arXiv subjects

Lekha Patel

Publications and source records attributed to Lekha Patel.

11 recordsLinked to original sources

arXiv2026

AeroMELD: A Linear Embedding of Aerosol Populations for Diagnostics and Latent Dynamics

Accurately representing atmospheric aerosol populations is essential for simulating aerosol-cloud interactions, radiative forcing, and ice nucleation, yet existing reduced schemes impose structural assumptions that limit their ability to capture composition diversity and mixing state. Machine-learning approaches offer more flexible representations, but standard autoencoders do not preserve the mathematical structure of aerosol populations and therefore cannot support physically meaningful process operators. We introduce AeroMELD (Aerosol Measure Embedding for Latent Dynamics), a mathematically grounded framework for constructing low-dimensional latent variables that retain this structure. We show that any permutation-invariant linear encoder must take a scale-shape decomposition, with total number concentration represented explicitly and latent shape given by a barycentric combination of per-particle embeddings. This aggregated latent state retains the diagnostic expressiveness of a Deep Sets model by moving the nonlinear post-aggregation stage into the learned diagnostic map while preserving latent linearity. Using particle-resolved data as ground truth, we encode weighted particle populations directly rather than binned aerosol states; size-resolved mass and number distributions serve only as diagnostic targets and visual summaries. The latent space accurately reconstructs these distributions, CCN spectra, optical coefficients, and immersion-freezing behavior while preserving the linear population structure needed for hybrid ML-physics models. Although the experiments focus on diagnostic reconstruction, the embedding is designed so that emissions and mixing can be represented exactly and nonlinear microphysical processes learned in a controlled latent space. This work establishes a foundation for learning aerosol-process evolution directly in latent space.

cs.LG↗

arXiv2026

Controller-Augmented Hidden Markov Models: A Computational Framework for Constrained Sequential Inference

Hidden Markov models are foundational for sequential inference, but their Markovian assumption fails under pathwise constraints such as precedence requirements, visitation cardinalities, or monotonic state progression, which induce long-range dependencies that invalidate standard dynamic programming algorithms. To deal with this, we present Controller-Augmented Hidden Markov Models (CHMMs), a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history, after which standard forward--backward and Viterbi recursions on the augmented chain compute exact constrained posteriors and maximum a posteriori paths in both discrete and continuous time, the latter through uniformization. We establish four theoretical guarantees: exactness of constrained inference, monotone ascent of constrained EM, inference complexity linear in the controller cardinality, and a total-variation bound under constraint misspecification. A catalog of controller encodings covering 11 constraint families across the ordering, visitation, path, and temporal categories operationalizes the framework. Empirically, we evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks of substantively different character: gene-structure decoding in \emph{Drosophila melanogaster}, free-living activity recognition in CASAS smart-home environments, and protocol-defined human activity recognition from wearable sensors. The results reveal a clean local-versus-cumulative dichotomy in which controller augmentation is uniquely able to recover globally feasible trajectories on cumulative-constraint regimes, whilst simpler decoders are matched in validity on locally-dominated regimes. Together, theory and experiment characterize when exact controller augmentation is necessary and when simpler approaches suffice.

stat.ME↗

arXiv2026

Robust Simulation Based Inference Through Robust Optimal Transport

When a statistical model $\{P_{\theta} : \theta \in \Theta\}$ lacks analytically tractable likelihoods, parametric statistical inference based on data generated from an unknown underlying distribution $P$ can still be performed as long as simulations from the model are possible. This approach is called Simulation Based Inference (SBI). Statistical models are rarely exactly correct (that is, $P \notin \{P_{\theta}: \theta \in \Theta\}$), and Robust SBI focuses on inferring a reasonable parameter even under model mis-specification. We focus on the setting where $P$ possesses potentially both geometric and Total Variation type discrepancies from $P_{\theta^*}$. For this problem, we use a Kullback-Liebler informed robust Optimal Transport divergence, motivated by Empirical Likelihood considerations. We introduce a stochastic sub-gradient ascent algorithm with a convergence guarantee for estimating the semi-discrete version of this robust Optimal Transport divergence, and design a parallelized SBI algorithm which employs the regular bootstrap on top of minimum semi-discrete robust Optimal Transport for parameter uncertainty quantification. We demonstrate mathematically why the divergence is robust under a joint geometric plus Total Variation type contamination and then illustrate the robustness of inferences on a complex benchmark SBI task.

stat.ME↗

arXiv2026

Integrative Learning of Dynamically Evolving Multiplex Graphs and Nodal Attributes Using Neural Network Gaussian Processes with an Application to Dynamic Terrorism Graphs

