Starting with a collection of traces generated by process executions, process discovery is the task of constructing a simple model that describes the process, where simplicity is often measured in terms of model size. The challenge of process discovery is that the process of interest is unknown, and that while the input traces constitute positive examples of process executions, no negative examples are available. Many commercial tools discover Directly-Follows Graphs, in which nodes represent the observable actions of the process, and directed arcs indicate execution order possibilities over the actions. We propose a new approach for discovering sound Directly-Follows Graphs that is grounded in grammatical inference over the input traces. To promote the discovery of small graphs that also describe the process accurately we design and evaluate a genetic algorithm that supports the convergence of the inference parameters to the areas that lead to the discovery of interesting models. Experiments over real-world datasets confirm that our new approach can construct smaller models that represent the input traces and their frequencies more accurately than the state-of-the-art technique. Reasoning over the frequencies of encoded traces also becomes possible, due to the stochastic semantics of the action graphs we propose, which, for the first time, are interpreted as models that describe the stochastic languages of action traces.

Neural Temporal Difference (TD) Learning is an approximate temporal difference method for policy evaluation that uses a neural network for function approximation. Analysis of Neural TD Learning has proven to be challenging. In this paper we provide a convergence analysis of Neural TD Learning with a projection onto $B(\theta_0, \omega)$, a ball of fixed radius $\omega$ around the initial point $\theta_0$. We show an approximation bound of $O(\epsilon) + \tilde{O} (1/\sqrt{m})$ where $\epsilon$ is the approximation quality of the best neural network in $B(\theta_0, \omega)$ and $m$ is the width of all hidden layers in the network.

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.

Cooperation in multi-agent learning (MAL) is a topic at the intersection of numerous disciplines, including game theory, economics, social sciences, and evolutionary biology. Research in this area aims to understand both how agents can coordinate effectively when goals are aligned and how they may cooperate in settings where gains from working together are possible but possibilities for conflict abound. In this paper we provide an overview of the fundamental concepts, problem settings and algorithms of multi-agent learning. This encompasses reinforcement learning, multi-agent sequential decision-making, challenges associated with multi-agent cooperation, and a comprehensive review of recent progress, along with an evaluation of relevant metrics. Finally we discuss open challenges in the field with the aim of inspiring new avenues for research.

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.

Knowledge tracing (KT) aims to monitor students' evolving knowledge states through their learning interactions with concept-related questions, and can be indirectly evaluated by predicting how students will perform on future questions. In this paper, we observe that there is a common phenomenon of answer bias, i.e., a highly unbalanced distribution of correct and incorrect answers for each question. Existing models tend to memorize the answer bias as a shortcut for achieving high prediction performance in KT, thereby failing to fully understand students' knowledge states. To address this issue, we approach the KT task from a causality perspective. A causal graph of KT is first established, from which we identify that the impact of answer bias lies in the direct causal effect of questions on students' responses. A novel COunterfactual REasoning (CORE) framework for KT is further proposed, which separately captures the total causal effect and direct causal effect during training, and mitigates answer bias by subtracting the latter from the former in testing. The CORE framework is applicable to various existing KT models, and we implement it based on the prevailing DKT, DKVMN, and AKT models, respectively. Extensive experiments on three benchmark datasets demonstrate the effectiveness of CORE in making the debiased inference for KT. We have released our code at https://github.com/lucky7-code/CORE.

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)

Dynamic neural networks are a recent technique that promises a remedy for the increasing size of modern deep learning models by dynamically adapting their computational cost to the difficulty of the inputs. In this way, the model can adjust to a limited computational budget. However, the poor quality of uncertainty estimates in deep learning models makes it difficult to distinguish between hard and easy samples. To address this challenge, we present a computationally efficient approach for post-hoc uncertainty quantification in dynamic neural networks. We show that adequately quantifying and accounting for both aleatoric and epistemic uncertainty through a probabilistic treatment of the last layers improves the predictive performance and aids decision-making when determining the computational budget. In the experiments, we show improvements on CIFAR-100, ImageNet, and Caltech-256 in terms of accuracy, capturing uncertainty, and calibration error.