With the widespread adoption of Non-Intrusive Load Monitoring (NILM) in building energy management, ensuring the high quality of NILM data has become imperative. However, practical applications of NILM face challenges associated with data loss, significantly impacting accuracy and reliability in energy management. This paper addresses the issue of NILM data loss by introducing an innovative tensor completion(TC) model- Proportional-Integral-Derivative (PID)-incorporated Non-negative Latent Factorization of Tensors (PNLFT) with twofold ideas: 1) To tackle the issue of slow convergence in Latent Factorization of Tensors (LFT) using Stochastic Gradient Descent (SGD), a Proportional-Integral-Derivative controller is introduced during the learning process. The PID controller utilizes historical and current information to control learning residuals. 2) Considering the characteristics of NILM data, non-negative update rules are proposed in the model's learning scheme. Experimental results on three datasets demonstrate that, compared to state-of-the-art models, the proposed model exhibits noteworthy enhancements in both convergence speed and accuracy.

Stephen Salter, who has died aged 85, was the inventor of the Salter's Duck, a wave-power device that was the first of its kind and promised to provide a new source of renewable energy for the world – until it was effectively killed off by the nuclear industry. In 1982, after eight years of development under Salter's direction at Edinburgh University, the United Kingdom Atomic Energy Authority (UKAEA) was asked by the government to see if the duck might be a cost-effective way of making large quantities of electricity. To the great surprise of Salter, and others, the UKAEA came to the conclusion that it was uneconomic, and that no further government funding should be given to the project. A decade later it emerged that thanks to a misplaced decimal point, the review had made Salter's duck look 10 times more expensive than the experiments showed it was likely to be. The UKAEA claimed this was just a mistake, but Salter, who had never been allowed to see the results of the secret evaluation, put it another way: asking the nuclear industry to evaluate an alternative source of energy was like putting King Herod in charge of a children's home, he suggested.

Bayesian optimization (BO) with Gaussian processes (GP) has become an indispensable algorithm for black box optimization problems. Not without a dash of irony, BO is often considered a black box itself, lacking ways to provide reasons as to why certain parameters are proposed to be evaluated. This is particularly relevant in human-in-the-loop applications of BO, such as in robotics. We address this issue by proposing ShapleyBO, a framework for interpreting BO's proposals by game-theoretic Shapley values.They quantify each parameter's contribution to BO's acquisition function. Exploiting the linearity of Shapley values, we are further able to identify how strongly each parameter drives BO's exploration and exploitation for additive acquisition functions like the confidence bound. We also show that ShapleyBO can disentangle the contributions to exploration into those that explore aleatoric and epistemic uncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human machine interface (HMI), allowing users to interfere with BO in case proposals do not align with human reasoning. We demonstrate this HMI's benefits for the use case of personalizing wearable robotic devices (assistive back exosuits) by human-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO can achieve lower regret than teams without.

Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this challenge by proposing a two-step optimization framework. Initially, we identify the effective dimension reduction (EDR) subspace for the objective function using the minimum average variance estimation (MAVE) method. Subsequently, we construct a Gaussian process model within this EDR subspace and optimize it using the expected improvement criterion. Our algorithm offers the flexibility to operate these steps either concurrently or in sequence. In the sequential approach, we meticulously balance the exploration-exploitation trade-off by distributing the sampling budget between subspace estimation and function optimization, and the convergence rate of our algorithm in high-dimensional contexts has been established. Numerical experiments validate the efficacy of our method in challenging scenarios.

We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion. To set the stage for gradient-based methods, we first establish that the average reward is a smooth function of policies and provide sensitivity bounds for the differential value functions, under certain conditions on ergodicity and the second largest eigenvalue of the underlying Markov decision process (MDP). We prove that three algorithms, policy gradient, proximal-Q, and natural policy gradient (NPG), converge to an $\epsilon$-Nash equilibrium with time complexity $O(\frac{1}{\epsilon^2})$, given a gradient/differential Q function oracle. When policy gradients have to be estimated, we propose an algorithm with $\tilde{O}(\frac{1}{\min_{s,a}\pi(a|s)\delta})$ sample complexity to achieve $\delta$ approximation error w.r.t~the $\ell_2$ norm. Equipped with the estimator, we derive the first sample complexity analysis for a policy gradient ascent algorithm, featuring a sample complexity of $\tilde{O}(1/\epsilon^5)$. Simulation studies are presented.

