Potassium disorders are generally asymptomatic, potentially lethal, and common in patients with renal or cardiac disease. The morphology of the electrocardiogram (ECG) signal is very sensitive to the changes in potassium ions, so ECG has a high potential for detecting dyskalemias before laboratory results. In this regard, this paper introduces a new system for ECG-based potassium measurement. The proposed system consists of three main steps. First, cohort selection & data labeling were carried out by using a 5- minute interval between ECGs and potassium measurements and defining three labels: hypokalemia, normal, and hyperkalemia. After that, feature extraction & selection were performed. The extracted features are RR interval, PR interval, QRS duration, QT interval, QTc interval, P axis, QRS axis, T axis, and ACCI. Kruskal-Wallis technique was also used to assess the importance of the features and to select discriminative ones. Finally, an ANFIS model based on FCM clustering (FCM-ANFIS) was designed based on the selected features. The used database is ECG-ViEW II. Results showed that T axis compared with other features has a significant relationship with potassium levels (P<0.01, r=0.62). The absolute error of FCM-ANFIS is 0.4+-0.3 mM, its mean absolute percentage error (MAPE) is 9.99%, and its r-squared value is 0.74. Its classification accuracy is 85.71%. In detecting hypokalemia and hyperkalemia, the sensitivities are 60% and 80%, respectively, and the specificities are 100% and 97.3%, respectively. This research has shed light on the design of noninvasive instruments to measure potassium concentration and to detect dyskalemias, thereby reducing cardiac events.

Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this work, we aim to learn a graph from incomplete time-series observations. From another viewpoint, we consider the problem of semi-blind recovery of time-varying graph signals where the underlying graph model is unknown. We propose an algorithm based on the method of block successive upperbound minimization (BSUM), for simultaneous inference of the signal and the graph from incomplete data. Simulation results on synthetic and real time-series demonstrate the performance of the proposed method for graph learning and signal recovery.

The accurate predictions and principled uncertainty measures provided by GP regression incur O(n^3) cost which is prohibitive for modern-day large-scale applications. This has motivated extensive work on computationally efficient approximations. We introduce a new perspective by exploring robustness properties and limiting behaviour of GP nearest-neighbour (GPnn) prediction. We demonstrate through theory and simulation that as the data-size n increases, accuracy of estimated parameters and GP model assumptions become increasingly irrelevant to GPnn predictive accuracy. Consequently, it is sufficient to spend small amounts of work on parameter estimation in order to achieve high MSE accuracy, even in the presence of gross misspecification. In contrast, as n tends to infinity, uncertainty calibration and NLL are shown to remain sensitive to just one parameter, the additive noise-variance; but we show that this source of inaccuracy can be corrected for, thereby achieving both well-calibrated uncertainty measures and accurate predictions at remarkably low computational cost. We exhibit a very simple GPnn regression algorithm with stand-out performance compared to other state-of-the-art GP approximations as measured on large UCI datasets. It operates at a small fraction of those other methods' training costs, for example on a basic laptop taking about 30 seconds to train on a dataset of size n = 1.6 x 10^6.

Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To alleviate this computational bottleneck, we develop a linear complexity Gibbs sampling framework for GLMB density computation. Specifically, we propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an $\mathcal{O}(T(P+M))$ complexity, where $T$ is the number of iterations of the algorithm, $P$ and $M$ are the number hypothesized objects and measurements. This innovation enables the GLMB filter implementation to be reduced from an $\mathcal{O}(TP^{2}M)$ complexity to $\mathcal{O}(T(P+M+\log T)+PM)$. Moreover, the proposed framework provides the flexibility for trade-offs between tracking performance and computational load. Convergence of the proposed Gibbs sampler is established, and numerical studies are presented to validate the proposed GLMB filter implementation.

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of normal distributions by a finite mixture of normal distributions; and (ii) the use of variational approximations to efficiently estimate prior hyperparameters and compute approximate posteriors. Combining these two ideas results in fast and flexible methods, with computational speed comparable to fast penalized regression methods such as the Lasso, and with competitive prediction accuracy across a wide range of scenarios. Further, we provide new results that establish conceptual connections between our empirical Bayes methods and penalized methods. Specifically, we show that the posterior mean from our method solves a penalized regression problem, with the form of the penalty function being learned from the data by directly solving an optimization problem (rather than being tuned by cross-validation). Our methods are implemented in an R package, mr.ash.alpha,

