Towards Knowledge Graph (KG) completion, probabilistic logic reasoning approaches enable effective rule mining but incur high computational cost, while embedding-based methods offer high efficiency but confront limited semantic understanding. Neuro-symbolic approaches combine both by employing embeddings to approximate probabilistic distributions, yet face challenges in weight optimization and hurdles in scaling up from large probability graphs. To address these issues, we propose DPLogic, a differentiable probabilistic logic reasoning framework for KG completion. Initially, we construct a Markov logic network by selecting crucial formulas and constraining groundings to relevant subgraphs, effectively boosting the scalability of the framework. Subsequently, we represent formula weights through relation-specific embeddings by introducing neural logical operators, creating a differentiable pathway for end-to-end optimization. Finally, we obtain the distribution of unobserved KG triplets by facilitating the joint optimization of embedding-based and probabilistic distributions through an EM algorithm. Empirical findings on standardized datasets illustrate that our proposed DPLogic consistently surpasses state-of-the-art methodologies in terms of both efficacy and efficiency.

Multivariate time series (MTS) forecasting is crucial for predicting the future states of complexly coupled variables based on historical observations. To effectively capture the intricate interdependencies within MTS, graph-based methods have emerged as powerful tools. However, existing graph construction methods often produce structures that fail to preserve key temporal and cross-variable dependencies, introducing redundant or irrelevant connections. To address these challenges, we propose a structural entropy-based approach for MTS forecasting. The approach optimizes graph structures by reducing structural redundancy, thereby improving forecasting accuracy. Initially, we represent the temporal dependences by constructing an encoding tree incrementally. Through hierarchical organization of time steps, the temporal evolution is adaptively captured. Subsequently, we give the community-aware representation by building an encoding tree over the variables in MTS, extracting homogeneous communities from the tree structure while integrating community influence to better capture inter-variable dependencies. Finally,we present a training algorithm designed to generate accurate predictions for MTS, accompanied by a unified loss function that integrates forecasting inaccuracies with variations in structural entropy. Empirical findings on real-world datasets substantiate that our approach outperforms state-of-the-art models in capturing dependencies and enhancing forecasting precision.

Bayesian Network (BN) has been widely employed for many applications like medical diagnosis due to its ability to deal with probabilistic inferences. Real-world inference tasks in BN cannot be robustly processed by classic search-based inference algorithms, since the conditional probabilities w.r.t. given arbitrary evidence values may be missing (i.e., not included) in the conditional probability tables (CPTs). Most of the existing methods, relying on imputation models, density estimation models or deep neural networks, cannot accurately learn these missing probabilities. To this end, we incorporate the idea of learning and search for robust probabilistic inferences in BN. Firstly, we decompose the probabilistic inference task into missing and existing probability factors, ensuring the consistency of their probability spaces. Secondly, we define the Wasserstein distance between missing and existing probability factors, and incorporate the idea of generative adversarial network to obtain missing probability factors with the minimal Wasserstein distance. Finally, we give the algorithm for robust probabilistic inferences with arbitrary evidence values, which could also be used to deal with the probabilistic inferences with arbitrary query values. Extensive experiments on synthetic and real-world datasets are conducted to demonstrate the superiority of our proposed method.

Bayesian network (BN) structure learning on the discrete observations is crucial for representing uncertainty in data. However, existing single-structure learning methods are commonly trapped in local optimum or yielding structures that may lead to poorly calibrated predictions. Although posterior approximation methods can quantify the epistemic uncertainty over the learned BN structures, they cannot reliably identify the optimal BN structures. To tackle these issues, we propose a GFlowNet with Gradient-based Optimization (GFlowOpt) for the BN structure learning method. Initially, we employ Bayesian Information Criterion (BIC) scores as the rewards of BN structures, and adopt a contrastive learning-based training technique on GFlowNet to efficiently generate much better DAG representations. Subsequently, we train a proxy model on the continuous DAG representations by adopting the gradient-ascent-based optimization method to search more high proxy-scoring discrete candidate DAGs. Finally, we adopt Hill Climbing (HC) on these candidate DAGs to search high-scoring DAGs as the ultimate BN structures. Extensive experiments conducted on benchmark datasets demonstrate that the superiority of our proposed method compared with other state-of-the-art methods.

