Heterogeneous graph neural networks have become popular in various domains. However, their generalizability and interpretability are limited due to the discrepancy between their inherent inference flows and human reasoning logic or underlying causal relationships for the learning problem. This study introduces a novel solution, HG-SCM (Heterogeneous Graph as Structural Causal Model). It can mimic the human perception and decision process through two key steps: constructing intelligible variables based on semantics derived from the graph schema and automatically learning task-level causal relationships among these variables by incorporating advanced causal discovery techniques. We compared HG-SCM to seven state-of-the-art baseline models on three real-world datasets, under three distinct and ubiquitous out-of-distribution settings. HG-SCM achieved the highest average performance rank with minimal standard deviation, substantiating its effectiveness and superiority in terms of both predictive power and generalizability. Additionally, the visualization and analysis of the auto-learned causal diagrams for the three tasks aligned well with domain knowledge and human cognition, demonstrating prominent interpretability. HG-SCM's human-like nature and its enhanced generalizability and interpretability make it a promising solution for special scenarios where transparency and trustworthiness are paramount.

The probability of an event is in the range of [0, 1]. In a sample space S, the value of probability determines whether an outcome is true or false. The probability of an event Pr(A) that will never occur = 0. The probability of the event Pr(B) that will certainly occur = 1. This makes both events A and B thus a certainty. Furthermore, the sum of probabilities Pr(E1) + Pr(E2) + ... + Pr(En) of a finite set of events in a given sample space S = 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. Firstly, this paper discusses Bayes' theorem, then complement of probability and the difference of probability for occurrences of learning-events, before applying these in the prediction of learning objects in student learning. Given the sum total of 1; to make recommendation for student learning, this paper submits that the difference of argMaxPr(S) and probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates: i) the probability of skill-set events that has occurred that would lead to higher level learning; ii) the probability of the events that has not occurred that requires subject-matter relearning; iii) accuracy of decision tree in the prediction of student performance into class labels; and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning [1].

The theory of Bayesian learning incorporates the use of Student-t Processes to model heavy-tailed distributions and datasets with outliers. However, despite Student-t Processes having a similar computational complexity as Gaussian Processes, there has been limited emphasis on the sparse representation of this model. This is mainly due to the increased difficulty in modeling and computation compared to previous sparse Gaussian Processes. Our motivation is to address the need for a sparse representation framework that reduces computational complexity, allowing Student-t Processes to be more flexible for real-world datasets. To achieve this, we leverage the conditional distribution of Student-t Processes to introduce sparse inducing points. Bayesian methods and variational inference are then utilized to derive a well-defined lower bound, facilitating more efficient optimization of our model through stochastic gradient descent. We propose two methods for computing the variational lower bound, one utilizing Monte Carlo sampling and the other employing Jensen's inequality to compute the KL regularization term in the loss function. We propose adopting these approaches as viable alternatives to Gaussian processes when the data might contain outliers or exhibit heavy-tailed behavior, and we provide specific recommendations for their applicability. We evaluate the two proposed approaches on various synthetic and real-world datasets from UCI and Kaggle, demonstrating their effectiveness compared to baseline methods in terms of computational complexity and accuracy, as well as their robustness to outliers.

Leveraging neural networks as surrogate models for turbulence simulation is a topic of growing interest. At the same time, embodying the inherent uncertainty of simulations in the predictions of surrogate models remains very challenging. The present study makes a first attempt to use denoising diffusion probabilistic models (DDPMs) to train an uncertainty-aware surrogate model for turbulence simulations. Due to its prevalence, the simulation of flows around airfoils with various shapes, Reynolds numbers, and angles of attack is chosen as the learning objective. Our results show that DDPMs can successfully capture the whole distribution of solutions and, as a consequence, accurately estimate the uncertainty of the simulations. The performance of DDPMs is also compared with varying baselines in the form of Bayesian neural networks and heteroscedastic models. Experiments demonstrate that DDPMs outperform the other methods regarding a variety of accuracy metrics. Besides, it offers the advantage of providing access to the complete distributions of uncertainties rather than providing a set of parameters. As such, it can yield realistic and detailed samples from the distribution of solutions. All source codes and datasets utilized in this study are publicly available.

In the driving scene, the road agents usually conduct frequent interactions and intention understanding of the surroundings. Ego-agent (each road agent itself) predicts what behavior will be engaged by other road users all the time and expects a shared and consistent understanding for safe movement. Behavioral Intention Prediction (BIP) simulates such a human consideration process and fulfills the early prediction of specific behaviors. Similar to other prediction tasks, such as trajectory prediction, data-driven deep learning methods have taken the primary pipeline in research. The rapid development of BIP inevitably leads to new issues and challenges. To catalyze future research, this work provides a comprehensive review of BIP from the available datasets, key factors and challenges, pedestrian-centric and vehicle-centric BIP approaches, and BIP-aware applications. Based on the investigation, data-driven deep learning approaches have become the primary pipelines. The behavioral intention types are still monotonous in most current datasets and methods (e.g., Crossing (C) and Not Crossing (NC) for pedestrians and Lane Changing (LC) for vehicles) in this field. In addition, for the safe-critical scenarios (e.g., near-crashing situations), current research is limited. Through this investigation, we identify open issues in behavioral intention prediction and suggest possible insights for future research.

