In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K perturbation of the identity matrix, corresponding to a signal plus noise model. A new test statistic based on the estimates of the eigenvalues of the different covariance matrices is proposed. In particular, we show that this statistic is consistent and with controlled type I error in the high-dimensional asymptotic regime where the sample sizes $N_1,\ldots,N_L$ of each time series and the dimension $M$ both converge to infinity at the same rate, while $K$ and $L$ are kept fixed. We also provide some simulations on synthetic and real data (SAR images) which demonstrate significant improvements over some classical methods such as the GLRT, or other alternative methods relevant for the high-dimensional regime and the low-rank model.
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In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output communication system with multiple antennas at both the base station (BS) and the user. We plan to maximize the achievable rate through jointly optimizing the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix under the constraints of the transmit power at the BS and the unit-modulus reflection at the RIS. Regarding the non-trivial problem form, we initially reformulate it into an considerable problem to make it tractable by utilizing the relationship between the achievable rate and the weighted minimum mean squared error. Next, the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix are alternately optimized. In particular, the optimal transmit precoding matrix and receive combining matrix are obtained in closed forms. Furthermore, a pair of computationally efficient methods are proposed for the RIS reflection matrix, namely the semi-definite relaxation (SDR) method and the successive closed form (SCF) method. We theoretically prove that both methods are ensured to converge, and the SCF-based algorithm is able to converges to a Karush-Kuhn-Tucker point of the problem.
In this paper, we investigate the performance of ambient backscatter communication non-orthogonal multiple access (AmBC-NOMA)-assisted short packet communication for high-mobility vehicle-to-everything transmissions. In the proposed system, a roadside unit (RSU) transmits a superimposed signal to a typical NOMA user pair. Simultaneously, the backscatter device (BD) transmits its own signal towards the user pair by reflecting and modulating the RSU's superimposed signals. Due to vehicles' mobility, we consider realistic assumptions of time-selective fading and channel estimation errors. Theoretical expressions for the average block error rates (BLERs) of both users are derived. Furthermore, analysis and insights on transmit signal-to-noise ratio, vehicles' mobility, imperfect channel estimation, the reflection efficiency at the BD, and blocklength are provided. Numerical results validate the theoretical findings and reveal that the AmBC-NOMA system outperforms its orthogonal multiple access counterpart in terms of BLER performance.
In this paper, we generalize the Jacobi eigenvalue algorithm to compute all eigenvalues and eigenvectors of a dual quaternion Hermitian matrix and show the convergence. We also propose a three-step Jacobi eigenvalue algorithm to compute the eigenvalues when a dual quaternion Hermitian matrix has two eigenvalues with identical standard parts but different dual parts and prove the convergence. Numerical experiments are presented to illustrate the efficiency and stability of the proposed Jacobi eigenvalue algorithm compaired to the power method and the Rayleigh quotient iteration method.
The study of behavioral diversity in Multi-Agent Reinforcement Learning (MARL) is a nascent yet promising field. In this context, the present work deals with the question of how to control the diversity of a multi-agent system. With no existing approaches to control diversity to a set value, current solutions focus on blindly promoting it via intrinsic rewards or additional loss functions, effectively changing the learning objective and lacking a principled measure for it. To address this, we introduce Diversity Control (DiCo), a method able to control diversity to an exact value of a given metric by representing policies as the sum of a parameter-shared component and dynamically scaled per-agent components. By applying constraints directly to the policy architecture, DiCo leaves the learning objective unchanged, enabling its applicability to any actor-critic MARL algorithm. We theoretically prove that DiCo achieves the desired diversity, and we provide several experiments, both in cooperative and competitive tasks, that show how DiCo can be employed as a novel paradigm to increase performance and sample efficiency in MARL. Multimedia results are available on the paper's website: //sites.google.com/view/dico-marl.