Autonomous vehicles (AVs) have the potential to prevent accidents caused by drivers' error and reduce road traffic risks. Due to the nature of heavy vehicles, whose collisions cause more serious crashes, the weights of vehicles need to be considered when making driving strategies aimed at reducing the potential risks and their consequences in the context of autonomous driving. This study develops an autonomous driving strategy based on risk anticipation, considering the weights of surrounding vehicles and using hierarchical deep reinforcement learning. A risk indicator integrating surrounding vehicles' weights, based on the risk field theory, is proposed and incorporated into autonomous driving decisions. A hybrid action space is designed to allow for left lane changes, right lane changes and car-following, which enables AVs to act more freely and realistically whenever possible. To solve the above hybrid decision-making problem, a hierarchical proximal policy optimization (HPPO) algorithm is developed and an attention mechanism is incorporated, providing great advantages in maintaining stable performance. An indicator, potential collision energy in conflicts (PCEC), is newly proposed to evaluate the performance of the developed AV driving strategy from both the perspectives of the likelihood and the consequences of potential accidents. An application is carried out and the simulation results demonstrate that our model provides driving strategies that reduce both the likelihood and consequences of potential accidents, at the same time maintaining driving efficiency. The developed method is especially meaningful for AVs driving on highways, where heavy vehicles make up a high proportion of the traffic.

We propose a nonparametric and time-varying directed information graph (TV-DIG) framework to estimate the evolving causal structure in time series networks, thereby addressing the limitations of traditional econometric models in capturing high-dimensional, nonlinear, and time-varying interconnections among series. This framework employs an information-theoretic measure rooted in a generalized version of Granger-causality, which is applicable to both linear and nonlinear dynamics. Our framework offers advancements in measuring systemic risk and establishes meaningful connections with established econometric models, including vector autoregression and switching models. We evaluate the efficacy of our proposed model through simulation experiments and empirical analysis, reporting promising results in recovering simulated time-varying networks with nonlinear and multivariate structures. We apply this framework to identify and monitor the evolution of interconnectedness and systemic risk among major assets and industrial sectors within the financial network. We focus on cryptocurrencies' potential systemic risks to financial stability, including spillover effects on other sectors during crises like the COVID-19 pandemic and the Federal Reserve's 2020 emergency response. Our findings reveals significant, previously underrecognized pre-2020 influences of cryptocurrencies on certain financial sectors, highlighting their potential systemic risks and offering a systematic approach in tracking evolving cross-sector interactions within financial networks.

Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if. . . , then. . . " rules, which form the backbone of rough set rule induction. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. This observation highlights the potential of these models for resolving data inconsistencies and managing noise.

The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation methods for machine learning models. More traditionally, from a statistical perspective, feature importance is defined in terms of conditional independence. So far, these two approaches to interpretability and feature importance have been considered separate and distinct. In this work, we show that Shapley-based explanation methods and conditional independence testing are closely related. We introduce the SHAPley EXplanation Randomization Test (SHAP-XRT), a testing procedure inspired by the Conditional Randomization Test (CRT) for a specific notion of local (i.e., on a sample) conditional independence. With it, we prove that for binary classification problems, the marginal contributions in the Shapley value provide lower and upper bounds to the expected $p$-values of their respective tests. Furthermore, we show that the Shapley value itself provides an upper bound to the expected $p$-value of a global (i.e., overall) null hypothesis. As a result, we further our understanding of Shapley-based explanation methods from a novel perspective and characterize the conditions under which one can make statistically valid claims about feature importance via the Shapley value.

Making decisions is a great challenge in distributed autonomous environments due to enormous state spaces and uncertainty. Many online planning algorithms rely on statistical sampling to avoid searching the whole state space, while still being able to make acceptable decisions. However, planning often has to be performed under strict computational constraints making online planning in multi-agent systems highly limited, which could lead to poor system performance, especially in stochastic domains. In this paper, we propose Emergent Value function Approximation for Distributed Environments (EVADE), an approach to integrate global experience into multi-agent online planning in stochastic domains to consider global effects during local planning. For this purpose, a value function is approximated online based on the emergent system behaviour by using methods of reinforcement learning. We empirically evaluated EVADE with two statistical multi-agent online planning algorithms in a highly complex and stochastic smart factory environment, where multiple agents need to process various items at a shared set of machines. Our experiments show that EVADE can effectively improve the performance of multi-agent online planning while offering efficiency w.r.t. the breadth and depth of the planning process.