This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions. First, we introduce Pilot MAGI (pMAGI), a novel methodological upgrade on the base MAGI method that confers significantly-improved numerical stability, parameter inference, and trajectory reconstruction. Second, we demonstrate, for the first time to our knowledge, how one can combine MAGI-based methods with dynamical systems theory to provide probabilistic classifications of whether a system is stable or chaotic. Third, we demonstrate how pMAGI performs favorably in many settings against much more computationally-expensive and overparameterized methods. Fourth, we introduce Pilot MAGI Sequential Prediction (PMSP), a novel method building upon pMAGI that allows one to predict the trajectory of ODE-based dynamical systems multiple time steps into the future, given only sparse and noisy observations. We show that PMSP can output accurate future predictions even on chaotic dynamical systems and significantly outperform PINN-based methods. Overall, we contribute to the literature two novel methods, pMAGI and PMSP, that serve as Bayesian, uncertainty-quantified competitors to the Physics-Informed Neural Network.

The advancement of Offline Reinforcement Learning (RL) and Offline Multi-Agent Reinforcement Learning (MARL) critically depends on the availability of high-quality, pre-collected offline datasets that represent real-world complexities and practical applications. However, existing datasets often fall short in their simplicity and lack of realism. To address this gap, we propose Hokoff, a comprehensive set of pre-collected datasets that covers both offline RL and offline MARL, accompanied by a robust framework, to facilitate further research. This data is derived from Honor of Kings, a recognized Multiplayer Online Battle Arena (MOBA) game known for its intricate nature, closely resembling real-life situations. Utilizing this framework, we benchmark a variety of offline RL and offline MARL algorithms. We also introduce a novel baseline algorithm tailored for the inherent hierarchical action space of the game. We reveal the incompetency of current offline RL approaches in handling task complexity, generalization and multi-task learning.

We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and the training data. We consider two categories of generalization guarantees: 1) Guarantees in expectation: These bounds measure performance in the average case. Here, the dependence between the algorithm and the data is often captured by information measures. While these measures offer an intuitive interpretation, they overlook the geometry of the algorithm's hypothesis class. Here, we introduce bounds using the Wasserstein distance to incorporate geometry, and a structured, systematic method to derive bounds capturing the dependence between the algorithm and an individual datum, and between the algorithm and subsets of the training data. 2) PAC-Bayesian guarantees: These bounds measure the performance level with high probability. Here, the dependence between the algorithm and the data is often measured by the relative entropy. We establish connections between the Seeger--Langford and Catoni's bounds, revealing that the former is optimized by the Gibbs posterior. We introduce novel, tighter bounds for various types of loss functions. To achieve this, we introduce a new technique to optimize parameters in probabilistic statements. To study the limitations of these approaches, we present a counter-example where most of the information-theoretic bounds fail while traditional approaches do not. Finally, we explore the relationship between privacy and generalization. We show that algorithms with a bounded maximal leakage generalize. For discrete data, we derive new bounds for differentially private algorithms that guarantee generalization even with a constant privacy parameter, which is in contrast to previous bounds in the literature.

An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work has demonstrated that a class of hybrid state-space model known as recurrent switching linear dynamical systems (rSLDS) discover meaningful behavioural units via the piecewise linear decomposition of complex continuous dynamics (Linderman et al., 2016). Furthermore, they model how the underlying continuous states drive these discrete mode switches. We propose that the rich representations formed by an rSLDS can provide useful abstractions for planning and control. We present a novel hierarchical model-based algorithm inspired by Active Inference in which a discrete MDP sits above a low-level linear-quadratic controller. The recurrent transition dynamics learned by the rSLDS allow us to (1) specify temporally-abstracted sub-goals in a method reminiscent of the options framework, (2) lift the exploration into discrete space allowing us to exploit information-theoretic exploration bonuses and (3) `cache' the approximate solutions to low-level problems in the discrete planner. We successfully apply our model to the sparse Continuous Mountain Car task, demonstrating fast system identification via enhanced exploration and non-trivial planning through the delineation of abstract sub-goals.

There is a wide variety of methods, tools and resources for processing text in the English language. However this is not the case for the Greek language even though it has a long documented history spanning at least 3,400 years of written records (including texts in syllabic script), and 28 centuries (Archaic period - new) of written text with alphabet [1, 2]. The over 2500 years literary tradition of Greek is also notable. To aid those that are interested in using, developing or advancing the techniques for Greek processing, in this paper we survey related works and resources organized in categories. We hope this collection and categorization of works to be useful for students and researchers interested in NLP tasks, Information Retrieval and Knowledge Management for the Greek language.

