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Active reconfigurable intelligent surface (ARIS) is a promising way to compensate for multiplicative fading attenuation by amplifying and reflecting event signals to selected users. This paper investigates the performance of ARIS assisted non-orthogonal multiple access (NOMA) networks over cascaded Nakagami-m fading channels. The effects of hardware impairments (HIS) and reflection coefficients on ARIS-NOMA networks with imperfect successive interference cancellation (ipSIC) and perfect successive interference cancellation (pSIC) are considered. More specifically, we develop new precise and asymptotic expressions of outage probability and ergodic data rate with ipSIC/pSIC for ARIS-NOMA-HIS networks. According to the approximated analyses, the diversity orders and multiplexing gains for couple of non-orthogonal users are attained in detail. Additionally, the energy efficiency of ARIS-NOMA-HIS networks is surveyed in delay-limited and delay-tolerant transmission schemes. The simulation findings are presented to demonstrate that: i) The outage behaviors and ergodic data rates of ARIS-NOMA-HIS networks precede that of ARIS aided orthogonal multiple access (OMA) and passive reconfigurable intelligent surface (PRIS) aided OMA; ii) As the reflection coefficient of ARIS increases, ARIS-NOMA-HIS networks have the ability to provide the strengthened outage performance; and iii) ARIS-NOMA-HIS networks are more energy efficient than ARIS/PRIS-OMA networks and conventional cooperative schemes.

The integration of experimental data into mathematical and computational models is crucial for enhancing their predictive power in real-world scenarios. However, the performance of data assimilation algorithms can be significantly degraded when measurements are corrupted by biased noise, altering the signal magnitude, or when the system dynamics lack smoothness, such as in the presence of fast oscillations or discontinuities. This paper focuses on variational state estimation using the so-called Parameterized Background Data Weak method, which relies on a parameterized background by a set of constraints, enabling state estimation by solving a minimization problem on a reduced-order background model, subject to constraints imposed by the input measurements. To address biased noise in observations, a modified formulation is proposed, incorporating a correction mechanism to handle rapid oscillations by treating them as slow-decaying modes based on a two-scale splitting of the classical reconstruction algorithm. The effectiveness of the proposed algorithms is demonstrated through various examples, including discontinuous signals and simulated Doppler ultrasound data.

We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize, guaranteeing maximal descent in the direction of the stochastic gradient of the current step. We first establish theoretical convergence bounds for our method within the context of smooth non-convex stochastic optimization, matching state-of-the-art bounds while only assuming knowledge of the smoothness parameter. We then present a practical implementation of our algorithm and conduct systematic experiments across diverse datasets and optimization algorithms, comparing our scheme with existing state-of-the-art learning-rate schedulers. Our findings indicate that our method needs minimal tuning when compared to existing approaches, removing the need for auxiliary manual schedules and warm-up phases and achieving comparable performance with drastically reduced parameter tuning.

We introduce and compare computational techniques for sharp extreme event probability estimates in stochastic differential equations with small additive Gaussian noise. In particular, we focus on strategies that are scalable, i.e. their efficiency does not degrade upon temporal and possibly spatial refinement. For that purpose, we extend algorithms based on the Laplace method for estimating the probability of an extreme event to infinite dimensional path space. The method estimates the limiting exponential scaling using a single realization of the random variable, the large deviation minimizer. Finding this minimizer amounts to solving an optimization problem governed by a differential equation. The probability estimate becomes sharp when it additionally includes prefactor information, which necessitates computing the determinant of a second derivative operator to evaluate a Gaussian integral around the minimizer. We present an approach in infinite dimensions based on Fredholm determinants, and develop numerical algorithms to compute these determinants efficiently for the high-dimensional systems that arise upon discretization. We also give an interpretation of this approach using Gaussian process covariances and transition tubes. An example model problem, for which we provide an open-source python implementation, is used throughout the paper to illustrate all methods discussed. To study the performance of the methods, we consider examples of stochastic differential and stochastic partial differential equations, including the randomly forced incompressible three-dimensional Navier-Stokes equations.

