This paper presents a novel approach for nonlinear assimilation called score-based sequential Langevin sampling (SSLS) within a recursive Bayesian framework. SSLS decomposes the assimilation process into a sequence of prediction and update steps, utilizing dynamic models for prediction and observation data for updating via score-based Langevin Monte Carlo. An annealing strategy is incorporated to enhance convergence and facilitate multi-modal sampling. The convergence of SSLS in TV-distance is analyzed under certain conditions, providing insights into error behavior related to hyper-parameters. Numerical examples demonstrate its outstanding performance in high-dimensional and nonlinear scenarios, as well as in situations with sparse or partial measurements. Furthermore, SSLS effectively quantifies the uncertainty associated with the estimated states, highlighting its potential for error calibration.

Here, we show that in the data-rich setting where you only train on each datapoint once (or equivalently, you only train for one epoch), standard "maximum likelihood" training optimizes the true data generating process (DGP) loss, which is equivalent to the test loss. Further, we show that the Bayesian model average optimizes the same objective, albeit while taking the expectation over uncertainty induced by finite data. As standard maximum likelihood training in the single-epoch setting optimizes the same objective as Bayesian inference, we argue that we do not expect Bayesian inference to offer any advantages in terms of overfitting or calibration in these settings. This explains the diminishing importance of Bayes in areas such as LLMs, which are often trained with one (or very few) epochs.

This chapter explores the symbiotic relationship between Artificial Intelligence (AI) and trust in networked systems, focusing on how these two elements reinforce each other in strategic cybersecurity contexts. Using a game-theoretic framework, this chapter presents approaches to trust evaluation, the strategic role of AI in cybersecurity, and governance frameworks that ensure responsible AI deployment. We investigate how trust, when dynamically managed through AI, can form a resilient security ecosystem. By examining trust as both an AI output and an AI requirement, this chapter sets the foundation for a positive feedback loop where AI enhances network security and the trust placed in AI systems fosters their adoption. The rapid development of network systems has been a catalyst for innovations such as 5G communications, edge computing, and network slicing [6], driving the transformation of Industry 4.0 [18] and introducing new services for critical infrastructures.

Trajectory prediction for multi-agents in complex scenarios is crucial for applications like autonomous driving. However, existing methods often overlook environmental biases, which leads to poor generalization. Additionally, hardware constraints limit the use of large-scale data across environments, and continual learning settings exacerbate the challenge of catastrophic forgetting. To address these issues, we propose the Continual Causal Intervention (C$^{2}$INet) method for generalizable multi-agent trajectory prediction within a continual learning framework. Using variational inference, we align environment-related prior with posterior estimator of confounding factors in the latent space, thereby intervening in causal correlations that affect trajectory representation. Furthermore, we store optimal variational priors across various scenarios using a memory queue, ensuring continuous debiasing during incremental task training. The proposed C$^{2}$INet enhances adaptability to diverse tasks while preserving previous task information to prevent catastrophic forgetting. It also incorporates pruning strategies to mitigate overfitting. Comparative evaluations on three real and synthetic complex datasets against state-of-the-art methods demonstrate that our proposed method consistently achieves reliable prediction performance, effectively mitigating confounding factors unique to different scenarios. This highlights the practical value of our method for real-world applications.

Probabilistic circuits (PCs) is a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits. Existing multiplication algorithms require that the circuits respect the same structure, i.e. variable scopes decomposes according to the same vtree. In this work, we propose and study the task of restructuring structured(-decomposable) PCs, that is, transforming a structured PC such that it conforms to a target vtree. We propose a generic approach for this problem and show that it leads to novel polynomial-time algorithms for multiplying circuits respecting different vtrees, as well as a practical depth-reduction algorithm that preserves structured decomposibility. Our work opens up new avenues for tractable PC inference, suggesting the possibility of training with less restrictive PC structures while enabling efficient inference by changing their structures at inference time.

This article addresses the challenge of parameter calibration in stochastic models where the likelihood function is not analytically available. We propose a gradient-based simulated parameter estimation framework, leveraging a multi-time scale algorithm that tackles the issue of ratio bias in both maximum likelihood estimation and posterior density estimation problems. Additionally, we introduce a nested simulation optimization structure, providing theoretical analyses including strong convergence, asymptotic normality, convergence rate, and budget allocation strategies for the proposed algorithm. The framework is further extended to neural network training, offering a novel perspective on stochastic approximation in machine learning. Numerical experiments show that our algorithm can improve the estimation accuracy and save computational costs.

