Noisy Positive-Unlabeled Learning with Self-Training for Speculative Knowledge Graph Reasoning (2023)

Abstract: This paper studies speculative reasoning task on real-world knowledge graphs (KG) that contain both false negative issue (i.e., potential true facts being excluded) and false positive issue (i.e., unreliable or outdated facts being included). State-of-the-art methods fall short in the speculative reasoning ability, as they assume the correctness of a fact is solely determined by its presence in KG, making them vulnerable to false negative/positive issues. The new reasoning task is formulated as a noisy Positive-Unlabeled learning problem. We propose a variational framework, namely nPUGraph, that jointly estimates the correctness of both collected and uncollected facts (which we call label posterior) and updates model parameters during training. The label posterior estimation facilitates speculative reasoning from two perspectives. First, it improves the robustness of a label posterior-aware graph encoder against false positive links. Second, it identifies missing facts to provide high-quality grounds of reasoning. They are unified in a simple yet effective self-training procedure. Empirically, extensive experiments on three benchmark KG and one Twitter dataset with various degrees of false negative/positive cases demonstrate the effectiveness of nPUGraph.

## introduction knowledge graphs (kg), which store real-world facts in triples (head entity, relation, tail entity), have facilitated a wide spectrum of knowledgeintensive applications @xcite @xcite @xcite . automatically reasoning facts based on observed ones, a.k.a. knowledge graph reasoning (kgr) @xcite , becomes increasingly vital since it allows for expansion of the existing kg at a low cost. numerous efforts have been devoted to kgr task @xcite @xcite @xcite , which assume the correctness of a fact is solely determined by its presence in kg. they ideally view facts included in kg as positive samples and excluded facts as negative samples. however, most real-world reasoning has to be performed based on sparse and unreliable observations, where there may be true facts excluded or false facts included. reasoning facts based on sparse and unreliable observations (which we call speculative kg reasoning) are still underexplored. in this paper, we aim to enable the speculative reasoning ability on real-world kg. the fulfillment of the goal needs to address two commonly existing issues, as shown in figure 1: 1) the false negative issue (i.e., sparse observation): due to the graph incompleteness, facts excluded from the kg can be used as implicit grounds of reasoning. this is particularly applicable to non-obvious facts. for example, personal information such as the birthplace of politicians may be missing when constructing a political kg, as they are not explicitly stated in the political corpus @xcite . however, it can be critical while reasoning personal facts like nationality. 2) the false positive issue (i.e., noisy observation): facts included in the kg may be unre-liable and should not be directly grounded without inspection. it can happen when relations between entities are incorrectly collected or when facts are extracted from outdated or unreliable sources. for example, mary elizabeth is no longer the prime minister of the united kingdom, which may affect the reasoning accuracy of her current workplace. these issues generally affect both one-hop reasoning @xcite and multi-hop reasoning @xcite . the main focus of this paper is investigating the one-hop speculative reasoning task as it lays the basis for complicated multi-hop reasoning capability. speculative kg reasoning differs from conventional kg reasoning in that the correctness of each collected/uncollected fact needs to be dynamically estimated as part of the learning process, such that the grounds of reasoning can be accordingly calibrated. unfortunately, most existing work, if not all, lacks such inspection capability. knowledge graph embedding methods @xcite @xcite @xcite and graph neural network (gnn) methods @xcite @xcite @xcite can easily overfit the false negative/positive cases because of their training objective that ranks the collected facts higher than other uncollected facts in terms of plausibility. recent attempts on uncertain kg @xcite measure the uncertainty scores for facts, which can be utilized to detect false negative/positive samples. however, they explicitly require the ground truth uncertainty scores as supervision for reasoning model training, which are usually unavailable in practice. motivated by these observations, we formulate the speculative kg reasoning task as a noisy positive-unlabeled learning problem. the facts contained in the kg are seen as noisy positive samples with a certain level of label noise, and the facts excluded from the kg are treated as unlabeled samples, which include both negative ones and possible factual ones. instead of determining the correctness of facts before training the reasoning model without inspection, we learn the two perspectives in an end-to-end training process. to this end, we propose npugraph, a novel variational framework that regards the underlying correctness of collected/uncollected facts in the kg as latent variables for the reasoning process. we jointly update model parameters and estimate the posterior likelihood of the correctness of each collected/uncollected fact (referred to as label posterior), through maximizing a theoretical lower bound of the log-likelihood of each fact being collected or uncollected. the estimated label posterior further facilitates the speculative kg reasoning from two aspects: 1) it removes false positive facts contained in kg and improves the representation quality. we accordingly propose a label posterior-aware encoder to incorporate information only from entity neighbors induced by facts with a high posterior probability, under the assumption that the true positive facts from the collected facts provide more reliable information for reasoning. 2) it complements the grounds of reasoning by selecting missing but possibly plausible facts with high label posterior, which are iteratively added to acquire more informative samples for model training. these two procedures are ultimately unified in a simple yet effective self-training strategy that alternates between the data sampling based on latest label posteriors and the model training based on latest data samples. empirically, npugraph outperforms eleven state-of-the-art baselines on three benchmark kg data and one twitter data we collected by large margins. additionally, its robustness is demonstrated in speculative reasoning on data with multiple ratios of false negative/positive cases. our contributions are summarized as follows: (1) we open up a practical but underexplored problem space of speculative kg reasoning, and formulate it as a noisy positive-unlabeled learning task; (2) we take the first step in tackling this problem by proposing a variational framework npu-graph to jointly optimize reasoning model parameters and estimate fact label posteriors; (3) we propose a simple yet effective self-training strategy for npugraph to simultaneously deal with false negative/positive issues; (4) we perform extensive evaluations to verify the effectiveness of npugraph on both benchmark kg and twitter interaction data with a wide range of data perturbations. ## conclusion we studied speculative kg reasoning based on sparse and unreliable observations, which contains both false negative issue and false positive issue. we formulated the task as a noisy positive-unlabeled learning problem and proposed a variational framework npugraph to jointly update model parameters and estimate the posterior likelihood of collected/uncollected facts being true or false, where the underlying correctness is viewed as latent variables. during the training process, a label posterior-aware encoder and a self-training strategy were proposed to further address the false positive/negative issues. we found label posterior estimation plays an important role in moving toward speculative kg reasoning in reality, and the estimation can be fulfilled by optimizing an alternative objective without additional cost. extensive experiments verified the effectiveness of npugraph on both benchmark kgs and twitter interaction data with various degrees of data perturbations.