It is widely recognised that communication is key to successful interaction. Humans communicate with each other through both explicit (direct, deliberate communication over an established channel with clear intent to reach a defined recipient [1]) and implicit channels. Implicit communication is a subtle, indirect mode of conveying information, often relying on context, nonverbal cues, and shared understanding between communicators to convey meaning without explicit verbalization [2]. Implicit communication is particularly crucial for human-robot interaction as it enhances a robot's ability to proactively understand and respond to human needs, emotions, and intentions, thereby facilitating more natural and effective communication and collaboration between humans and robots. Unfortunately, most current human-robot interaction (HRI) studies focusing on implicit communication explicitly model the intention of human participants [3] [4], or rely on existing intention knowledge [5].

In recent years, predictive maintenance (PMx) has gained prominence for its potential to enhance efficiency, automation, accuracy, and cost-effectiveness while reducing human involvement. Importantly, PMx has evolved in tandem with digital advancements, such as Big Data and the Internet of Things (IOT). These technological strides have enabled Artificial Intelligence (AI) to revolutionize PMx processes, with increasing capacities for real-time automation of monitoring, analysis, and prediction tasks. However, PMx still faces challenges such as poor explainability and sample inefficiency in data-driven methods and high complexity in physics-based models, hindering broader adoption. This paper posits that Digital Twins (DTs) can be integrated into PMx to overcome these challenges, paving the way for more automated PMx applications across various stakeholders. Despite their potential, current DTs have not fully matured to bridge existing gaps. Our paper provides a comprehensive roadmap for DT evolution, addressing current limitations to foster large-scale automated PMx progression. We structure our approach in three stages: First, we reference prior work where we identified and defined the Information Requirements (IRs) and Functional Requirements (FRs) for PMx, forming the blueprint for a unified framework. Second, we conduct a literature review to assess current DT applications integrating these IRs and FRs, revealing standardized DT models and tools that support automated PMx. Lastly, we highlight gaps in current DT implementations, particularly those IRs and FRs not fully supported, and outline the necessary components for a comprehensive, automated PMx system. Our paper concludes with research directions aimed at seamlessly integrating DTs into the PMx paradigm to achieve this ambitious vision.

Due to their flexibility and theoretical tractability Gaussian process (GP) regression models have become a central topic in modern statistics and machine learning. While the true posterior in these models is given explicitly, numerical evaluations depend on the inversion of the augmented kernel matrix $ K + \sigma^2 I $, which requires up to $ O(n^3) $ operations. For large sample sizes n, which are typically given in modern applications, this is computationally infeasible and necessitates the use of an approximate version of the posterior. Although such methods are widely used in practice, they typically have very limtied theoretical underpinning. In this context, we analyze a class of recently proposed approximation algorithms from the field of Probabilistic numerics. They can be interpreted in terms of Lanczos approximate eigenvectors of the kernel matrix or a conjugate gradient approximation of the posterior mean, which are particularly advantageous in truly large scale applications, as they are fundamentally only based on matrix vector multiplications amenable to the GPU acceleration of modern software frameworks. We combine result from the numerical analysis literature with state of the art concentration results for spectra of kernel matrices to obtain minimax contraction rates. Our theoretical findings are illustrated by numerical experiments.

The evaluation of synthetic data generation is crucial, especially in the retail sector where data accuracy is paramount. This paper introduces a comprehensive framework for assessing synthetic retail data, focusing on fidelity, utility, and privacy. Our approach differentiates between continuous and discrete data attributes, providing precise evaluation criteria. Fidelity is measured through stability and generalizability. Stability ensures synthetic data accurately replicates known data distributions, while generalizability confirms its robustness in novel scenarios. Utility is demonstrated through the synthetic data's effectiveness in critical retail tasks such as demand forecasting and dynamic pricing, proving its value in predictive analytics and strategic planning. Privacy is safeguarded using Differential Privacy, ensuring synthetic data maintains a perfect balance between resembling training and holdout datasets without compromising security. Our findings validate that this framework provides reliable and scalable evaluation for synthetic retail data. It ensures high fidelity, utility, and privacy, making it an essential tool for advancing retail data science. This framework meets the evolving needs of the retail industry with precision and confidence, paving the way for future advancements in synthetic data methodologies.

