Enhancing Multivariate Time Series Forecasting with Mutual Information-driven Cross-Variable and Temporal Modeling

Recent advancements have underscored the impact of deep learning techniques on multivariate time series forecasting (MTSF). Generally, these techniques are bifurcated into two categories: Channel-independence and Channel-mixing approaches. Although Channel-independence methods typically yield better results, Channel-mixing could theoretically offer improvements by leveraging inter-variable correlations. Nonetheless, we argue that the integration of uncorrelated information in channel-mixing methods could curtail the potential enhancement in MTSF model performance. To substantiate this claim, we introduce the Cross-variable Decorrelation Aware feature Modeling (CDAM) for Channel-mixing approaches, aiming to refine Channel-mixing by minimizing redundant information between channels while enhancing relevant mutual information. Furthermore, we introduce the Temporal correlation Aware Modeling (TAM) to exploit temporal correlations, a step beyond conventional single-step forecasting methods. This strategy maximizes the mutual information between adjacent sub-sequences of both the forecasted and target series. Combining CDAM and TAM, our novel framework significantly surpasses existing models, including those previously considered state-of-the-art, in comprehensive tests.

MATA*: Combining Learnable Node Matching with A* Algorithm for Approximate Graph Edit Distance Computation

Graph Edit Distance (GED) is a general and domain-agnostic metric to measure graph similarity, widely used in graph search or retrieving tasks. However, the exact GED computation is known to be NP-complete. For instance, the widely used A* algorithms explore the entire search space to find the optimal solution which inevitably suffers scalability issues. Learning-based methods apply graph representation techniques to learn the GED by formulating a regression task, which can not recover the edit path and lead to inaccurate GED approximation (i.e., the predicted GED is smaller than the exact). To this end, in this work, we present a data-driven hybrid approach MATA* for approximate GED computation based on Graph Neural Networks (GNNs) and A* algorithms, which models from the perspective of learning to match nodes instead of directly regressing GED. Specifically, aware of the structure-dominant operations (i.e.,node and edge insertion/deletion) property in GED computation, a structure-enhanced GNN is firstly designed to jointly learn local and high-order structural information for node embeddings for node matchings. Second, top-k candidate nodes are produced via a differentiable top-k operation to enable the training for node matchings, which is adhering to another property of GED, i.e., multiple optimal node matchings. Third, benefiting from the candidate nodes, MATA* only performs on the promising search directions, reaching the solution efficiently. Finally, extensive experiments show the superiority of MATA* as it significantly outperforms the combinatorial search-based, learning-based and hybrid methods and scales well to large-size graphs.

Mitigating Semantic Confusion from Hostile Neighborhood for Graph Active Learning

Graph Active Learning (GAL), which aims to find the most informative nodes in graphs for annotation to maximize the Graph Neural Networks (GNNs) performance, has attracted many research efforts but remains non-trivial challenges. One major challenge is that existing GAL strategies may introduce semantic confusion to the selected training set, particularly when graphs are noisy. Specifically, most existing methods assume all aggregating features to be helpful, ignoring the semantically negative effect between inter-class edges under the message-passing mechanism. In this work, we present Semantic-aware Active learning framework for Graphs (SAG) to mitigate the semantic confusion problem. Pairwise similarities and dissimilarities of nodes with semantic features are introduced to jointly evaluate the node influence. A new prototype-based criterion and query policy are also designed to maintain diversity and class balance of the selected nodes, respectively. Extensive experiments on the public benchmark graphs and a real-world financial dataset demonstrate that SAG significantly improves node classification performances and consistently outperforms previous methods. Moreover, comprehensive analysis and ablation study also verify the effectiveness of the proposed framework.

Contrastive Shapelet Learning for Unsupervised Multivariate Time Series Representation Learning

Recent studies have shown great promise in unsupervised representation learning (URL) for multivariate time series, because URL has the capability in learning generalizable representation for many downstream tasks without using inaccessible labels. However, existing approaches usually adopt the models originally designed for other domains (e.g., computer vision) to encode the time series data and rely on strong assumptions to design learning objectives, which limits their ability to perform well. To deal with these problems, we propose a novel URL framework for multivariate time series by learning time-series-specific shapelet-based representation through a popular contrasting learning paradigm. To the best of our knowledge, this is the first work that explores the shapelet-based embedding in the unsupervised general-purpose representation learning. A unified shapelet-based encoder and a novel learning objective with multi-grained contrasting and multi-scale alignment are particularly designed to achieve our goal, and a data augmentation library is employed to improve the generalization. We conduct extensive experiments using tens of real-world datasets to assess the representation quality on many downstream tasks, including classification, clustering, and anomaly detection. The results demonstrate the superiority of our method against not only URL competitors, but also techniques specially designed for downstream tasks. Our code has been made publicly available at https://github.com/real2fish/CSL.

