Causal discovery from observational data is pivotal for deciphering complex relationships. Causal Structure Learning (CSL), which focuses on deriving causal Directed Acyclic Graphs (DAGs) from data, faces challenges due to vast DAG spaces and data sparsity. The integration of Large Language Models (LLMs), recognized for their causal reasoning capabilities, offers a promising direction to enhance CSL by infusing it with knowledge-based causal inferences. However, existing approaches utilizing LLMs for CSL have encountered issues, including unreliable constraints from imperfect LLM inferences and the computational intensity of full pairwise variable analyses. In response, we introduce the Iterative LLM Supervised CSL (ILS-CSL) framework. ILS-CSL innovatively integrates LLM-based causal inference with CSL in an iterative process, refining the causal DAG using feedback from LLMs. This method not only utilizes LLM resources more efficiently but also generates more robust and high-quality structural constraints compared to previous methodologies. Our comprehensive evaluation across eight real-world datasets demonstrates ILS-CSL's superior performance, setting a new standard in CSL efficacy and showcasing its potential to significantly advance the field of causal discovery. The codes are available at \url{https://github.com/tyMadara/ILS-CSL}.

Over the last decades, many prognostic models based on artificial intelligence techniques have been used to provide detailed predictions in healthcare. Unfortunately, the real-world observational data used to train and validate these models are almost always affected by biases that can strongly impact the outcomes validity: two examples are values missing not-at-random and selection bias. Addressing them is a key element in achieving transportability and in studying the causal relationships that are critical in clinical decision making, going beyond simpler statistical approaches based on probabilistic association. In this context, we propose a novel approach that combines selection diagrams, missingness graphs, causal discovery and prior knowledge into a single graphical model to estimate the cardiovascular risk of adolescent and young females who survived breast cancer. We learn this model from data comprising two different cohorts of patients. The resulting causal network model is validated by expert clinicians in terms of risk assessment, accuracy and explainability, and provides a prognostic model that outperforms competing machine learning methods.

Autonomous materials research labs require the ability to combine and learn from diverse data streams. This is especially true for learning material synthesis-process-structure-property relationships, key to accelerating materials optimization and discovery as well as accelerating mechanistic understanding. We present the Synthesis-process-structure-property relAtionship coreGionalized lEarner (SAGE) algorithm. A fully Bayesian algorithm that uses multimodal coregionalization to merge knowledge across data sources to learn synthesis-process-structure-property relationships. SAGE outputs a probabilistic posterior for the relationships including the most likely relationships given the data.

We consider a human-assisted autonomy sensor fusion for dynamic target localization in a Bayesian framework. To compensate for the shortcomings of an autonomous tracking system, we propose to collect spatial sensing information from human operators who visually monitor the target and can provide target localization information in the form of free sketches encircling the area where the target is located. Our focus in this paper is to construct an adaptive probabilistic model for human-provided inputs where the adaption terms capture the level of reliability of the human inputs. The next contribution of this paper is a novel joint Bayesian learning method to fuse human and autonomous sensor inputs in a manner that the dynamic changes in human detection reliability are also captured and accounted for. A unique aspect of this Bayesian modeling framework is its analytical closed-form update equations, endowing our method with significant computational efficiency. Simulations demonstrate our results.

This paper addresses the problem of enabling a robot to search for a semantic object, i.e., an object with a semantic label, in an unknown and GPS-denied environment. For the robot in the unknown environment to detect and find the target semantic object, it must perform simultaneous localization and mapping (SLAM) at both geometric and semantic levels using its onboard sensors while planning and executing its motion based on the ever-updated SLAM results. In other words, the robot must be able to conduct simultaneous localization, semantic mapping, motion planning, and execution in real-time in the presence of sensing and motion uncertainty. This is an open problem as it combines semantic SLAM based on perception and real-time motion planning and execution under uncertainty. Moreover, the goals of the robot motion change on the fly depending on whether and how the robot can detect the target object. We propose a novel approach to tackle the problem, leveraging semantic SLAM, Bayesian Networks, Markov Decision Process, and Real-Time Dynamic Programming. The results in simulation and real experiments demonstrate the effectiveness and efficiency of our approach.

Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative SciML models are physics-informed neural networks (PINNs) and neural operators (NOs). While UQ in SciML has been increasingly investigated in recent years, very few works have focused on addressing the uncertainty caused by the noisy inputs, such as spatial-temporal coordinates in PINNs and input functions in NOs. The presence of noise in the inputs of the models can pose significantly more challenges compared to noise in the outputs of the models, primarily due to the inherent nonlinearity of most SciML algorithms. As a result, UQ for noisy inputs becomes a crucial factor for reliable and trustworthy deployment of these models in applications involving physical knowledge. To this end, we introduce a Bayesian approach to quantify uncertainty arising from noisy inputs-outputs in PINNs and NOs. We show that this approach can be seamlessly integrated into PINNs and NOs, when they are employed to encode the physical information. PINNs incorporate physics by including physics-informed terms via automatic differentiation, either in the loss function or the likelihood, and often take as input the spatial-temporal coordinate. Therefore, the present method equips PINNs with the capability to address problems where the observed coordinate is subject to noise. On the other hand, pretrained NOs are also commonly employed as equation-free surrogates in solving differential equations and Bayesian inverse problems, in which they take functions as inputs. The proposed approach enables them to handle noisy measurements for both input and output functions with UQ.