In his "ship of state" allegory (\textit{Republic}, Book VI, 488) Plato poses a question -- how can a crew of sailors presumed to know little about the art of navigation recognize the true pilot among them? The allegory argues that a simple majority voting procedure cannot safely determine who is most qualified to pilot a ship when the voting members are ignorant or biased. We formalize Plato's concerns by considering the problem in AI safety of monitoring noisy AI agents in unsupervised settings. An algorithm evaluating AI agents using unlabeled data would be subject to the evaluation dilemma - how would we know the evaluation algorithm was correct itself? This endless validation chain can be avoided by considering purely algebraic functions of the observed responses. We can construct complete postulates than can prove or disprove the logical consistency of any grading algorithm. A complete set of postulates exists whenever we are evaluating $N$ experts that took $T$ tests with $Q$ questions with $R$ responses each. We discuss evaluating binary classifiers that have taken a single test - the $(N,T=1,Q,R=2)$ tests. We show how some of the postulates have been previously identified in the ML literature but not recognized as such - the \textbf{agreement equations} of Platanios. The complete postulates for pair correlated binary classifiers are considered and we show how it allows for error correlations to be quickly calculated. An algebraic evaluator based on the assumption that the ensemble is error independent is compared with grading by majority voting on evaluations using the \uciadult and and \texttt{two-norm} datasets. Throughout, we demonstrate how the formalism of logical consistency via algebraic postulates of evaluation can help increase the safety of machines using AI algorithms.

Ford Motor China Co.,ltd, Shanghai, 200082, China Abstract The comprehensiveness of vehicle-to-everything (V2X) recognition enriches and holistically shapes the global Birds-Eye-View (BEV) perception, incorporating rich semantics and integrating driving scene information, thereby serving features of trajectory prediction, decision-making and driving planning. Utilizing V2X message sets to form BEV format proves to be an effective perception method for connected and automated vehicles (CAVs). Specifically, MAP, SPAT and RSI data contributes to the achievement of road connectivity, synchronized traffic signal navigation and obstacle warning. Moreover, using time-sequential BSMs information from multiple vehicles allows for the perception of current state and the prediction of future trajectories. Therefore, this paper develops a comprehensive autonomous driving model that relies on BEV-V2X perception, Interacting Multiple model Unscented Kalman Filter (IMM-UKF)-based trajectory prediction, and deep reinforcement learning (DRL)-based decision making and planing. We establish a DRL environment with reward-shaping methods to formulate a unified set of optimal driving behaviors that encompass obstacle avoidance, lane changes, overtaking, turning maneuver, and synchronized traffic signal navigation. Consequently, a complex traffic intersection scenario was simulated, and the well-trained model was applied for driving control. The observed driving behavior closely resembled that of an experienced driver, exhibiting anticipatory actions and revealing notable operational highlights of driving policy. Ford Motor China Co.,ltd, Shanghai, 200082, China I. INTRODUCTION Cooperative Intelligent Transport Systems (C-ITS) based on vehicle-to-everything (V2X) communication has considerably developed in recent years, bringing us closer to utilizing V2X for autonomous driving and assistance guidance [1-2]. Due to the numerous substantial benefits provided by C-ITS, governmental authorities worldwide have initiated the allocation of dedicated spectrum for V2X technologies, on a license-exempt basis in the 5.9 GHz band for the cellular based Cellular-V2X (C-V2X) PC5 technology [3-4]. The characteristics of 5G technologies including enhanced Mobile Broadband (eMBB) and massive Machine Type Communications (mMTC) are pivotal in vehicular communications [5-6]. Furthermore, facilitating Ultra-Reliable and Low-Latency Communications (URLLC) of 5G is a fundamental element of advanced V2X applications [7-8].

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms' ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data.

Bayesian causal discovery aims to infer the posterior distribution over causal models from observed data, quantifying epistemic uncertainty and benefiting downstream tasks. However, computational challenges arise due to joint inference over combinatorial space of Directed Acyclic Graphs (DAGs) and nonlinear functions. Despite recent progress towards efficient posterior inference over DAGs, existing methods are either limited to variational inference on node permutation matrices for linear causal models, leading to compromised inference accuracy, or continuous relaxation of adjacency matrices constrained by a DAG regularizer, which cannot ensure resulting graphs are DAGs. In this work, we introduce a scalable Bayesian causal discovery framework based on a combination of stochastic gradient Markov Chain Monte Carlo (SG-MCMC) and Variational Inference (VI) that overcomes these limitations. Our approach directly samples DAGs from the posterior without requiring any DAG regularization, simultaneously draws function parameter samples and is applicable to both linear and nonlinear causal models. To enable our approach, we derive a novel equivalence to the permutation-based DAG learning, which opens up possibilities of using any relaxed gradient estimator defined over permutations. To our knowledge, this is the first framework applying gradient-based MCMC sampling for causal discovery. Empirical evaluation on synthetic and real-world datasets demonstrate our approach's effectiveness compared to state-of-the-art baselines.

Generating samples from a complex (e.g., non-Gaussian, high-dimensional) probability distribution is a core computational challenge in diverse applications, ranging from computational statistics and machine learning to molecular simulation. A recurring setting is where the density ρ of the target distribution is specified up to a normalizing constant--for example, in Bayesian modeling, where ρ represents the posterior density. Here, evaluations of the score log ρ are often available as well, even for complex statistical models [Villa et al., 2021]. Alternatively, many new methods enable effective score estimation from data, without explicit density estimation; examples include score estimation from time series observations in chaotic dynamical systems [Chandramoorthy and Wang, 2022, Ni, 2020] and score-based modeling of image distributions [Song et al., 2020b,a]. In these settings, transport or "flow"-driven algorithms for generating samples have seen extensive success. The central idea is to construct a transport map from a simple, prescribed source distribution to the target distribution of interest. One class of transport approaches, e.g., as represented by variational inference with normalizing flows, involves constructing a parametric class of invertible maps and minimizing some statistical divergence between the pushforward (see Section 2) of the source by a member of this class and the target. A different, essentially nonparametric, class of transport approaches are based on particle systems, e.g., Stein variational gradient descent (SVGD)