In this paper, we introduce a data augmentation approach specifically tailored to enhance intersectional fairness in classification tasks. Our method capitalizes on the hierarchical structure inherent to intersectionality, by viewing groups as intersections of their parent categories. This perspective allows us to augment data for smaller groups by learning a transformation function that combines data from these parent groups. Our empirical analysis, conducted on four diverse datasets including both text and images, reveals that classifiers trained with this data augmentation approach achieve superior intersectional fairness and are more robust to ``leveling down'' when compared to methods optimizing traditional group fairness metrics.
Synergizing Spatial Optimization with Large Language Models for Open-Domain Urban Itinerary Planning
In this paper, we introduce the novel task of Open-domain Urban Itinerary Planning (OUIP), a paradigm designed to generate personalized urban itineraries from user requests articulated in natural language. This approach is different from traditional itinerary planning, which often restricts the granularity of user inputs, thus hindering genuine personalization. To this end, we present ItiNera, an OUIP system that synergizes spatial optimization with large language models (LLMs) to provide services that customize urban itineraries based on users' needs. Upon receiving the user's itinerary request, the LLM first decomposes it into detailed components, identifying key requirements, including preferences and dislikes. Then, we use these specifics to select candidate POIs from a large-scale collection using embedding-based Preference-aware POI Retrieval. Finally, a preference score-based Cluster-aware Spatial Optimization module clusters, filters, and orders these POIs, followed by the LLM for detailed POI selection and organization to craft a personalized, spatially coherent itinerary. Moreover, we created an LLM-based pipeline to update and personalize a user-owned POI database. This ensures up-to-date POI information, supports itinerary planning, pre-trip research, POI collection, recommendations, and more. To the best of our knowledge, this study marks the first integration of LLMs to innovate itinerary planning, with potential extensions for various urban travel and exploration activities. Offline and online evaluations demonstrate the capacity of our system to deliver more responsive, personalized, and spatially coherent itineraries than current solutions. Our system, deployed on an online platform, has attracted thousands of users for their urban travel planning.
In this paper, we have expanded the current status of semantic communication limited to processing one task to a more general system that can handle multiple tasks concurrently. In pursuit of this, we first introduced our definition of the "semantic source", enabling the interpretation of multiple semantics based on a single observation. A semantic encoder design is then introduced, featuring the division of the encoder into a common unit and multiple specific units enabling cooperative multi-task processing. Simulation results demonstrate the effectiveness of the proposed semantic source and the system design. Our approach employs information maximization (infomax) and end-to-end design principles.
Addressing the statistical challenge of computing the multivariate normal (MVN) probability in high dimensions holds significant potential for enhancing various applications. One common way to compute high-dimensional MVN probabilities is the Separation-of-Variables (SOV) algorithm. This algorithm is known for its high computational complexity of O(n^3) and space complexity of O(n^2), mainly due to a Cholesky factorization operation for an n X n covariance matrix, where $n$ represents the dimensionality of the MVN problem. This work proposes a high-performance computing framework that allows scaling the SOV algorithm and, subsequently, the confidence region detection algorithm. The framework leverages parallel linear algebra algorithms with a task-based programming model to achieve performance scalability in computing process probabilities, especially on large-scale systems. In addition, we enhance our implementation by incorporating Tile Low-Rank (TLR) approximation techniques to reduce algorithmic complexity without compromising the necessary accuracy. To evaluate the performance and accuracy of our framework, we conduct assessments using simulated data and a wind speed dataset. Our proposed implementation effectively handles high-dimensional multivariate normal (MVN) probability computations on shared and distributed-memory systems using finite precision arithmetics and TLR approximation computation. Performance results show a significant speedup of up to 20X in solving the MVN problem using TLR approximation compared to the reference dense solution without sacrificing the application's accuracy. The qualitative results on synthetic and real datasets demonstrate how we maintain high accuracy in detecting confidence regions even when relying on TLR approximation to perform the underlying linear algebra operations.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.
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