Reinforcement Learning (RL) has experienced significant advancement over the past decade, prompting a growing interest in applications within finance. This survey critically evaluates 167 publications, exploring diverse RL applications and frameworks in finance. Financial markets, marked by their complexity, multi-agent nature, information asymmetry, and inherent randomness, serve as an intriguing test-bed for RL. Traditional finance offers certain solutions, and RL advances these with a more dynamic approach, incorporating machine learning methods, including transfer learning, meta-learning, and multi-agent solutions. This survey dissects key RL components through the lens of Quantitative Finance. We uncover emerging themes, propose areas for future research, and critique the strengths and weaknesses of existing methods.

Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan (Dated: Augest 20, 2024) Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the quantum wave function amplitude represented by a tensor tree. The key idea is dynamically optimizing the tree structure that minimizes the bond mutual information. The proposed method offers enhanced performance and uncovers hidden relational structures in the target data. We illustrate potential practical applications with four examples: (i) random patterns, (ii) QMNIST hand-written digits, (iii) Bayesian networks, and (iv) the stock price fluctuation pattern in S&P500. In (i) and (ii), strongly correlated variables were concentrated near the center of the network; in (iii), the causality pattern was identified; and, in (iv), a structure corresponding to the eleven sectors emerged. Generative models thrive on the adaptability of architectures the performance of resulting generative models suggest tailored to the data's characteristics. However, is often chosen manually, such as using RNNs for how we can choose the best network structure for a time series and sequential data.

Online rating systems are often used in numerous web or mobile applications, e.g., Amazon and TripAdvisor, to assess the ground-truth quality of products. Due to herding effects, the aggregation of historical ratings (or historical collective opinion) can significantly influence subsequent ratings, leading to misleading and erroneous assessments. We study how to manage product ratings via rating aggregation rules and shortlisted representative reviews, for the purpose of correcting the assessment error. We first develop a mathematical model to characterize important factors of herding effects in product ratings. We then identify sufficient conditions (via the stochastic approximation theory), under which the historical collective opinion converges to the ground-truth collective opinion of the whole user population. These conditions identify a class of rating aggregation rules and review selection mechanisms that can reveal the ground-truth product quality. We also quantify the speed of convergence (via the martingale theory), which reflects the efficiency of rating aggregation rules and review selection mechanisms. We prove that the herding effects slow down the speed of convergence while an accurate review selection mechanism can speed it up. We also study the speed of convergence numerically and reveal trade-offs in selecting rating aggregation rules and review selection mechanisms. To show the utility of our framework, we design a maximum likelihood algorithm to infer model parameters from ratings, and conduct experiments on rating datasets from Amazon and TripAdvisor. We show that proper recency aware rating aggregation rules can improve the speed of convergence in Amazon and TripAdvisor by 41% and 62% respectively.

An obstetric goal for a laboring mother is to achieve a vaginal delivery as it reduces the risks inherent in major abdominal surgery (i.e., a Cesarean section). Various medical interventions may be used by a physician to increase the likelihood of this occurring while minimizing maternal and fetal morbidity. However, patients with prelabor rupture of membranes (PROM) have only two commonly used options for cervical ripening, Pitocin and misoprostol. Little research exists on the benefits/risks for these two key drugs for PROM patients. A major limitation with most induction-of-labor related research is the inability to account for differences in \textit{Bishop scores} that are commonly used in obstetrical practice to determine the next induction agent offered to the patient. This creates a confounding factor, which biases the results, but has not been realized in the literature. In this work, we use a Bayesian model of the relationships between the relevant factors, informed by expert physicians, to separate the confounding variable from its actual impact. In doing so, we provide strong evidence that pitocin and buccal misoprostol are equally effective and safe; thus, physicians have more choice in clinical care than previously realized. This is particularly important for developing countries where neither medication may be readily available, and prior guidelines may create an artificial barrier to needed medication.

As Artificial Intelligence (AI) changes how businesses work, there is a growing need for people who can work in this sector. This paper investigates how well universities in United Kingdom offering courses in AI, prepare students for jobs in the real world. To gain insight into the differences between university curricula and industry demands we review the contents of taught courses and job advertisement portals. By using custom data scraping tools to gather information from job advertisements and university curricula, and frequency and Naive Bayes classifier analysis, this study will show exactly what skills industry is looking for. In this study we identified 12 skill categories that were used for mapping. The study showed that the university curriculum in the AI domain is well balanced in most technical skills, including Programming and Machine learning subjects, but have a gap in Data Science and Maths and Statistics skill categories.