standard baselines, including early and late fusion deep neural networks and the multimodal graph-based model MaGNet, yielding higher AUC, accuracy, sensitivity, and specificity under subject-wise cross-validation on NACC. These results show that diffusion-based synthetic pretraining with Graph Transformers can improve generalization in low-sample, imbalanced clinical prediction settings.