We propose a covariance stationarity test for an otherwise dependent and possibly globally non-stationary time series. We work in a generalized version of the new setting in Jin, Wang and Wang (2015), who exploit Walsh (1923) functions in order to compare sub-sample covariances with the full sample counterpart. They impose strict stationarity under the null, only consider linear processes under either hypothesis in order to achieve a parametric estimator for an inverted high dimensional asymptotic covariance matrix, and do not consider any other orthonormal basis. Conversely, we work with a general orthonormal basis under mild conditions that include Haar wavelet and Walsh functions; and we allow for linear or nonlinear processes with possibly non-iid innovations. This is important in macroeconomics and finance where nonlinear feedback and random volatility occur in many settings. We completely sidestep asymptotic covariance matrix estimation and inversion by bootstrapping a max-correlation difference statistic, where the maximum is taken over the correlation lag $h$ and basis generated sub-sample counter $k$ (the number of systematic samples). We achieve a higher feasible rate of increase for the maximum lag and counter $\mathcal{H}_{T}$ and $\mathcal{K}_{T}$. Of particular note, our test is capable of detecting breaks in variance, and distant, or very mild, deviations from stationarity.
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A near-field wideband communication system is investigated in which a base station (BS) employs an extra-large scale antenna array (ELAA) to serve multiple users in its near-field region. To facilitate near-field multi-user beamforming and mitigate the spatial wideband effect, the BS employs a hybrid beamforming architecture based on true-time delayers (TTDs). In addition to the conventional fully-connected TTD-based hybrid beamforming architecture, a new sub-connected architecture is proposed to improve energy efficiency and reduce hardware requirements. Two wideband beamforming optimization approaches are proposed to maximize spectral efficiency for both architectures. 1) Fully-digital approximation (FDA) approach: In this method, the TTD-based hybrid beamformer is optimized by the block-coordinate descent and penalty method to approximate the optimal digital beamformer. This approach ensures convergence to the stationary point of the spectral efficiency maximization problem. 2) Heuristic two-stage (HTS) approach: In this approach, the analog and digital beamformers are designed in two stages. In particular, two low-complexity methods are proposed to design the high-dimensional analog beamformers based on approximate and exact line-of-sight channels, respectively. Subsequently, the low-dimensional digital beamformer is optimized based on the low-dimensional equivalent channels, resulting in reduced computational complexity and channel estimation complexity. Our numerical results show that 1) the proposed approach effectively eliminates the spatial wideband effect, and 2) the proposed sub-connected architecture is more energy efficient and has fewer hardware constraints on the TTD and system bandwidth compared to the fully-connected architecture.
We show that (local) confluence of terminating locally constrained rewrite systems is undecidable, even when the underlying theory is decidable. Several confluence criteria for logically constrained rewrite systems are known. These were obtained by replaying existing proofs for plain term rewrite systems in a constrained setting, involving a non-trivial effort. We present a simple transformation from logically constrained rewrite systems to term rewrite systems such that critical pairs of the latter correspond to constrained critical pairs of the former. The usefulness of the transformation is illustrated by lifting the advanced confluence results based on (almost) development closed critical pairs as well as on parallel critical pairs to the constrained setting.
Pervasive sensors have become essential in research for gathering real-world data. However, current studies often focus solely on objective data, neglecting subjective human contributions. We introduce an approach and system for collecting big-thick data, combining extensive sensor data (big data) with qualitative human feedback (thick data). This fusion enables effective collaboration between humans and machines, allowing machine learning to benefit from human behavior and interpretations. Emphasizing data quality, our system incorporates continuous monitoring and adaptive learning mechanisms to optimize data collection timing and context, ensuring relevance, accuracy, and reliability. The system comprises three key components: a) a tool for collecting sensor data and user feedback, b) components for experiment planning and execution monitoring, and c) a machine-learning component that enhances human-machine interaction.
In this paper, the interference cancellation information geometry approaches (IC-IGAs) for massive MIMO channel estimation are proposed. The proposed algorithms are low-complexity approximations of the minimum mean square error (MMSE) estimation. To illustrate the proposed algorithms, a unified framework of the information geometry approach for channel estimation and its geometric explanation are described first. Then, a modified form that has the same mean as the MMSE estimation is constructed. Based on this, the IC-IGA algorithm and the interference cancellation simplified information geometry approach (IC-SIGA) are derived by applying the information geometry framework. The a posteriori means on the equilibrium of the proposed algorithms are proved to be equal to the mean of MMSE estimation, and the complexity of the IC-SIGA algorithm in practical massive MIMO systems is further reduced by considering the beam-based statistical channel model (BSCM) and fast Fourier transform (FFT). Simulation results show that the proposed methods achieve similar performance as the existing information geometry approach (IGA) with lower complexity.
This paper introduces a novel neural network for efficiently solving Structured Inverse Eigenvalue Problems (SIEPs). The main contributions lie in two aspects: firstly, a unified framework is proposed that can handle various SIEPs instances. Particularly, an innovative method for handling nonnegativity constraints is devised using the ReLU function. Secondly, a novel neural network based on multilayer perceptrons, utilizing the Stiefel layer, is designed to efficiently solve SIEP. By incorporating the Stiefel layer through matrix orthogonal decomposition, the orthogonality of similarity transformations is ensured, leading to accurate solutions for SIEPs. Hence, we name this new network Stiefel Multilayer Perceptron (SMLP). Furthermore, SMLP is an unsupervised learning approach with a lightweight structure that is easy to train. Several numerical tests from literature and engineering domains demonstrate the efficiency of SMLP.
The news landscape is continuously evolving, with an ever-increasing volume of information from around the world. Automated event detection within this vast data repository is essential for monitoring, identifying, and categorizing significant news occurrences across diverse platforms. This paper presents an event detection framework that leverages Large Language Models (LLMs) combined with clustering analysis to detect news events from the Global Database of Events, Language, and Tone (GDELT). The framework enhances event clustering through both pre-event detection tasks (keyword extraction and text embedding) and post-event detection tasks (event summarization and topic labelling). We also evaluate the impact of various textual embeddings on the quality of clustering outcomes, ensuring robust news categorization. Additionally, we introduce a novel Cluster Stability Assessment Index (CSAI) to assess the validity and robustness of clustering results. CSAI utilizes multiple feature vectors to provide a new way of measuring clustering quality. Our experiments indicate that the use of LLM embedding in the event detection framework has significantly improved the results, demonstrating greater robustness in terms of CSAI scores. Moreover, post-event detection tasks generate meaningful insights, facilitating effective interpretation of event clustering results. Overall, our experimental results indicate that the proposed framework offers valuable insights and could enhance the accuracy in news analysis and reporting.
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required to be locally differentially private. To that end we provide achievability and converse bounds for different settings. This includes symmetric state discrimination in various regimes and the asymmetric case. On the way, we also prove new sample complexity bounds for the general unconstrained setting. An important tool in this endeavor are new entropy inequalities that we believe to be of independent interest.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.
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