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.

Multiagent systems grapple with partial observability (PO), and the decentralized POMDP (Dec-POMDP) model highlights the fundamental nature of this challenge. Whereas recent approaches to addressing PO have appealed to deep learning models, providing a rigorous understanding of how these models and their approximation errors affect agents' handling of PO and their interactions remain a challenge. In addressing this challenge, we investigate reconstructing global states from local action-observation histories in Dec-POMDPs using diffusion models. We first find that diffusion models conditioned on local history represent possible states as stable fixed points. In collectively observable (CO) Dec-POMDPs, individual diffusion models conditioned on agents' local histories share a unique fixed point corresponding to the global state, while in non-CO settings, the shared fixed points yield a distribution of possible states given joint history. We further find that, with deep learning approximation errors, fixed points can deviate from true states and the deviation is negatively correlated to the Jacobian rank. Inspired by this low-rank property, we bound the deviation by constructing a surrogate linear regression model that approximates the local behavior of diffusion models. With this bound, we propose a composite diffusion process iterating over agents with theoretical convergence guarantees to the true state.

The Dreamer agent provides various benefits of Model-Based Reinforcement Learning (MBRL) such as sample efficiency, reusable knowledge, and safe planning. However, its world model and policy networks inherit the limitations of recurrent neural networks and thus an important question is how an MBRL framework can benefit from the recent advances of transformers and what the challenges are in doing so. In this paper, we propose a transformer-based MBRL agent, called TransDreamer. We first introduce the Transformer State-Space Model, a world model that leverages a transformer for dynamics predictions. We then share this world model with a transformer-based policy network and obtain stability in training a transformer-based RL agent. In experiments, we apply the proposed model to 2D visual RL and 3D first-person visual RL tasks both requiring long-range memory access for memory-based reasoning. We show that the proposed model outperforms Dreamer in these complex tasks.

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.

Statistical process monitoring (SPM) methods are essential tools in quality management to check the stability of industrial processes, i.e., to dynamically classify the process state as in control (IC), under normal operating conditions, or out of control (OC), otherwise. Traditional SPM methods are based on unsupervised approaches, which are popular because in most industrial applications the true OC states of the process are not explicitly known. This hampered the development of supervised methods that could instead take advantage of process data containing labels on the true process state, although they still need improvement in dealing with class imbalance, as OC states are rare in high-quality processes, and the dynamic recognition of unseen classes, e.g., the number of possible OC states. This article presents a novel stream-based active learning strategy for SPM that enhances partially hidden Markov models to deal with data streams. The ultimate goal is to optimize labeling resources constrained by a limited budget and dynamically update the possible OC states. The proposed method performance in classifying the true state of the process is assessed through a simulation and a case study on the SPM of a resistance spot welding process in the automotive industry, which motivated this research.

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.

Recent years have seen a notable increase in the frequency and intensity of extreme weather events. With a rising number of power outages caused by these events, accurate prediction of power line outages is essential for safe and reliable operation of power grids. The Bayesian network is a probabilistic model that is very effective for predicting line outages under weather-related uncertainties. However, most existing studies in this area offer general risk assessments, but fall short of providing specific outage probabilities. In this work, we introduce a novel approach for predicting transmission line outage probabilities using a Bayesian network combined with Peter-Clark (PC) structural learning. Our approach not only enables precise outage probability calculations, but also demonstrates better scalability and robust performance, even with limited data. Case studies using data from BPA and NOAA show the effectiveness of this approach, while comparisons with several existing methods further highlight its advantages.