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages on developing efficient ``white-box'' ML schemes. Here, we give a brief review on the inspiring progresses made in TN-based ML. On one hand, interpretability of TN ML is accommodated with the solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be rendered from the powerful TN representations and the advanced computational techniques developed in quantum many-body physics. With the fast development on quantum computers, TN is expected to conceive novel schemes runnable on quantum hardware, heading towards the ``quantum artificial intelligence'' in the forthcoming future.

Imitation learning addresses the challenge of learning by observing an expert's demonstrations without access to reward signals from environments. Most existing imitation learning methods that do not require interacting with environments either model the expert distribution as the conditional probability p(a|s) (e.g., behavioral cloning, BC) or the joint probability p(s, a). Despite its simplicity, modeling the conditional probability with BC usually struggles with generalization. While modeling the joint probability can improve generalization performance, the inference procedure is often time-consuming, and the model can suffer from manifold overfitting. This work proposes an imitation learning framework that benefits from modeling both the conditional and joint probability of the expert distribution. Our proposed diffusion model-augmented behavioral cloning (DBC) employs a diffusion model trained to model expert behaviors and learns a policy to optimize both the BC loss (conditional) and our proposed diffusion model loss (joint). DBC outperforms baselines in various continuous control tasks in navigation, robot arm manipulation, dexterous manipulation, and locomotion. We design additional experiments to verify the limitations of modeling either the conditional probability or the joint probability of the expert distribution, as well as compare different generative models. Ablation studies justify the effectiveness of our design choices. Recently, the success of deep reinforcement learning (DRL) (Mnih et al., 2015; Lillicrap et al., 2016; Arulkumaran et al., 2017) has inspired the research community to develop DRL frameworks to control robots, aiming to automate the process of designing sensing, planning, and control algorithms by letting the robot learn in an end-to-end fashion. Yet, acquiring complex skills through trial and error can still lead to undesired behaviors even with sophisticated reward design (Christiano et al., 2017; Leike et al., 2018; Lee et al., 2019). Moreover, the exploring process could damage expensive robotic platforms or even be dangerous to humans (Garcıa and Fernández, 2015; Levine et al., 2020). To overcome this issue, imitation learning (i.e., learning from demonstration) (Schaal, 1997; Osa et al., 2018) has received growing attention, whose aim is to learn a policy from expert demonstrations, which are often more accessible than appropriate reward functions for reinforcement learning. Among various imitation learning directions, adversarial imitation learning (Ho and Ermon, 2016; Zolna et al., 2021; Kostrikov et al., 2019) and inverse reinforcement learning (Ng and Russell, 2000; Abbeel and Ng, 2004) have achieved encouraging results in a variety of domains. Yet, these methods require interacting with environments, which can still be expensive or even dangerous. On the other hand, behavioral cloning (BC) (Pomerleau, 1989; Bain and Sammut, 1995) does not require interacting with environments.

Gaussian denoising has emerged as a powerful principle for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect of Gaussian denoising have remained largely unexplored. In this work, we aim to address this gap by investigating the well-posedness of simulation-free continuous normalizing flows built on Gaussian denoising. Through a unified framework termed Gaussian interpolation flow, we establish the Lipschitz regularity of the flow velocity field, the existence and uniqueness of the flow, and the Lipschitz continuity of the flow map and the time-reversed flow map for several rich classes of target distributions. This analysis also sheds light on the auto-encoding and cycle-consistency properties of Gaussian interpolation flows. Additionally, we delve into the stability of these flows in source distributions and perturbations of the velocity field, using the quadratic Wasserstein distance as a metric. Our findings offer valuable insights into the learning techniques employed in Gaussian interpolation flows for generative modeling, providing a solid theoretical foundation for end-to-end error analyses of learning GIFs with empirical observations.

With the rise of electronic data, particularly Earth observation data, data-based geospatial modelling using machine learning (ML) has gained popularity in environmental research. Accurate geospatial predictions are vital for domain research based on ecosystem monitoring and quality assessment and for policy-making and action planning, considering effective management of natural resources. The accuracy and computation speed of ML has generally proved efficient. However, many questions have yet to be addressed to obtain precise and reproducible results suitable for further use in both research and practice. A better understanding of the ML concepts applicable to geospatial problems enhances the development of data science tools providing transparent information crucial for making decisions on global challenges such as biosphere degradation and climate change. This survey reviews common nuances in geospatial modelling, such as imbalanced data, spatial autocorrelation, prediction errors, model generalisation, domain specificity, and uncertainty estimation. We provide an overview of techniques and popular programming tools to overcome or account for the challenges. We also discuss prospects for geospatial Artificial Intelligence in environmental applications. To date, obtaining spatial predictions is an essential step in the monitoring, assessment, and prognosis tasks applicable to all kinds of Earth systems on both local and global scales (Figure 1).