Autonomous driving feedback control loops [2], [3], [4], [5], [6], [7], [8], [9],;10], [11] and decision-making systems [12], [13], [14], [15] depend on the effectiveness of information collection and learning the knowledge of vehicle motions, including the ego-vehicle and other nearby vehicles. Knowing the information, the autonomous vehicles can estimate the behaviors and future positions of others so as to determine the way of behaving in current traffic scenario. Therefore, the knowledge of vehicles at current moment on motions and states are particularly essential for autonomous driving. As for autonomous vehicles driving on the road, the sensor suite deployed on them commonly includes GPS, IMU, Lidars, Cameras and Radars. With the information collected from GPS and IMU, the ego vehicle can measure its states, including the global position, the heading angle that shows the orientation, the linear velocity and angular velocity as well as acceleration.

However, While VAEs are nowadays omnipresent in the field of machine in practice, they suffer from a problem called learning, it is also widely recognized that there remain posterior collapse, which occurs when the encoder in practice some major challenges that still require effective coincides, or collapses, with the prior taking no solutions. Notably, they suffer from the problem of information from the latent structure of the input posterior collapse, which occurs when the distribution corresponding data into consideration. In this work, we introduce to the encoder coincides, or collapses, with the an inverse Lipschitz neural network into the prior taking no information from the latent structure of the decoder and, based on this architecture, provide a input data into consideration. Also known as KL vanishing new method that can control in a simple and clear or over-pruning, this phenomenon makes VAEs incapable manner the degree of posterior collapse for a wide to produce pertinent representations and has been reportedly range of VAE models equipped with a concrete observed in many fields (e.g., Bowman et al. (2016); Fu et al. theoretical guarantee. We also illustrate the effectiveness (2019); Wang & Ziyin (2022); Yeung et al. (2017)). There of our method through several numerical exists now a large body of literature that examines its underlying experiments.

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient feature map and careful regularization of the Gram matrix, we demonstrate that the variance information of the resulting quantum Gaussian process can be preserved. We also show that quantum Gaussian processes can be used as a surrogate model for Bayesian optimization, a task that critically relies on the variance of the surrogate model. To demonstrate the performance of this quantum Bayesian optimization algorithm, we apply it to the hyperparameter optimization of a machine learning model which performs regression on a real-world dataset. We benchmark the quantum Bayesian optimization against its classical counterpart and show that quantum version can match its performance.

Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However, it remains an open problem to establish the circumstances in which maximum likelihood estimation is well-posed, that is, when the predictions of the regression model are insensitive to small perturbations of the data. This article identifies scenarios where the maximum likelihood estimator fails to be well-posed, in that the predictive distributions are not Lipschitz in the data with respect to the Hellinger distance. These failure cases occur in the noiseless data setting, for any Gaussian process with a stationary covariance function whose lengthscale parameter is estimated using maximum likelihood. Although the failure of maximum likelihood estimation is part of Gaussian process folklore, these rigorous theoretical results appear to be the first of their kind. The implication of these negative results is that well-posedness may need to be assessed post-hoc, on a case-by-case basis, when maximum likelihood estimation is used to train a Gaussian process model.

Nonlinear systems, such as with degrading hysteretic behavior, are often encountered in engineering applications. In addition, due to the ubiquitous presence of uncertainty and the modeling of such systems becomes increasingly difficult. On the other hand, datasets from pristine models developed without knowing the nature of the degrading effects can be easily obtained. In this paper, we use datasets from pristine models without considering the degrading effects of hysteretic systems as low-fidelity representations that capture many of the important characteristics of the true system's behavior to train a deep operator network (DeepONet). Three numerical examples are used to show that the proposed use of the DeepONets to model the discrepancies between the low-fidelity model and the true system's response leads to significant improvements in the prediction error in the presence of uncertainty in the model parameters for degrading hysteretic systems.