Exploring the dynamic co-evolution of multiplex graphs and nodal attributes is a compelling question in criminal and terrorism networks. This article is motivated by the study of dynamically evolving interactions among prominent terrorist organizations, considering various organizational attributes like size, ideology, leadership, and operational capacity. Statistically principled integration of multiplex graphs with nodal attributes is significantly challenging due to the need to leverage shared information within and across layers, account for uncertainty in predicting unobserved links, and capture temporal evolution of node attributes. These difficulties increase when layers are partially observed, as in terrorism networks where connections are deliberately hidden to obscure key relationships. To address these challenges, we present a principled methodological framework to integrate the multiplex graph layers and nodal attributes. The approach employs time-varying stochastic latent factor models, leveraging shared latent factors to capture graph structure and its co-evolution with node attributes. Latent factors are modeled using Gaussian processes with an infinitely wide deep neural network-based covariance function, termed neural network Gaussian processes (NN-GP). The NN-GP framework on latent factors exploits the predictive power of Bayesian deep neural network architecture while propagating uncertainty for reliability. Simulation studies highlight superior performance of the proposed approach in achieving inferential objectives. The approach, termed as dynamic joint learner, enables predictive inference (with uncertainty) of diverse unobserved dynamic relationships among prominent terrorist organizations and their organization-specific attributes, as well as clustering behavior in terms of friend-and-foe relationships, which could be informative in counter-terrorism research.

stat.AP↗

arXiv2025

Trust-Aware Multimodal Data Fusion for Yield Estimation: A Case Study of the 2020 Beirut Explosion

The estimation of explosive yield from heterogeneous observational data presents fundamental challenges in inverse problems, particularly when combining traditional physical measurements with modern artificial intelligence-interpreted modalities. We present a novel Bayesian fractional posterior framework that fuses seismic waves, crater dimensions, synthetic aperture radar imagery, and vision-language model interpreted ground-level images to estimate the yield of the 2020 Beirut explosion. Unlike conventional approaches that may treat data sources equally, our method learns trust weights for each modality through a Dirichlet prior, automatically calibrating the relative information content of disparate observations. Applied to the Beirut explosion, the framework yields an estimate of 0.34--0.48 kt TNT equivalent, representing 12 to 17 percent detonation efficiency relative to the 2.75 kt theoretical maximum from the blast's stored ammonium nitrate. The fractional posterior approach demonstrates superior uncertainty quantification compared to single-modality estimates while providing robustness against systematic biases. This work establishes a principled framework for integrating qualitative assessments with quantitative physical measurements, with applications to explosion monitoring, disaster response, and forensic analysis.

stat.AP↗

arXiv2025

Generative Modeling of Aerosol State Representations

Aerosol-cloud--radiation interactions remain among the most uncertain components of the Earth's climate system, in partdue to the high dimensionality of aerosol state representations and the difficulty of obtaining complete \textit{in situ} measurements. Addressing these challenges requires methods that distill complex aerosol properties into compact yet physically meaningful forms. Generative autoencoder models provide such a pathway. We present a framework for learning deep variational autoencoder (VAE) models of speciated mass and number concentration distributions, which capture detailed aerosol size-composition characteristics. By compressing hundreds of original dimensions into ten latent variables, the approach enables efficient storage and processing while preserving the fidelity of key diagnostics, including cloud condensation nuclei (CCN) spectra, optical scattering and absorption coefficients, and ice nucleation properties. Results show that CCN spectra are easiest to reconstruct accurately, optical properties are moderately difficult, and ice nucleation properties are the most challenging. To improve performance, we introduce a preprocessing optimization strategy that avoids repeated retraining and yields latent representations resilient to high-magnitude Gaussian noise, boosting accuracy for CCN spectra, optical coefficients, and frozen fraction spectra. Finally, we propose a novel realism metric -- based on the sliced Wasserstein distance between generated samples and a held-out test set -- for optimizing the KL divergence weight in VAEs. Together, these contributions enable compact, robust, and physically meaningful representations of aerosol states for large-scale climate applications.

physics.ao-ph↗

arXiv2025

Simultaneous global and local clustering in multiplex networks with covariate information

Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel (HMPSBM), that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A stochastic blockmodel is assumed in each layer, with probabilities of layer-level group memberships determined by a node's global group assignment. Our model uses a Bayesian framework, employing a probit stick-breaking process to construct node-specific mixing proportions over a set of shared Griffiths-Engen-McCloseky (GEM) distributions. These proportions determine layer-level community assignment, allowing for an unknown and varying number of groups across layers, while incorporating nodal covariate information to inform the global clustering. We propose a scalable variational inference procedure with parallelisable updates for application to large networks. Extensive simulation studies demonstrate our model's ability to accurately recover both global and layer-level clusters in complicated settings, and applications to real data showcase the model's effectiveness in uncovering interesting latent network structure.

stat.ME↗

arXiv2023

Memory Efficient And Minimax Distribution Estimation Under Wasserstein Distance Using Bayesian Histograms

