Increasingly frequent wildfires significantly affect solar energy production as the atmospheric aerosols generated by wildfires diminish the incoming solar radiation to the earth. Atmospheric aerosols are measured by Aerosol Optical Depth (AOD), and AOD data streams can be retrieved and monitored by geostationary satellites. However, multi-source remote-sensing data streams often present heterogeneous characteristics, including different data missing rates, measurement errors, systematic biases, and so on. To accurately estimate and predict the underlying AOD propagation process, there exist practical needs and theoretical interests to propose a physics-informed statistical approach for modeling wildfire AOD propagation by simultaneously utilizing, or fusing, multi-source heterogeneous satellite remote-sensing data streams. Leveraging a spectral approach, the proposed approach integrates multi-source satellite data streams with a fundamental advection-diffusion equation that governs the AOD propagation process. A bias correction process is included in the statistical model to account for the bias of the physics model and the truncation error of the Fourier series. The proposed approach is applied to California wildfires AOD data streams obtained from the National Oceanic and Atmospheric Administration. Comprehensive numerical examples are provided to demonstrate the predictive capabilities and model interpretability of the proposed approach. Computer code has been made available on GitHub.

We consider the Bayesian calibration of models describing the phenomenon of block copolymer (BCP) self-assembly using image data produced by microscopy or X-ray scattering techniques. To account for the random long-range disorder in BCP equilibrium structures, we introduce auxiliary variables to represent this aleatory uncertainty. These variables, however, result in an integrated likelihood for high-dimensional image data that is generally intractable to evaluate. We tackle this challenging Bayesian inference problem using a likelihood-free approach based on measure transport together with the construction of summary statistics for the image data. We also show that expected information gains (EIGs) from the observed data about the model parameters can be computed with no significant additional cost. Lastly, we present a numerical case study based on the Ohta--Kawasaki model for diblock copolymer thin film self-assembly and top-down microscopy characterization. For calibration, we introduce several domain-specific energy- and Fourier-based summary statistics, and quantify their informativeness using EIG. We demonstrate the power of the proposed approach to study the effect of data corruptions and experimental designs on the calibration results.

We investigate the cold posterior effect through the lens of PAC-Bayes generalization bounds. We argue that in the non-asymptotic setting, when the number of training samples is (relatively) small, discussions of the cold posterior effect should take into account that approximate Bayesian inference does not readily provide guarantees of performance on out-of-sample data. Instead, out-of-sample error is better described through a generalization bound. In this context, we explore the connections between the ELBO objective from variational inference and the PAC-Bayes objectives. We note that, while the ELBO and PAC-Bayes objectives are similar, the latter objectives naturally contain a temperature parameter $\lambda$ which is not restricted to be $\lambda=1$. For both regression and classification tasks, in the case of isotropic Laplace approximations to the posterior, we show how this PAC-Bayesian interpretation of the temperature parameter captures the cold posterior effect.

Most machine learning models are concerned with correlation. In contrast, Causal models are concerned with cause and effect relationships – for example – "How much would a power failure cost to a given manufacturing plant?" A structural causal model (SCM) represents causal dependencies using graphical models. Bayesian Networks are one of the most widely used SCMs. Bayesian Network consists of a DAG(Directed Acyclic Graph), a causal graph where nodes represent random variables and edges represent the relationship between them, and a conditional probability distribution (CPDs) associated with each of the random variables. Models can reflect both statistically significant information (learned from the data) and domain expertise simultaneously.

In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs representing network relationships between genes. An important application of SV-GMRFs is in inference of gene regulatory networks from spatially-resolved transcriptomics datasets. The current work on inference of SV-GMRFs are based on the regularized maximum likelihood estimation (MLE) and suffer from overwhelmingly high computational cost due to their highly nonlinear nature. To alleviate this challenge, we propose a simple and efficient optimization problem in lieu of MLE that comes equipped with strong statistical and computational guarantees. Our proposed optimization problem is extremely efficient in practice: we can solve instances of SV-GMRFs with more than 2 million variables in less than 2 minutes. We apply the developed framework to study how gene regulatory networks in Glioblastoma are spatially rewired within tissue, and identify prominent activity of the transcription factor HES4 and ribosomal proteins as characterizing the gene expression network in the tumor peri-vascular niche that is known to harbor treatment resistant stem cells.

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimensions and show that the proposed Bayesian NMF GRRN model leads to better predictions and avoids overfitting compared to existing Bayesian NMF approaches.

We consider the problem of deciding how best to target and prioritize existing vaccines that may offer protection against new variants of an infectious disease. Sequential experiments are a promising approach; however, challenges due to delayed feedback and the overall ebb and flow of disease prevalence make available methods inapplicable for this task. We present a method, partial likelihood Thompson sampling, that can handle these challenges. Our method involves running Thompson sampling with belief updates determined by partial likelihood each time we observe an event. To test our approach, we ran a semi-synthetic experiment based on 200 days of COVID-19 infection data in the US.

Making predictions robust is an important challenge. A separate challenge in federated learning (FL) is to reduce the number of communication rounds, particularly since doing so reduces performance in heterogeneous data settings. To tackle both issues, we take a Bayesian perspective on the problem of learning a global model. We show how the global predictive posterior can be approximated using client predictive posteriors. This is unlike other works which aggregate the local model space posteriors into the global model space posterior, and are susceptible to high approximation errors due to the posterior's high dimensional multimodal nature. In contrast, our method performs the aggregation on the predictive posteriors, which are typically easier to approximate owing to the low-dimensionality of the output space. We present an algorithm based on this idea, which performs MCMC sampling at each client to obtain an estimate of the local posterior, and then aggregates these in one round to obtain a global ensemble model. Through empirical evaluation on several classification and regression tasks, we show that despite using one round of communication, the method is competitive with other FL techniques, and outperforms them on heterogeneous settings. The code is publicly available at https://github.com/hasanmohsin/FedPredSpace_1Round.