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.

Mining the associations of electricity-carbon emission influencing factors is the basis for accurate prediction of carbon emissions. Traditional methods adopt statistical analysis of historical data to quantify the associations between electricity-carbon emission and various influencing factors. However, these methods still face challenges such as low accuracy and the inability to systematically incorporate domain knowledge when applied to large-scale electricity-carbon data. In this paper, we propose a knowledge graph (KG) based method for mining electricity-carbon emission influencing factors, starting from the question text that expresses the task of factor mining. Specifically, we first obtain the surrounding entities and relations in the electricity-carbon KG w.r.t. the topical entity in the question text, such that associative relations can be obtained and referred to as contextual relations. By incorporating the graph attention network, we enhance the base candidate sequence by adding more important contextual relations. Next, we give the idea for matching the given question and candidate relations via feedforward neural network and long short-term memory network. Ultimately, we present the training algorithm by max-pooling for feature vectors that reflect the matching degree to obtain a matching score. Entities in the sequences with higher scores, representing the most relevant carbon emission influencing factor, constitute the answer set. Experimental results verify the effectiveness of our proposed method.

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.