We present a first study of Bayesian forecasting of electricity prices traded on the German continuous intraday market which fully incorporates parameter uncertainty. Our target variable is the IDFull price index, forecasts are given in terms of posterior predictive distributions. For validation we use the exceedingly volatile electricity prices of 2022, which have hardly been the subject of forecasting studies before. As a benchmark model, we use all available intraday transactions at the time of forecast creation to compute a current value for the IDFull. According to the weak-form efficiency hypothesis, it would not be possible to significantly improve this benchmark built from last price information. We do, however, observe statistically significant improvement in terms of both point measures and probability scores. Finally, we challenge the declared gold standard of using LASSO for feature selection in electricity price forecasting by presenting strong statistical evidence that Orthogonal Matching Pursuit (OMP) leads to better forecasting performance.

Split learning (SL) is a promising approach for training artificial intelligence (AI) models, in which devices collaborate with a server to train an AI model in a distributed manner, based on a same fixed split point. However, due to the device heterogeneity and variation of channel conditions, this way is not optimal in training delay and energy consumption. In this paper, we design an adaptive split learning (ASL) scheme which can dynamically select split points for devices and allocate computing resource for the server in wireless edge networks. We formulate an optimization problem to minimize the average training latency subject to long-term energy consumption constraint. The difficulties in solving this problem are the lack of future information and mixed integer programming (MIP). To solve it, we propose an online algorithm leveraging the Lyapunov theory, named OPEN, which decomposes it into a new MIP problem only with the current information. Then, a two-layer optimization method is proposed to solve the MIP problem. Extensive simulation results demonstrate that the ASL scheme can reduce the average training delay and energy consumption by 53.7% and 22.1%, respectively, as compared to the existing SL schemes.

Many practical problems involve estimating low dimensional statistical quantities with high-dimensional models and datasets. Several approaches address these estimation tasks based on the theory of influence functions, such as debiased/double ML or targeted minimum loss estimation. This paper introduces \textit{Monte Carlo Efficient Influence Functions} (MC-EIF), a fully automated technique for approximating efficient influence functions that integrates seamlessly with existing differentiable probabilistic programming systems. MC-EIF automates efficient statistical estimation for a broad class of models and target functionals that would previously require rigorous custom analysis. We prove that MC-EIF is consistent, and that estimators using MC-EIF achieve optimal $\sqrt{N}$ convergence rates. We show empirically that estimators using MC-EIF are at parity with estimators using analytic EIFs. Finally, we demonstrate a novel capstone example using MC-EIF for optimal portfolio selection.

This paper examines an efficient method for quasi-random sampling of copulas in Monte Carlo computations. Traditional methods, like conditional distribution methods (CDM), have limitations when dealing with high-dimensional or implicit copulas, which refer to those that cannot be accurately represented by existing parametric copulas. Instead, this paper proposes the use of generative models, such as Generative Adversarial Networks (GANs), to generate quasi-random samples for any copula. GANs are a type of implicit generative models used to learn the distribution of complex data, thus facilitating easy sampling. In our study, GANs are employed to learn the mapping from a uniform distribution to copulas. Once this mapping is learned, obtaining quasi-random samples from the copula only requires inputting quasi-random samples from the uniform distribution. This approach offers a more flexible method for any copula. Additionally, we provide theoretical analysis of quasi-Monte Carlo estimators based on quasi-random samples of copulas. Through simulated and practical applications, particularly in the field of risk management, we validate the proposed method and demonstrate its superiority over various existing methods.

U.S. Ambassador to Japan Rahm Emanuel visited a Fukushima coastal city to support the local fishing industry after China and South Korea raised the alarm over water discharge began from the Fukushima Daiichi nuclear plant. As Japan prepares to mark the 13th anniversary of its worst-ever nuclear disaster, the man in charge of cleaning it up says his team is fighting to bring a sample out of the heart of the site's radioactive debris. A decades-long project to clean up the remains of the Fukushima Daiichi nuclear power plant is preparing to remove damaged fuel debris from the plant's reactors, but much about what's inside them is still a mystery. The key to unlocking that mystery -- and figuring out how to clean it up -- is a sample of melted fuel from inside a reactor, said Akira Ono, head of decommissioning for Tokyo Electric Power Company Holdings, in an interview with The Associated Press. Getting that sample would be like penetrating "the main keep of the castle" in the battle of decommissioning, Ono said.