Federated learning (FL) demonstrates its advantages in integrating distributed infrastructure, communication, computing and learning in a privacy-preserving manner. However, the robustness and capabilities of existing FL methods are challenged by limited and dynamic data and conditions, complexities including heterogeneities and uncertainties, and analytical explainability. Bayesian federated learning (BFL) has emerged as a promising approach to address these issues. This survey presents a critical overview of BFL, including its basic concepts, its relations to Bayesian learning in the context of FL, and a taxonomy of BFL from both Bayesian and federated perspectives. We categorize and discuss client- and server-side and FL-based BFL methods and their pros and cons. The limitations of the existing BFL methods and the future directions of BFL research further address the intricate requirements of real-life FL applications.

Time series clustering is a central machine learning task with applications in many fields. While the majority of the methods focus on real-valued time series, very few works consider series with discrete response. In this paper, the problem of clustering ordinal time series is addressed. To this aim, two novel distances between ordinal time series are introduced and used to construct fuzzy clustering procedures. Both metrics are functions of the estimated cumulative probabilities, thus automatically taking advantage of the ordering inherent to the series' range. The resulting clustering algorithms are computationally efficient and able to group series generated from similar stochastic processes, reaching accurate results even though the series come from a wide variety of models. Since the dynamic of the series may vary over the time, we adopt a fuzzy approach, thus enabling the procedures to locate each series into several clusters with different membership degrees. An extensive simulation study shows that the proposed methods outperform several alternative procedures. Weighted versions of the clustering algorithms are also presented and their advantages with respect to the original methods are discussed. Two specific applications involving economic time series illustrate the usefulness of the proposed approaches.

A digital twin (DT) leverages a virtual representation of the physical world, along with communication (e.g., 6G), computing (e.g., edge computing), and artificial intelligence (AI) technologies to enable many connected intelligence services. In order to handle the large amounts of network data based on digital twins (DTs), wireless systems can exploit the paradigm of semantic communication (SC) for facilitating informed decision-making under strict communication constraints by utilizing AI techniques such as causal reasoning. In this paper, a novel framework called causal semantic communication (CSC) is proposed for DT-based wireless systems. The CSC system is posed as an imitation learning (IL) problem, where the transmitter, with access to optimal network control policies using a DT, teaches the receiver using SC over a bandwidth limited wireless channel how to improve its knowledge to perform optimal control actions. The causal structure in the source data is extracted using novel approaches from the framework of deep end-to-end causal inference, thereby enabling the creation of a semantic representation that is causally invariant, which in turn helps generalize the learned knowledge of the system to unseen scenarios. The CSC decoder at the receiver is designed to extract and estimate semantic information while ensuring high semantic reliability. The receiver control policies, semantic decoder, and causal inference are formulated as a bi-level optimization problem within a variational inference framework. This problem is solved using a novel concept called network state models, inspired from world models in generative AI, that faithfully represents the environment dynamics leading to data generation. Simulation results demonstrate that the proposed CSC system outperforms state-of-the-art SC systems by achieving better semantic reliability and reduced semantic representation.

A central task in control theory, artificial intelligence, and formal methods is to synthesize reward-maximizing strategies for agents that operate in partially unknown environments. In environments modeled by gray-box Markov decision processes (MDPs), the impact of the agents' actions are known in terms of successor states but not the stochastics involved. In this paper, we devise a strategy synthesis algorithm for gray-box MDPs via reinforcement learning that utilizes interval MDPs as internal model. To compete with limited sampling access in reinforcement learning, we incorporate two novel concepts into our algorithm, focusing on rapid and successful learning rather than on stochastic guarantees and optimality: lower confidence bound exploration reinforces variants of already learned practical strategies and action scoping reduces the learning action space to promising actions. We illustrate benefits of our algorithms by means of a prototypical implementation applied on examples from the AI and formal methods communities.

While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest in recent years. We contribute PAC-Bayes generalisation bounds for heavy-tailed losses under the sole assumption of bounded variance of the loss function. Under that assumption, we extend previous results from \citet{kuzborskij2019efron}. Our key technical contribution is exploiting an extention of Markov's inequality for supermartingales. Our proof technique unifies and extends different PAC-Bayesian frameworks by providing bounds for unbounded martingales as well as bounds for batch and online learning with heavy-tailed losses.