We present LazyDINO, a transport map variational inference method for fast, scalable, and efficiently amortized solutions of high-dimensional nonlinear Bayesian inverse problems with expensive parameter-to-observable (PtO) maps. Our method consists of an offline phase in which we construct a derivative-informed neural surrogate of the PtO map using joint samples of the PtO map and its Jacobian. During the online phase, when given observational data, we seek rapid posterior approximation using surrogate-driven training of a lazy map [Brennan et al., NeurIPS, (2020)], i.e., a structure-exploiting transport map with low-dimensional nonlinearity. The trained lazy map then produces approximate posterior samples or density evaluations. Our surrogate construction is optimized for amortized Bayesian inversion using lazy map variational inference. We show that (i) the derivative-based reduced basis architecture [O'Leary-Roseberry et al., Comput. Methods Appl. Mech. Eng., 388 (2022)] minimizes the upper bound on the expected error in surrogate posterior approximation, and (ii) the derivative-informed training formulation [O'Leary-Roseberry et al., J. Comput. Phys., 496 (2024)] minimizes the expected error due to surrogate-driven transport map optimization. Our numerical results demonstrate that LazyDINO is highly efficient in cost amortization for Bayesian inversion. We observe one to two orders of magnitude reduction of offline cost for accurate posterior approximation, compared to simulation-based amortized inference via conditional transport and conventional surrogate-driven transport. In particular, LazyDINO outperforms Laplace approximation consistently using fewer than 1000 offline samples, while other amortized inference methods struggle and sometimes fail at 16,000 offline samples.

Untreated periodontitis causes inflammation within the supporting tissue of the teeth and can ultimately lead to tooth loss. Modeling periodontal outcomes is beneficial as they are difficult and time consuming to measure, but disparities in representation between demographic groups must be considered. There may not be enough participants to build group specific models and it can be ineffective, and even dangerous, to apply a model to participants in an underrepresented group if demographic differences were not considered during training. We propose an extension to RECaST Bayesian transfer learning framework. Our method jointly models multivariate outcomes, exhibiting significant improvement over the previous univariate RECaST method. Further, we introduce an online approach to model sequential data sets. Negative transfer is mitigated to ensure that the information shared from the other demographic groups does not negatively impact the modeling of the underrepresented participants. The Bayesian framework naturally provides uncertainty quantification on predictions. Especially important in medical applications, our method does not share data between domains. We demonstrate the effectiveness of our method in both predictive performance and uncertainty quantification on simulated data and on a database of dental records from the HealthPartners Institute.

Despite the dominant role of deep models in machine learning, limitations persist, including overconfident predictions, susceptibility to adversarial attacks, and underestimation of variability in predictions. The Bayesian paradigm provides a natural framework to overcome such issues and has become the gold standard for uncertainty estimation with deep models, also providing improved accuracy and a framework for tuning critical hyperparameters. However, exact Bayesian inference is challenging, typically involving variational algorithms that impose strong independence and distributional assumptions. Moreover, existing methods are sensitive to the architectural choice of the network. We address these issues by constructing a relaxed version of the standard feed-forward rectified neural network, and employing Polya-Gamma data augmentation tricks to render a conditionally linear and Gaussian model. Additionally, we use sparsity-promoting priors on the weights of the neural network for data-driven architectural design. To approximate the posterior, we derive a variational inference algorithm that avoids distributional assumptions and independence across layers and is a faster alternative to the usual Markov Chain Monte Carlo schemes.

Rapid and accurate estimation of post-earthquake ground failures and building damage is critical for effective post-disaster responses. Progression in remote sensing technologies has paved the way for rapid acquisition of detailed, localized data, enabling swift hazard estimation through analysis of correlation deviations between pre- and post-quake satellite imagery. However, discerning seismic hazards and their impacts is challenged by overlapping satellite signals from ground failures, building damage, and environmental noise. Previous advancements introduced a novel causal graph-based Bayesian network that continually refines seismic ground failure and building damage estimates derived from satellite imagery, accounting for the intricate interplay among geospatial elements, seismic activity, ground failures, building structures, damages, and satellite data. However, this model's neglect of spatial heterogeneity across different locations in a seismic region limits its precision in capturing the spatial diversity of seismic effects. In this study, we pioneer an approach that accounts for spatial intricacies by introducing a spatial variable influenced by the bilateral filter to capture relationships from surrounding hazards. The bilateral filter considers both spatial proximity of neighboring hazards and their ground shaking intensity values, ensuring refined modeling of spatial relationships. This integration achieves a balance between site-specific characteristics and spatial tendencies, offering a comprehensive representation of the post-disaster landscape. Our model, tested across multiple earthquake events, demonstrates significant improvements in capturing spatial heterogeneity in seismic hazard estimation. The results highlight enhanced accuracy and efficiency in post-earthquake large-scale multi-impact estimation, effectively informing rapid disaster responses.