Inducing Neural Collapse in Deep Long-tailed Learning

Although deep neural networks achieve tremendous success on various classification tasks, the generalization ability drops sheer when training datasets exhibit long-tailed distributions. One of the reasons is that the learned representations (i.e. features) from the imbalanced datasets are less effective than those from balanced datasets. Specifically, the learned representation under class-balanced distribution will present the Neural Collapse (NC) phenomena. NC indicates the features from the same category are close to each other and from different categories are maximally distant, showing an optimal linear separable state of classification. However, the pattern differs on imbalanced datasets and is partially responsible for the reduced performance of the model. In this work, we propose two explicit feature regularization terms to learn high-quality representation for class-imbalanced data. With the proposed regularization, NC phenomena will appear under the class-imbalanced distribution, and the generalization ability can be significantly improved. Our method is easily implemented, highly effective, and can be plugged into most existing methods. The extensive experimental results on widely-used benchmarks show the effectiveness of our method

Generative Oversampling for Imbalanced Data via Majority-Guided VAE

Learning with imbalanced data is a challenging problem in deep learning. Over-sampling is a widely used technique to re-balance the sampling distribution of training data. However, most existing over-sampling methods only use intra-class information of minority classes to augment the data but ignore the inter-class relationships with the majority ones, which is prone to overfitting, especially when the imbalance ratio is large. To address this issue, we propose a novel over-sampling model, called Majority-Guided VAE~(MGVAE), which generates new minority samples under the guidance of a majority-based prior. In this way, the newly generated minority samples can inherit the diversity and richness of the majority ones, thus mitigating overfitting in downstream tasks. Furthermore, to prevent model collapse under limited data, we first pre-train MGVAE on sufficient majority samples and then fine-tune based on minority samples with Elastic Weight Consolidation(EWC) regularization. Experimental results on benchmark image datasets and real-world tabular data show that MGVAE achieves competitive improvements over other over-sampling methods in downstream classification tasks, demonstrating the effectiveness of our method.

MTS-Mixers: Multivariate Time Series Forecasting via Factorized Temporal and Channel Mixing

Multivariate time series forecasting has been widely used in various practical scenarios. Recently, Transformer-based models have shown significant potential in forecasting tasks due to the capture of long-range dependencies. However, recent studies in the vision and NLP fields show that the role of attention modules is not clear, which can be replaced by other token aggregation operations. This paper investigates the contributions and deficiencies of attention mechanisms on the performance of time series forecasting. Specifically, we find that (1) attention is not necessary for capturing temporal dependencies, (2) the entanglement and redundancy in the capture of temporal and channel interaction affect the forecasting performance, and (3) it is important to model the mapping between the input and the prediction sequence. To this end, we propose MTS-Mixers, which use two factorized modules to capture temporal and channel dependencies. Experimental results on several real-world datasets show that MTS-Mixers outperform existing Transformer-based models with higher efficiency.

Ti-MAE: Self-Supervised Masked Time Series Autoencoders

Multivariate Time Series forecasting has been an increasingly popular topic in various applications and scenarios. Recently, contrastive learning and Transformer-based models have achieved good performance in many long-term series forecasting tasks. However, there are still several issues in existing methods. First, the training paradigm of contrastive learning and downstream prediction tasks are inconsistent, leading to inaccurate prediction results. Second, existing Transformer-based models which resort to similar patterns in historical time series data for predicting future values generally induce severe distribution shift problems, and do not fully leverage the sequence information compared to self-supervised methods. To address these issues, we propose a novel framework named Ti-MAE, in which the input time series are assumed to follow an integrate distribution. In detail, Ti-MAE randomly masks out embedded time series data and learns an autoencoder to reconstruct them at the point-level. Ti-MAE adopts mask modeling (rather than contrastive learning) as the auxiliary task and bridges the connection between existing representation learning and generative Transformer-based methods, reducing the difference between upstream and downstream forecasting tasks while maintaining the utilization of original time series data. Experiments on several public real-world datasets demonstrate that our framework of masked autoencoding could learn strong representations directly from the raw data, yielding better performance in time series forecasting and classification tasks.

Hyperbolic Curvature Graph Neural Network

Hyperbolic space is emerging as a promising learning space for representation learning, owning to its exponential growth volume. Compared with the flat Euclidean space, the curved hyperbolic space is far more ambient and embeddable, particularly for datasets with implicit tree-like architectures, such as hierarchies and power-law distributions. On the other hand, the structure of a real-world network is usually intricate, with some regions being tree-like, some being flat, and others being circular. Directly embedding heterogeneous structural networks into a homogeneous embedding space unavoidably brings inductive biases and distortions. Inspiringly, the discrete curvature can well describe the local structure of a node and its surroundings, which motivates us to investigate the information conveyed by the network topology explicitly in improving geometric learning. To this end, we explore the properties of the local discrete curvature of graph topology and the continuous global curvature of embedding space. Besides, a Hyperbolic Curvature-aware Graph Neural Network, HCGNN, is further proposed. In particular, HCGNN utilizes the discrete curvature to lead message passing of the surroundings and adaptively adjust the continuous curvature simultaneously. Extensive experiments on node classification and link prediction tasks show that the proposed method outperforms various competitive models by a large margin in both high and low hyperbolic graph data. Case studies further illustrate the efficacy of discrete curvature in finding local clusters and alleviating the distortion caused by hyperbolic geometry.

Hyperbolic Graph Representation Learning: A Tutorial

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to model complex patterns is essentially constrained by its polynomially growing capacity. Recently, hyperbolic spaces have emerged as a promising alternative for processing graph data with tree-like structure or power-law distribution, owing to the exponential growth property. Different from Euclidean space, which expands polynomially, the hyperbolic space grows exponentially which makes it gains natural advantages in abstracting tree-like or scale-free graphs with hierarchical organizations. In this tutorial, we aim to give an introduction to this emerging field of graph representation learning with the express purpose of being accessible to all audiences. We first give a brief introduction to graph representation learning as well as some preliminary Riemannian and hyperbolic geometry. We then comprehensively revisit the hyperbolic embedding techniques, including hyperbolic shallow models and hyperbolic neural networks. In addition, we introduce the technical details of the current hyperbolic graph neural networks by unifying them into a general framework and summarizing the variants of each component. Moreover, we further introduce a series of related applications in a variety of fields. In the last part, we discuss several advanced topics about hyperbolic geometry for graph representation learning, which potentially serve as guidelines for further flourishing the non-Euclidean graph learning community.