We study Bayesian histograms for distribution estimation on $[0,1]^d$ under the Wasserstein $W_v, 1 \leq v < \infty$ distance in the i.i.d sampling regime. We newly show that when $d < 2v$, histograms possess a special \textit{memory efficiency} property, whereby in reference to the sample size $n$, order $n^{d/2v}$ bins are needed to obtain minimax rate optimality. This result holds for the posterior mean histogram and with respect to posterior contraction: under the class of Borel probability measures and some classes of smooth densities. The attained memory footprint overcomes existing minimax optimal procedures by a polynomial factor in $n$; for example an $n^{1 - d/2v}$ factor reduction in the footprint when compared to the empirical measure, a minimax estimator in the Borel probability measure class. Additionally constructing both the posterior mean histogram and the posterior itself can be done super--linearly in $n$. Due to the popularity of the $W_1,W_2$ metrics and the coverage provided by the $d < 2v$ case, our results are of most practical interest in the $(d=1,v =1,2), (d=2,v=2), (d=3,v=2)$ settings and we provide simulations demonstrating the theory in several of these instances.

math.ST↗

arXiv2021

Simulating cloud-aerosol interactions made by ship emissions

Satellite imagery can detect temporary cloud trails or ship tracks formed from aerosols emitted from large ships traversing our oceans, a phenomenon that global climate models cannot directly reproduce. Ship tracks are observable examples of marine cloud brightening, a potential solar climate intervention that shows promise in helping combat climate change. Whether or not a ship's emission path visibly impacts the clouds above and how long a ship track visibly persists largely depends on the exhaust type and properties of the boundary layer with which it mixes. In order to be able to statistically infer the longevity of ship-emitted aerosols and characterize atmospheric conditions under which they form, a first step is to simulate, with mathematical surrogate model rather than an expensive physical model, the path of these cloud-aerosol interactions with parameters that are inferable from imagery. This will allow us to compare when/where we would expect to ship tracks to be visible, independent of atmospheric conditions, with what is actually observed from satellite imagery to be able to infer under what atmospheric conditions do ship tracks form. In this paper, we will discuss an approach to stochastically simulate the behavior of ship induced aerosols parcels within naturally generated clouds. Our method can use wind fields and potentially relevant atmospheric variables to determine the approximate movement and behavior of the cloud-aerosol tracks, and uses a stochastic differential equation (SDE) to model the persistence behavior of cloud-aerosol paths. This SDE incorporates both a drift and diffusion term which describes the movement of aerosol parcels via wind and their diffusivity through the atmosphere, respectively. We successfully demonstrate our proposed approach with an example using simulated wind fields and ship paths.

stat.AP↗

arXiv2021

Spatio-temporal extreme event modeling of terror insurgencies

Extreme events with potential deadly outcomes, such as those organized by terror groups, are highly unpredictable in nature and an imminent threat to society. In particular, quantifying the likelihood of a terror attack occurring in an arbitrary space-time region and its relative societal risk, would facilitate informed measures that would strengthen national security. This paper introduces a novel self-exciting marked spatio-temporal model for attacks whose inhomogeneous baseline intensity is written as a function of covariates. Its triggering intensity is succinctly modeled with a Gaussian Process prior distribution to flexibly capture intricate spatio-temporal dependencies between an arbitrary attack and previous terror events. By inferring the parameters of this model, we highlight specific space-time areas in which attacks are likely to occur. Furthermore, by measuring the outcome of an attack in terms of the number of casualties it produces, we introduce a novel mixture distribution for the number of casualties. This distribution flexibly handles low and high number of casualties and the discrete nature of the data through a {\it Generalized ZipF} distribution. We rely on a customized Markov chain Monte Carlo (MCMC) method to estimate the model parameters. We illustrate the methodology with data from the open source Global Terrorism Database (GTD) that correspond to attacks in Afghanistan from 2013-2018. We show that our model is able to predict the intensity of future attacks for 2019-2021 while considering various covariates of interest such as population density, number of regional languages spoken, and the density of population supporting the opposing government.

stat.AP↗

arXiv2020

A Monte Carlo EM Algorithm for the Parameter Estimation of Aggregated Hawkes Processes

A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical limits on the accuracy of measurements, aggregated data is common. In order to use point processes to model such event data, tools for handling parameter estimation are essential. Here we consider parameter estimation of the Hawkes process, a type of self-exciting point process that has found application in the modeling of financial stock markets, earthquakes and social media cascades. We develop a novel optimization approach to parameter estimation of aggregated Hawkes processes using a Monte Carlo Expectation-Maximization (MC-EM) algorithm. Through a detailed simulation study, we demonstrate that existing methods are capable of producing severely biased and highly variable parameter estimates and that our novel MC-EM method significantly outperforms them in all studied circumstances. These results highlight the importance of correct handling of aggregated data.

stat.ME↗