This paper studies speculative reasoning task on real-world knowledge graphs (KG) that contain both \textit{false negative issue} (i.e., potential true facts being excluded) and \textit{false positive issue} (i.e., unreliable or outdated facts being included).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 \textit{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.

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