As the critical task in query optimization, cardinality estimation is fulfilled by learning the joint probability distribution of table attributes in most of the existing data-driven methods. However, these methods still suffer the efficiency bottleneck, since the exponential combinations of table joins lead to massive probability inferences. To address this issue, we propose the Bayesian Probability Forest (BPF) framework to reduce the calculation of probability inferences. By integrating mutual information and query frequency, we first propose a novel metric to learn the graphical structure of BPF, ensuring that the distance between high-frequency attributes and root node could be minimized. Then, we propose an efficient method for cardinality estimation in BPF. Specifically, the decomposition of cardinality estimation task is proposed to reduce the number of probability inferences, and elimination strategies are given to avoid the redundant calculations w.r.t. low-frequency attributes. Empirical investigations on real-world datasets demonstrate the superiority of our method over other cutting-edge competitors. Our codes are publicly available at https://github.com/CardEstGroup/bpf-ce.git.

As a fundamental task in the graph machine learning paradigm, link prediction aims to predict missing links in a graph. Recently, Graph Neural Networks (GNNs) have demonstrated significant superiority in learning graph representations and become the mainstream solution for link prediction tasks. However, existing GNN-based methods may exhibit suboptimal performance due to their inability to effectively distinguish automorphic nodes with identical structures. To address this issue, we propose a hierarchical structure-enhanced graph representation framework for link prediction based on structural information theory. Specifically, we first design an efficient algorithm to construct an encoding tree from the input graph by minimizing its structural entropy. The encoding tree is a multi-level hierarchical abstraction of the graph, providing an effective way to organize both global (higher levels) and local (lower levels) structural information for each node. Then, we enhance node embeddings with the hierarchical structural encoding, capturing nuanced structural patterns for distinguishing automorphic nodes. Finally, we train GNN models at different levels of the encoding tree to generate powerful link representations for prediction. Extensive experiments on several real-world datasets demonstrate the effectiveness and scalability of our proposed method. Our code is available at https://github.com/Bayunmaoyu/HSELP.

Multivariate time series forecasting remains a critical yet challenging task across various real-world applications, due to the complex inter-series and intra-series dependencies. While time series decomposition has emerged as a powerful paradigm for capturing intricate temporal patterns, many existing methods fail to fully exploit the predictive potential of the trend component, often relying on fixed decomposition strategies that may retain unpredictable or noisy elements. To address these limitations, we propose a complexity-aware trend extraction method that adaptively controls the complexity of the extracted trend, yielding a more predictable and robust trend component, thereby significantly improving forecasting accuracy. To better model inter-series dependencies and reduce noise interference in variable interactions, we introduce an information-theoretic constraint by leveraging mutual information to regulate the flow of information across variables. Furthermore, our framework strategically incorporates future trend characteristics into the forecasting process through a cross-attention mechanism that queries informative historical patterns, enabling more accurate predictions. Extensive experiments conducted on several real-world datasets demonstrate the effectiveness and superiority of our proposed method compared with other state-of-the-art methods. Our code is available at https://github.com/unarytree/MTSF.

The task of finding associative entities in knowledge graph (KG) is to provide a ranking list of entities according to their association degrees. However, many entities are not only linked in KG but also associated in terms of user behaviors, which facilitates finding associative entities accurately. This manuscript incorporates KG with user-generated data to propose the Association Entity Graph Model (AEGM) to evaluate the association degrees. They first propose the joint weighting function to evaluate the entity associations and prove its submodularity theoretically as well as the greedy algorithm to select the candidates efficiently. They define the entity association information to score the entity association and give the hill climbing search based algorithm for AEGM construction. Following, they embed AEGM to calculate the association degrees and obtain the associative entities efficiently. Extensive experiments on three datasets show that the proposed method can achieve a better performance than some state-of-the-art competitors in accurately finding associative entities.

