Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In this article, we study the FQR model for densely sampled, high-dimensional functional data without relying on parametric error or independent stochastic process assumptions, with the focus on statistical inference under this challenging regime along with scalable implementation. This is achieved by a simple but powerful distributed strategy, in which we first perform separate quantile regression to compute $M$-estimators at each sampling location, and then carry out estimation and inference for the entire coefficient functions by properly exploiting the uncertainty quantification and dependence structure of $M$-estimators. We derive a uniform Bahadur representation and a strong Gaussian approximation result for the $M$-estimators on the discrete sampling grid, leading to dimension reduction and serving as the basis for inference. An interpolation-based estimator with minimax optimality is proposed, and large sample properties for point and simultaneous interval estimators are established. The obtained minimax optimal rate under the FQR model shows an interesting phase transition phenomenon that has been previously observed in functional mean regression. The proposed methods are illustrated via simulations and an application to a mass spectrometry proteomics dataset.
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Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transport cost between two different data sets; if some changes happen to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently find the variable to pivot within expected $O(1)$ time, and complete each pivoting operation within expected $O(|V|)$ time where $V$ is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transport cost that needs at least one traversal over all $|E| = O(|V|^2)$ variables, where $|E|$ denotes the number of edges in the network. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.
Vehicle-to-Everything (V2X) collaborative perception has recently gained significant attention due to its capability to enhance scene understanding by integrating information from various agents, e.g., vehicles, and infrastructure. However, current works often treat the information from each agent equally, ignoring the inherent domain gap caused by the utilization of different LiDAR sensors of each agent, thus leading to suboptimal performance. In this paper, we propose DI-V2X, that aims to learn Domain-Invariant representations through a new distillation framework to mitigate the domain discrepancy in the context of V2X 3D object detection. DI-V2X comprises three essential components: a domain-mixing instance augmentation (DMA) module, a progressive domain-invariant distillation (PDD) module, and a domain-adaptive fusion (DAF) module. Specifically, DMA builds a domain-mixing 3D instance bank for the teacher and student models during training, resulting in aligned data representation. Next, PDD encourages the student models from different domains to gradually learn a domain-invariant feature representation towards the teacher, where the overlapping regions between agents are employed as guidance to facilitate the distillation process. Furthermore, DAF closes the domain gap between the students by incorporating calibration-aware domain-adaptive attention. Extensive experiments on the challenging DAIR-V2X and V2XSet benchmark datasets demonstrate DI-V2X achieves remarkable performance, outperforming all the previous V2X models. Code is available at //github.com/Serenos/DI-V2X
In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data analysis, and they have been widely used in the area of econometrics. Nevertheless, the non-smoothness of objective functions and constraints present computational challenges for many existing solvers in the presence of ultra-high dimensional covariates. In this paper, we design efficient and parallelizable algorithms for solving sparse SVM problems with high dimensional data through feature space split. The proposed algorithm is based on the alternating direction method of multiplier (ADMM). We establish the rate of convergence of the proposed ADMM method and compare it with existing solvers in various high and ultra-high dimensional settings. The compatibility of the proposed algorithm with parallel computing can further alleviate the storage and scalability limitations of a single machine in large-scale data processing.
Age of Information (AoI) has been proposed to quantify the freshness of information for emerging real-time applications such as remote monitoring and control in wireless networked control systems (WNCSs). Minimization of the average AoI and its outage probability can ensure timely and stable transmission. Energy efficiency (EE) also plays an important role in WNCSs, as many devices are featured by low cost and limited battery. Multi-connectivity over multiple links enables a decrease in AoI, at the cost of energy. We tackle the unresolved problem of selecting the optimal number of connections that is both AoI-optimal and energy-efficient, while avoiding risky states. To address this issue, the average AoI and peak AoI (PAoI), as well as PAoI violation probability are formulated as functions of the number of connections. Then the EE-PAoI ratio is introduced to allow a tradeoff between AoI and energy, which is maximized by the proposed risk-aware, AoI-optimal and energy-efficient connectivity scheme. To obtain this, we analyze the property of the formulated EE-PAoI ratio and prove the monotonicity of PAoI violation probability. Interestingly, we reveal that the multi-connectivity scheme is not always preferable, and the signal-to-noise ratio (SNR) threshold that determines the selection of the multi-connectivity scheme is derived as a function of the coding rate. Also, the optimal number of connections is obtained and shown to be a decreasing function of the transmit power. Simulation results demonstrate that the proposed scheme enables more than 15 folds of EE-PAoI gain at the low SNR than the single-connectivity scheme.
