Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for that can be found in Uncertainty Quantification (UQ) which is just beginning to emerge in the context of PINNs. Assessing how well the trained PINN complies with imposed differential equation is the key to tackling uncertainty, yet there is lack of comprehensive methodology for this task. We propose a framework for UQ in Bayesian PINNs (B-PINNs) that incorporates the discrepancy between the B-PINN solution and the unknown true solution. We exploit recent results on error bounds for PINNs on linear dynamical systems and demonstrate the predictive uncertainty on a class of linear ODEs.

Optimization of directed acyclic graph (DAG) structures has many applications, such as neural architecture search (NAS) and probabilistic graphical model learning. Encoding DAGs into real vectors is a dominant component in most neural-network-based DAG optimization frameworks. Currently, most DAG encoders use an asynchronous message passing scheme which sequentially processes nodes according to the dependency between nodes in a DAG. That is, a node must not be processed until all its predecessors are processed. As a result, they are inherently not parallelizable. In this work, we propose a Parallelizable Attention-based Computation structure Encoder (PACE) that processes nodes simultaneously and encodes DAGs in parallel. We demonstrate the superiority of PACE through encoder-dependent optimization subroutines that search the optimal DAG structure based on the learned DAG embeddings. Experiments show that PACE not only improves the effectiveness over previous sequential DAG encoders with a significantly boosted training and inference speed, but also generates smooth latent (DAG encoding) spaces that are beneficial to downstream optimization subroutines. Our source code is available at \url{https://github.com/zehao-dong/PACE}

The existing methods for trajectory prediction are difficult to describe trajectory of moving objects in complex and uncertain environment accurately. In order to solve this problem, this paper proposes an adaptive trajectory prediction method for moving objects based on variation Gaussian mixture model (VGMM) in dynamic environment (ESATP). Firstly, based on the traditional mixture Gaussian model, we use the approximate variational Bayesian inference method to process the mixture Gaussian distribution in model training procedure. Secondly, variational Bayesian expectation maximization iterative is used to learn the model parameters and prior information is used to get a more precise prediction model. Finally, for the input trajectories, parameter adaptive selection algorithm is used automatically to adjust the combination of parameters. Experiment results perform that the ESATP method in the experiment showed high predictive accuracy, and maintain a high time efficiency. This model can be used in products of mobile vehicle positioning.

Efficient localization plays a vital role in many modern applications of Unmanned Ground Vehicles (UGV) and Unmanned aerial vehicles (UAVs), which would contribute to improved control, safety, power economy, etc. The ubiquitous 5G NR (New Radio) cellular network will provide new opportunities for enhancing localization of UAVs and UGVs. In this paper, we review the radio frequency (RF) based approaches for localization. We review the RF features that can be utilized for localization and investigate the current methods suitable for Unmanned vehicles under two general categories: range-based and fingerprinting. The existing state-of-the-art literature on RF-based localization for both UAVs and UGVs is examined, and the envisioned 5G NR for localization enhancement, and the future research direction are explored.

This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a unified model of syntactic structures in formal grammars. Second, functors compute semantics by turning diagrams into logical, tensor, neural or quantum computation. Third, the resulting functorial models can be composed to form games where equilibria are the solutions of language processing tasks. This framework is implemented as part of DisCoPy, the Python library for computing with string diagrams. We describe the correspondence between categorical, linguistic and computational structures, and demonstrate their applications in compositional natural language processing.