Machine learning (ML) and Artificial Intelligence (AI) have fueled remarkable advancements, particularly in healthcare. Within medical imaging, ML models hold the promise of improving disease diagnoses, treatment planning, and post-treatment monitoring. Various computer vision tasks like image classification, object detection, and image segmentation are poised to become routine in clinical analysis. However, privacy concerns surrounding patient data hinder the assembly of large training datasets needed for developing and training accurate, robust, and generalizable models. Federated Learning (FL) emerges as a compelling solution, enabling organizations to collaborate on ML model training by sharing model training information (gradients) rather than data (e.g., medical images). FL's distributed learning framework facilitates inter-institutional collaboration while preserving patient privacy. However, FL, while robust in privacy preservation, faces several challenges. Sensitive information can still be gleaned from shared gradients that are passed on between organizations during model training. Additionally, in medical imaging, quantifying model confidence\uncertainty accurately is crucial due to the noise and artifacts present in the data. Uncertainty estimation in FL encounters unique hurdles due to data heterogeneity across organizations. This paper offers a comprehensive review of FL, privacy preservation, and uncertainty estimation, with a focus on medical imaging. Alongside a survey of current research, we identify gaps in the field and suggest future directions for FL research to enhance privacy and address noisy medical imaging data challenges.

We investigate the problem of center estimation in the high dimensional binary sub-Gaussian Mixture Model with Hidden Markov structure on the labels. We first study the limitations of existing results in the high dimensional setting and then propose a minimax optimal procedure for the problem of center estimation. Among other findings, we show that our procedure reaches the optimal rate that is of order $\sqrt{\delta d/n} + d/n$ instead of $\sqrt{d/n} + d/n$ where $\delta \in(0,1)$ is a dependence parameter between labels. Along the way, we also develop an adaptive variant of our procedure that is globally minimax optimal. In order to do so, we rely on a more refined and localized analysis of the estimation risk. Overall, leveraging the hidden Markovian dependence between the labels, we show that it is possible to get a strict improvement of the rates adaptively at almost no cost.

Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine learning with time constraints or accuracy requirements and real-time systems. The structural constraints of SPNs supporting fast inference, however, lead to increased learning-time complexity and can be an obstacle to building highly expressive SPNs. This study aimed to develop a Bayesian learning approach that can be efficiently implemented on large-scale SPNs. We derived a new full conditional probability of Gibbs sampling by marginalizing multiple random variables to expeditiously obtain the posterior distribution. The complexity analysis revealed that our sampling algorithm works efficiently even for the largest possible SPN. Furthermore, we proposed a hyperparameter tuning method that balances the diversity of the prior distribution and optimization efficiency in large-scale SPNs. Our method has improved learning-time complexity and demonstrated computational speed tens to more than one hundred times faster and superior predictive performance in numerical experiments on more than 20 datasets.

We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field approximation to the nuisance coordinates and carefully modelling the conditional distribution of the target given the nuisance. This requires only a preprocessing step and preserves the computational advantages of mean-field variational Bayes, while ensuring accurate and reliable inference for the target parameter, including for uncertainty quantification. We investigate the numerical performance of our algorithm, showing that it performs competitively with existing methods. We further establish accompanying theoretical guarantees for estimation and uncertainty quantification in the form of a Bernstein--von Mises theorem.

Large Language Models (LLMs) often suffer from overconfidence during inference, particularly when adapted to downstream domain-specific tasks with limited data. Previous work addresses this issue by employing approximate Bayesian estimation after the LLMs are trained, enabling them to quantify uncertainty. However, such post-training approaches' performance is severely limited by the parameters learned during training. In this paper, we go beyond post-training Bayesianization and propose Bayesian Low-Rank Adaptation by Backpropagation (BLoB), an algorithm that continuously and jointly adjusts both the mean and covariance of LLM parameters throughout the whole fine-tuning process. Our empirical results verify the effectiveness of BLoB in terms of generalization and uncertainty estimation, when evaluated on both in-distribution and out-of-distribution data.

Thompson sampling (TS) is one of the most popular exploration techniques in reinforcement learning (RL). However, most TS algorithms with theoretical guarantees are difficult to implement and not generalizable to Deep RL. While the emerging approximate sampling-based exploration schemes are promising, most existing algorithms are specific to linear Markov Decision Processes (MDP) with suboptimal regret bounds, or only use the most basic samplers such as Langevin Monte Carlo. In this work, we propose an algorithmic framework that incorporates different approximate sampling methods with the recently proposed Feel-Good Thompson Sampling (FGTS) approach (Zhang, 2022; Dann et al., 2021), which was previously known to be computationally intractable in general. When applied to linear MDPs, our regret analysis yields the best known dependency of regret on dimensionality, surpassing existing randomized algorithms. Additionally, we provide explicit sampling complexity for each employed sampler. Empirically, we show that in tasks where deep exploration is necessary, our proposed algorithms that combine FGTS and approximate sampling perform significantly better compared to other strong baselines. On several challenging games from the Atari 57 suite, our algorithms achieve performance that is either better than or on par with other strong baselines from the deep RL literature.