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Tensor clustering has become an important topic, specifically in spatio-temporal modeling, due to its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of the day or day of the week). Our motivating example is from subway passenger flow modeling, where similarities between stations are commonly found. However, the challenges lie in the innate high-dimensionality of tensors and also the potential existence of anomalies. This is because the three tasks, i.e., dimension reduction, clustering, and anomaly decomposition, are inter-correlated to each other, and treating them in a separate manner will render a suboptimal performance. Thus, in this work, we design a tensor-based subspace clustering and anomaly decomposition technique for simultaneously outlier-robust dimension reduction and clustering for high-dimensional tensors. To achieve this, a novel low-rank robust subspace clustering decomposition model is proposed by combining Tucker decomposition, sparse anomaly decomposition, and subspace clustering. An effective algorithm based on Block Coordinate Descent is proposed to update the parameters. Prudent experiments prove the effectiveness of the proposed framework via the simulation study, with a gain of +25% clustering accuracy than benchmark methods in a hard case. The interrelations of the three tasks are also analyzed via ablation studies, validating the interrelation assumption. Moreover, a case study in the station clustering based on real passenger flow data is conducted, with quite valuable insights discovered.

Diffusion Probabilistic Models stand as a critical tool in generative modelling, enabling the generation of complex data distributions. This family of generative models yields record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse process, remains a challenge due to slow convergence rates and high computational costs. In this paper, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with Denoising Diffusion Probabilistic Models (DDPMs), our framework operates with approximately a quarter of the parameters, and $\sim$ 30\% of the Floating Point Operations (FLOPs) compared to standard U-Nets in DDPMs. Furthermore, our model is notably faster in inference than the baseline when measured in fair and equal conditions. We also provide a mathematical intuition as to why our proposed reverse process is faster as well as a mathematical discussion of the empirical tradeoffs in the denoising downstream task. Finally, we argue that our method is compatible with existing performance enhancement techniques, enabling further improvements in efficiency, quality, and speed.

While advances continue to be made in model-based clustering, challenges persist in modeling various data types such as panel data. Multivariate panel data present difficulties for clustering algorithms due to the unique correlation structure, a consequence of taking observations on several subjects over multiple time points. Additionally, panel data are often plagued by missing data and dropouts, presenting issues for estimation algorithms. This research presents a family of hidden Markov models that compensate for the unique correlation structures that arise in panel data. A modified expectation-maximization algorithm capable of handling missing not at random data and dropout is presented and used to perform model estimation.

Microvascular networks are challenging to model because these structures are currently near the diffraction limit for most advanced three-dimensional imaging modalities, including confocal and light sheet microscopy. This makes semantic segmentation difficult, because individual components of these networks fluctuate within the confines of individual pixels. Level set methods are ideally suited to solve this problem by providing surface and topological constraints on the resulting model, however these active contour techniques are extremely time intensive and impractical for terabyte-scale images. We propose a reformulation and implementation of the region-scalable fitting (RSF) level set model that makes it amenable to three-dimensional evaluation using both single-instruction multiple data (SIMD) and single-program multiple-data (SPMD) parallel processing. This enables evaluation of the level set equation on independent regions of the data set using graphics processing units (GPUs), making large-scale segmentation of high-resolution networks practical and inexpensive. We tested this 3D parallel RSF approach on multiple data sets acquired using state-of-the-art imaging techniques to acquire microvascular data, including micro-CT, light sheet fluorescence microscopy (LSFM) and milling microscopy. To assess the performance and accuracy of the RSF model, we conducted a Monte-Carlo-based validation technique to compare results to other segmentation methods. We also provide a rigorous profiling to show the gains in processing speed leveraging parallel hardware. This study showcases the practical application of the RSF model, emphasizing its utility in the challenging domain of segmenting large-scale high-topology network structures with a particular focus on building microvascular models.

Achieving high-performance in multi-object tracking algorithms heavily relies on modeling spatio-temporal relationships during the data association stage. Mainstream approaches encompass rule-based and deep learning-based methods for spatio-temporal relationship modeling. While the former relies on physical motion laws, offering wider applicability but yielding suboptimal results for complex object movements, the latter, though achieving high-performance, lacks interpretability and involves complex module designs. This work aims to simplify deep learning-based spatio-temporal relationship models and introduce interpretability into features for data association. Specifically, a lightweight single-layer transformer encoder is utilized to model spatio-temporal relationships. To make features more interpretative, two contrastive regularization losses based on representation alignment are proposed, derived from spatio-temporal consistency rules. By applying weighted summation to affinity matrices, the aligned features can seamlessly integrate into the data association stage of the original tracking workflow. Experimental results showcase that our model enhances the majority of existing tracking networks' performance without excessive complexity, with minimal increase in training overhead and nearly negligible computational and storage costs.

Federated learning aims to construct a global model that fits the dataset distributed across local devices without direct access to private data, leveraging communication between a server and the local devices. In the context of a practical communication scheme, we study the completion time required to achieve a target performance. Specifically, we analyze the number of iterations required for federated learning to reach a specific optimality gap from a minimum global loss. Subsequently, we characterize the time required for each iteration under two fundamental multiple access schemes: time-division multiple access (TDMA) and random access (RA). We propose a step-wise batch allocation, demonstrated to be optimal for TDMA-based federated learning systems. Additionally, we show that the non-zero batch gap between devices provided by the proposed step-wise batch allocation significantly reduces the completion time for RA-based learning systems. Numerical evaluations validate these analytical results through real-data experiments, highlighting the remarkable potential for substantial completion time reduction.

Combining large language models with logical reasoning enhances their capacity to address problems in a robust and reliable manner. Nevertheless, the intricate nature of logical reasoning poses challenges to gathering reliable data from the web for building comprehensive training datasets, subsequently affecting the performance on downstream tasks. To address this, we introduce a novel logic-driven data augmentation approach, AMR-LDA. AMR-LDA converts the original text into an Abstract Meaning Representation (AMR) graph, a structured semantic representation that encapsulates the logic structure of the sentence, upon which operations are performed to generate logically modified AMR graphs. The modified AMR graphs are subsequently converted back into text to create augmented data. Notably, our methodology is architecture-agnostic and enhances both generative large language models, such as GPT-3.5 and GPT-4, through prompt augmentation, and discriminative large language models through contrastive learning with logic-driven data augmentation. Empirical evidence underscores the efficacy of our proposed method with improvement in performance across seven downstream tasks, such as reading comprehension requiring logical reasoning, textual entailment, and natural language inference. Furthermore, our method leads on the ReClor leaderboard (//eval.ai/web/challenges/challenge-page/503/leaderboard/1347). The source code and data are publicly available //bit.ly/3OWKe8r.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evolve over time. In this paper, we present Dynamic Self-Attention Network (DySAT), a novel neural architecture that operates on dynamic graphs and learns node representations that capture both structural properties and temporal evolutionary patterns. Specifically, DySAT computes node representations by jointly employing self-attention layers along two dimensions: structural neighborhood and temporal dynamics. We conduct link prediction experiments on two classes of graphs: communication networks and bipartite rating networks. Our experimental results show that DySAT has a significant performance gain over several different state-of-the-art graph embedding baselines.