Naive Bayes is a machine learning algorithm that is used for classification tasks. It is based on the idea of applying Bayes' theorem, which describes the probability of an event based on prior knowledge of conditions that might be related to the event. The algorithm makes the assumption that all of the features in the dataset are independent of each other, which is why it is called "naive." This means that the presence or absence of one feature does not affect the probability of the other features. To classify a new data point, the algorithm first calculates the probability of the new data point belonging to each class. It then chooses the class with the highest probability as the predicted class for the new data point. To calculate the probability of a new data point belonging to a given class, the algorithm uses Bayes' theorem, which states that the probability of A given B is equal to the probability of B given A times the probability of A, divided by the probability of B. For example, suppose we have a dataset with two classes: "spam" and "not spam." We can use Bayes' theorem to calculate the probability that a new email belongs to the "spam" class, given that it contains the word "Viagra." We first need to calculate the probability of the word "Viagra" appearing in a "spam" email, and the probability of the word "Viagra" appearing in a "not spam" email. We then multiply these probabilities by the overall probability of the email belonging to the "spam" class, and divide by the probability of the word "Viagra" appearing in any email. Once we have calculated the probabilities for each class, we choose the class with the highest probability as the predicted class for the new data point. Naive Bayes is a simple and effective algorithm for classification tasks, and it can be used with a variety of different types of data.

Despite the empirical successes of self-supervised learning (SSL) methods, it is unclear what characteristics of their representations lead to high downstream accuracies. In this work, we characterize properties that SSL representations should ideally satisfy. Specifically, we prove necessary and sufficient conditions such that for any task invariant to given data augmentations, desired probes (e.g., linear or MLP) trained on that representation attain perfect accuracy. These requirements lead to a unifying conceptual framework for improving existing SSL methods and deriving new ones. For contrastive learning, our framework prescribes simple but significant improvements to previous methods such as using asymmetric projection heads. For non-contrastive learning, we use our framework to derive a simple and novel objective. Our resulting SSL algorithms outperform baselines on standard benchmarks, including SwAV+multicrops on linear probing of ImageNet.

The most widely studied explainable AI (XAI) approaches are unsound. This is the case with well-known model-agnostic explanation approaches, and it is also the case with approaches based on saliency maps. One solution is to consider intrinsic interpretability, which does not exhibit the drawback of unsoundness. Unfortunately, intrinsic interpretability can display unwieldy explanation redundancy. Formal explainability represents the alternative to these non-rigorous approaches, with one example being PI-explanations. Unfortunately, PI-explanations also exhibit important drawbacks, the most visible of which is arguably their size. Recently, it has been observed that the (absolute) rigor of PI-explanations can be traded off for a smaller explanation size, by computing the so-called relevant sets. Given some positive {\delta}, a set S of features is {\delta}-relevant if, when the features in S are fixed, the probability of getting the target class exceeds {\delta}. However, even for very simple classifiers, the complexity of computing relevant sets of features is prohibitive, with the decision problem being NPPP-complete for circuit-based classifiers. In contrast with earlier negative results, this paper investigates practical approaches for computing relevant sets for a number of widely used classifiers that include Decision Trees (DTs), Naive Bayes Classifiers (NBCs), and several families of classifiers obtained from propositional languages. Moreover, the paper shows that, in practice, and for these families of classifiers, relevant sets are easy to compute. Furthermore, the experiments confirm that succinct sets of relevant features can be obtained for the families of classifiers considered.

The cyber-physical convergence is opening up new business opportunities for industrial operators. The need for deep integration of the cyber and the physical worlds establishes a rich business agenda towards consolidating new system and network engineering approaches. This revolution would not be possible without the rich and heterogeneous sources of data, as well as the ability of their intelligent exploitation, mainly due to the fact that data will serve as a fundamental resource to promote Industry 4.0. One of the most fruitful research and practice areas emerging from this data-rich, cyber-physical, smart factory environment is the data-driven process monitoring field, which applies machine learning methodologies to enable predictive maintenance applications. In this paper, we examine popular time series forecasting techniques as well as supervised machine learning algorithms in the applied context of Industry 4.0, by transforming and preprocessing the historical industrial dataset of a packing machine's operational state recordings (real data coming from the production line of a manufacturing plant from the food and beverage domain). In our methodology, we use only a single signal concerning the machine's operational status to make our predictions, without considering other operational variables or fault and warning signals, hence its characterization as ``agnostic''. In this respect, the results demonstrate that the adopted methods achieve a quite promising performance on three targeted use cases.