To alleviate the cost of regression testing in continuous integration (CI), a large number of machine learning-based (ML-based) test case prioritization techniques have been proposed. However, it is yet unknown how they perform under the same experimental setup, because they are evaluated on different datasets with different metrics. To bridge this gap, we conduct the first comprehensive study on these ML-based techniques in this paper. We investigate the performance of 11 representative ML-based prioritization techniques for CI on 11 open-source subjects and obtain a series of findings. For example, the performance of the techniques changes across CI cycles, mainly resulting from the changing amount of training data, instead of code evolution and test removal/addition. Based on the findings, we give some actionable suggestions on enhancing the effectiveness of ML-based techniques, e.g., pretraining a prioritization technique with cross-subject data to get it thoroughly trained and then finetuning it with within-subject data dramatically improves its performance. In particular, the pretrained MART achieves state-of-the-art performance, producing the optimal sequence on 80% subjects, while the existing best technique, the original MART, only produces the optimal sequence on 50% subjects.

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user-item rating matrix into user and item latent matrices. This approach relies on learning from user-item interactions, which may not effectively capture the underlying shared dependencies between users or items. Therefore, there is scope to explicitly capture shared dependencies to further improve recommendation accuracy and the interpretability of learning results by summarizing user-item interactions. Based on these insights, we propose "Hierarchical Matrix Factorization" (HMF), which incorporates clustering concepts to capture the hierarchy, where leaf nodes and other nodes correspond to users/items and clusters, respectively. Central to our approach, called hierarchical embeddings, is the additional decomposition of the user and item latent matrices (embeddings) into probabilistic connection matrices, which link the hierarchy, and a root cluster latent matrix. Thus, each node is represented by the weighted average of the embeddings of its parent clusters. The embeddings are differentiable, allowing simultaneous learning of interactions and clustering using a single gradient descent method. Furthermore, the obtained cluster-specific interactions naturally summarize user-item interactions and provide interpretability. Experimental results on rating and ranking predictions demonstrated the competitiveness of HMF over vanilla and hierarchical MF methods, especially its robustness in sparse interactions. Additionally, it was confirmed that the clustering integration of HMF has the potential for faster learning convergence and mitigation of overfitting compared to MF, and also provides interpretability through a cluster-centered case study.

The common spatial pattern analysis (CSP) is a widely used signal processing technique in brain-computer interface (BCI) systems to increase the signal-to-noise ratio in electroencephalogram (EEG) recordings. Despite its popularity, the CSP's performance is often hindered by the nonstationarity and artifacts in EEG signals. The minmax CSP improves the robustness of the CSP by using data-driven covariance matrices to accommodate the uncertainties. We show that by utilizing the optimality conditions, the minmax CSP can be recast as an eigenvector-dependent nonlinear eigenvalue problem (NEPv). We introduce a self-consistent field (SCF) iteration with line search that solves the NEPv of the minmax CSP. Local quadratic convergence of the SCF for solving the NEPv is illustrated using synthetic datasets. More importantly, experiments with real-world EEG datasets show the improved motor imagery classification rates and shorter running time of the proposed SCF-based solver compared to the existing algorithm for the minmax CSP.

Ultra-reliable low-latency communication (URLLC) constitutes a key service class of the fifth generation and beyond cellular networks. Notably, designing and supporting URLLC poses a herculean task due to the fundamental need to identify and accurately characterize the underlying statistical models in which the system operates, e.g., interference statistics, channel conditions, and the behavior of protocols. In general, multi-layer end-to-end approaches considering all the potential delay and error sources and proper statistical tools and methodologies are inevitably required for providing strong reliability and latency guarantees. This paper contributes to the body of knowledge in the latter aspect by providing a tutorial on several statistical tools and methodologies that are useful for designing and analyzing URLLC systems. Specifically, we overview the frameworks related to i) reliability theory, ii) short packet communications, iii) inequalities, distribution bounds, and tail approximations, iv) rare events simulation, vi) queuing theory and information freshness, and v) large-scale tools such as stochastic geometry, clustering, compressed sensing, and mean-field games. Moreover, we often refer to prominent data-driven algorithms within the scope of the discussed tools/methodologies. Throughout the paper, we briefly review the state-of-the-art works using the addressed tools and methodologies, and their link to URLLC systems. Moreover, we discuss novel application examples focused on physical and medium access control layers. Finally, key research challenges and directions are highlighted to elucidate how URLLC analysis/design research may evolve in the coming years.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.