Bayesian network (BN) is a directed acyclic graph (DAG) representing the dependence relations among random variables with conditional probability tables (CPTs). The efficiency and accuracy of multiple probabilistic inferences in BN could not be guaranteed by most of the existing approximate inference methods. To address this issue, we propose the methods of Transformer based BN embedding (TBNE) and TBNE based probabilistic inferences. Specifically, we first adopt mutual information to measure the weight of parent-child node pairs and transform BN into multiple bidirectional weighted graphs (BWGs), while preserving the DAG and CPTs. Then, we redesign the Transformer model by incorporating the node importance and shortest path encodings, and extend the self-attention module of Transformer to generate node embeddings of BWGs. Following, we cast the probabilistic inference as the decoding information maximization of the path in BN from the perspective of information theory. Finally, we give an efficient algorithm for multiple probabilistic inferences by calculating embedding similarities between evidence and query nodes in BN. Experimental results show that our inference method is more efficient than the state-of-the-art competitors by several orders of magnitude while maintaining almost the same results.

Abstract Knowledge graph (KG) has become the vital resource for various applications like question answering and recommendation system. However, several relations in KG only have few observed triples, which makes it necessary to develop the method for few-shot relation prediction. In this paper, we propose the Convolutional Neural Network with Self-Attention Relation Prediction (CARP) model to predict new facts with few observed triples. First, to learn the relation property features, we build a feature encoder by using the convolutional neural network with self-attention from the few observed triples rather than background knowledge. Then, by incorporating the learned features, we give an embedding network to learn the representation of incomplete triples. Finally, we give the loss function and training algorithm of our CARP model. Experimental results on three real-world datasets show that our proposed method improves Hits@10 by 48% on average over the state-of-the-art competitors.

Recent advances in localization techniques have fundamentally enhanced social networking services, allowing users to share their locations and location-related contents. This has further increased the popularity of location-based social networks (LBSNs) and produces a huge amount of trajectories composed of continuous and complex spatio-temporal points from people’s daily lives. How to accurately aggregate large-scale trajectories is an important and challenging task. Conventional clustering algorithms (e.g., k -means or k -mediods) cannot be directly employed to process trajectory data due to their serialization, triviality and redundancy. Aiming to overcome the drawbacks of traditional k -means algorithm and k -mediods, including their sensitivity to the selection of the initial k value, the cluster centers and easy convergence to a locally optimal solution, we first propose an optimized k -means algorithm (namely OKM ) to obtain k optimal initial clustering centers based on the density of trajectory points. Second, because k -means is sensitive to noisy points, we propose an improved k -mediods algorithm called IKMD based on an acceptable radius r by considering users’ geographic location in LBSNs. The value of k can be calculated based on r , and the optimal k points are selected as the initial clustering centers with high densities to reduce the cost of distance calculation. Thirdly, we thoroughly analyze the advantages of IKMD by comparing it with the commonly used clustering approaches through illustrative examples. Last, we conduct extensive experiments to evaluate the performance of IKMD against seven clustering approaches including the proposed optimized k -means algorithm, k -mediods algorithm, traditional density-based k -mediods algorithm and the state-of-the-arts trajectory clustering methods. The results demonstrate that IKMD significantly outperforms existing algorithms in the cost of distance calculation and the convergence speed. The methods proposed is proved to contribute to a larger effort targeted at advancing the study of intelligent trajectory data analytics.

Bike-sharing systems are becoming popular and generate a large volume of trajectory data. In a bike-sharing system, users can borrow and return bikes at different stations. In particular, a bike-sharing system will be affected by weather, the time period, and other dynamic factors, which challenges the scheduling of shared bikes. In this article, a new shared-bike demand forecasting model based on dynamic convolutional neural networks, called SDF , is proposed to predict the demand of shared bikes. SDF chooses the most relevant weather features from real weather data by using the Pearson correlation coefficient and transforms them into a two-dimensional dynamic feature matrix, taking into account the states of stations from historical data. The feature information in the matrix is extracted, learned, and trained with a newly proposed dynamic convolutional neural network to predict the demand of shared bikes in a dynamical and intelligent fashion. The phase of parameter update is optimized from three aspects: the loss function, optimization algorithm, and learning rate. Then, an accurate shared-bike demand forecasting model is designed based on the basic idea of minimizing the loss value. By comparing with classical machine learning models, the weight sharing strategy employed by SDF reduces the complexity of the network. It allows a high prediction accuracy to be achieved within a relatively short period of time. Extensive experiments are conducted on real-world bike-sharing datasets to evaluate SDF. The results show that SDF significantly outperforms classical machine learning models in prediction accuracy and efficiency.