Multi-access edge computing (MEC) is a promising solution to the computation-intensive, low-latency rendering tasks of the metaverse. However, how to optimally allocate limited communication and computation resources at the edge to a large number of users in the metaverse is quite challenging. In this paper, we propose an adaptive edge resource allocation method based on multi-agent soft actor-critic with graph convolutional networks (SAC-GCN). Specifically, SAC-GCN models the multi-user metaverse environment as a graph where each agent is denoted by a node. Each agent learns the interplay between agents by graph convolutional networks with self-attention mechanism to further determine the resource usage for one user in the metaverse. The effectiveness of SAC-GCN is demonstrated through the analysis of user experience, balance of resource allocation, and resource utilization rate by taking a virtual city park metaverse as an example. Experimental results indicate that SAC-GCN outperforms other resource allocation methods in improving overall user experience, balancing resource allocation, and increasing resource utilization rate by at least 27%, 11%, and 8%, respectively.
This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and discrete Fourier transform (DFT). The main goal is to extend the well-known theory of DFT in signal processing (SP) to other applications involving polynomials in a ring such as homomorphic encryption (HE). HE allows any third party to operate on the encrypted data without decrypting it in advance. Since most HE schemes are constructed from the ring-learning with errors (R-LWE) problem, efficient polynomial modular multiplication implementation becomes critical. Any improvement in the execution of these building blocks would have significant consequences for the global performance of HE. This lecture note describes three approaches to implementing long polynomial modular multiplication using the number theoretic transform (NTT): zero-padded convolution, without zero-padding, also referred to as negative wrapped convolution (NWC), and low-complexity NWC (LC-NWC).
Gait recognition is a biometric technology that has received extensive attention. Most existing gait recognition algorithms are unimodal, and a few multimodal gait recognition algorithms perform multimodal fusion only once. None of these algorithms may fully exploit the complementary advantages of the multiple modalities. In this paper, by considering the temporal and spatial characteristics of gait data, we propose a multi-stage feature fusion strategy (MSFFS), which performs multimodal fusions at different stages in the feature extraction process. Also, we propose an adaptive feature fusion module (AFFM) that considers the semantic association between silhouettes and skeletons. The fusion process fuses different silhouette areas with their more related skeleton joints. Since visual appearance changes and time passage co-occur in a gait period, we propose a multiscale spatial-temporal feature extractor (MSSTFE) to learn the spatial-temporal linkage features thoroughly. Specifically, MSSTFE extracts and aggregates spatial-temporal linkages information at different spatial scales. Combining the strategy and modules mentioned above, we propose a multi-stage adaptive feature fusion (MSAFF) neural network, which shows state-of-the-art performance in many experiments on three datasets. Besides, MSAFF is equipped with feature dimensional pooling (FD Pooling), which can significantly reduce the dimension of the gait representations without hindering the accuracy. //github.com/ShinanZou/MSAFF
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Named entity recognition (NER) is the task to identify text spans that mention named entities, and to classify them into predefined categories such as person, location, organization etc. NER serves as the basis for a variety of natural language applications such as question answering, text summarization, and machine translation. Although early NER systems are successful in producing decent recognition accuracy, they often require much human effort in carefully designing rules or features. In recent years, deep learning, empowered by continuous real-valued vector representations and semantic composition through nonlinear processing, has been employed in NER systems, yielding stat-of-the-art performance. In this paper, we provide a comprehensive review on existing deep learning techniques for NER. We first introduce NER resources, including tagged NER corpora and off-the-shelf NER tools. Then, we systematically categorize existing works based on a taxonomy along three axes: distributed representations for input, context encoder, and tag decoder. Next, we survey the most representative methods for recent applied techniques of deep learning in new NER problem settings and applications. Finally, we present readers with the challenges faced by NER systems and outline future directions in this area.
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, thereby allowing manual manipulation in predicting the final answer.
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