Federated Learning (FL) is a decentralized machine learning framework that enables learning from data distributed across multiple remote devices, enhancing communication efficiency and data privacy. Due to limited communication resources, a scheduling policy is often applied to select a subset of devices for participation in each FL round. The scheduling process confronts significant challenges due to the need for fair workload distribution, efficient resource utilization, scalability in environments with numerous edge devices, and statistically heterogeneous data across devices. This paper proposes a load metric for scheduling policies based on the Age of Information and addresses the above challenges by minimizing the load metric variance across the clients. Furthermore, a decentralized Markov scheduling policy is presented, that ensures a balanced workload distribution while eliminating the management overhead irrespective of the network size due to independent client decision-making. We establish the optimal parameters of the Markov chain model and validate our approach through simulations. The results demonstrate that reducing the load metric variance not only promotes fairness and improves operational efficiency, but also enhances the convergence rate of the learning models.

Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies may capture different feature sets (e.g., corresponding to rows in a matrix) and/or different sample populations (corresponding to columns). This has motivated a large body of work on integrative matrix factorization approaches that identify and decompose low-dimensional signal that is shared across multiple matrices or specific to a given matrix. We propose an empirical variational Bayesian approach to this problem that has several advantages over existing techniques, including the flexibility to accommodate shared signal over any number of row or column sets (i.e., bidimensional integration), an intuitive model-based objective function that yields appropriate shrinkage for the inferred signals, and a relatively efficient estimation algorithm with no tuning parameters. A general result establishes conditions for the uniqueness of the underlying decomposition for a broad family of methods that includes the proposed approach. For scenarios with missing data, we describe an associated iterative imputation approach that is novel for the single-matrix context and a powerful approach for "blockwise" imputation (in which an entire row or column is missing) in various linked matrix contexts. Extensive simulations show that the method performs very well under different scenarios with respect to recovering underlying low-rank signal, accurately decomposing shared and specific signals, and accurately imputing missing data. The approach is applied to gene expression and miRNA data from breast cancer tissue and normal breast tissue, for which it gives an informative decomposition of variation and outperforms alternative strategies for missing data imputation.

Wearable devices are increasingly used as tools for biomedical research, as the continuous stream of behavioral and physiological data they collect can provide insights about our health in everyday contexts. Long-term tracking, defined in the timescale of months of year, can provide insights of patterns and changes as indicators of health changes. These insights can make medicine and healthcare more predictive, preventive, personalized, and participative (The 4P's). However, the challenges in modeling, understanding and processing longitudinal data are a significant barrier to their adoption in research studies and clinical settings. In this paper, we review and discuss three models used to make sense of longitudinal data: routines, rhythms and stability metrics. We present the challenges associated with the processing and analysis of longitudinal wearable sensor data, with a special focus on how to handle the different temporal dynamics at various granularities. We then discuss current limitations and identify directions for future work. This review is essential to the advancement of computational modeling and analysis of longitudinal sensor data for pervasive healthcare.

Reinforcement Learning (RL) algorithms have been used to address the challenging problems in the offloading process of vehicular ad hoc networks (VANET). More recently, they have been utilized to improve the dissemination of high-definition (HD) Maps. Nevertheless, implementing solutions such as deep Q-learning (DQN) and Actor-critic at the autonomous vehicle (AV) may lead to an increase in the computational load, causing a heavy burden on the computational devices and higher costs. Moreover, their implementation might raise compatibility issues between technologies due to the required modifications to the standards. Therefore, in this paper, we assess the scalability of an application utilizing a Q-learning single-agent solution in a distributed multi-agent environment. This application improves the network performance by taking advantage of a smaller state, and action space whilst using a multi-agent approach. The proposed solution is extensively evaluated with different test cases involving reward function considering individual or overall network performance, number of agents, and centralized and distributed learning comparison. The experimental results demonstrate that the time latencies of our proposed solution conducted in voice, video, HD Map, and best-effort cases have significant improvements, with 40.4%, 36%, 43%, and 12% respectively, compared to the performances with the single-agent approach.

Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample paths of GPs is of interest. As GP sampling requires generating high-dimensional Gaussian random vectors, it is computationally challenging if a direct method, such as the Cholesky decomposition, is used. In this paper, we propose a scalable algorithm for sampling random realizations of the prior and posterior of GP models. The proposed algorithm leverages inducing points approximation with sparse grids, as well as additive Schwarz preconditioners, which reduce computational complexity, and ensure fast convergence. We demonstrate the efficacy and accuracy of the proposed method through a series of experiments and comparisons with other recent works.

While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. EFI involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. EFI also provides an innovative framework for semi-supervised learning.

Sequential Monte Carlo (SMC) methods are powerful tools for Bayesian inference but suffer from requiring many particles for accurate estimates, leading to high computational costs. We introduce persistent sampling (PS), an extension of SMC that mitigates this issue by allowing particles from previous iterations to persist. This generates a growing, weighted ensemble of particles distributed across iterations. In each iteration, PS utilizes multiple importance sampling and resampling from the mixture of all previous distributions to produce the next generation of particles. This addresses particle impoverishment and mode collapse, resulting in more accurate posterior approximations. Furthermore, this approach provides lower-variance marginal likelihood estimates for model comparison. Additionally, the persistent particles improve transition kernel adaptation for efficient exploration. Experiments on complex distributions show that PS consistently outperforms standard methods, achieving lower squared bias in posterior moment estimation and significantly reduced marginal likelihood errors, all at a lower computational cost. PS offers a robust, efficient, and scalable framework for Bayesian inference.

The need for scalable and expressive models in machine learning is paramount, particularly in applications requiring both structural depth and flexibility. Traditional deep learning methods, such as multilayer perceptrons (MLP), offer depth but lack ability to integrate structural characteristics of deep learning architectures with non-parametric flexibility of kernel methods. To address this, deep kernel learning (DKL) was introduced, where inputs to a base kernel are transformed using a deep learning architecture. These kernels can replace standard kernels, allowing both expressive power and scalability. The advent of Kolmogorov-Arnold Networks (KAN) has generated considerable attention and discussion among researchers in scientific domain. In this paper, we introduce a scalable deep kernel using KAN (DKL-KAN) as an effective alternative to DKL using MLP (DKL-MLP). Our approach involves simultaneously optimizing these kernel attributes using marginal likelihood within a Gaussian process framework. We analyze two variants of DKL-KAN for a fair comparison with DKL-MLP: one with same number of neurons and layers as DKL-MLP, and another with approximately same number of trainable parameters. To handle large datasets, we use kernel interpolation for scalable structured Gaussian processes (KISS-GP) for low-dimensional inputs and KISS-GP with product kernels for high-dimensional inputs. The efficacy of DKL-KAN is evaluated in terms of computational training time and test prediction accuracy across a wide range of applications. Additionally, the effectiveness of DKL-KAN is also examined in modeling discontinuities and accurately estimating prediction uncertainty. The results indicate that DKL-KAN outperforms DKL-MLP on datasets with a low number of observations. Conversely, DKL-MLP exhibits better scalability and higher test prediction accuracy on datasets with large number of observations.

This paper describes the development of a causal diagnosis approach for troubleshooting an industrial environment on the basis of the technical language expressed in Return on Experience records. The proposed method leverages the vectorized linguistic knowledge contained in the distributed representation of a Large Language Model, and the causal associations entailed by the embedded failure modes and mechanisms of the industrial assets. The paper presents the elementary but essential concepts of the solution, which is conceived as a causality-aware retrieval augmented generation system, and illustrates them experimentally on a real-world Predictive Maintenance setting. Finally, it discusses avenues of improvement for the maturity of the utilized causal technology to meet the robustness challenges of increasingly complex scenarios in the industry.

Distributional reinforcement learning improves performance by effectively capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In this paper, we present a regret analysis for distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting. We first introduce a key notion of Bellman unbiasedness for a tractable and exactly learnable update via statistical functional dynamic programming. Our theoretical results show that approximating the infinite-dimensional return distribution with a finite number of moment functionals is the only method to learn the statistical information unbiasedly, including nonlinear statistical functionals. Second, we propose a provably efficient algorithm, $\texttt{SF-LSVI}$, achieving a regret bound of $\tilde{O}(d_E H^{\frac{3}{2}}\sqrt{K})$ where $H$ is the horizon, $K$ is the number of episodes, and $d_E$ is the eluder dimension of a function class.