Learning First-Order Logic Embeddings via Matrix Factorization
Learning First-Order Logic Embeddings via Matrix Factorization
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发表时间：
2016-07
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通讯作者：
William Yang Wang;William W. Cohen
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作者：
William Yang Wang;William W. Cohen
人工智能中许多复杂的推理任务（包括关系提取、知识库补全和信息集成）都可以用概率一阶逻辑表述为推理问题。然而，由于逻辑事实和谓词的离散性，在概率关系模型中推广符号表示和表示一阶逻辑公式是具有挑战性的。在这项工作中，我们采取了一种相当激进的方法：我们的目标是从头开始学习一阶逻辑的连续低维嵌入。特别是，我们首先考虑基于结构梯度的结构学习方法，从事实中生成可信的推理公式；然后，我们使用背景事实、训练示例和这些推理公式构建接地证明图。为了学习公式的嵌入，我们将训练样本映射到二进制矩阵的行中，并将推理公式映射到列中。使用可扩展矩阵分解方法，我们然后通过低秩近似方法学习示例和逻辑公式的潜在连续表示。在实验中，我们通过比较两个数据集上几种最先进的基线，在知识库完成任务中证明了一阶逻辑嵌入推理的有效性。
Many complex reasoning tasks in Artificial Intelligence (including relation extraction, knowledge base completion, and information integration) can be formulated as inference problems using a probabilistic first-order logic. However, due to the discrete nature of logical facts and predicates, it is challenging to generalize symbolic representations and represent first-order logic formulas in probabilistic relational models. In this work, we take a rather radical approach: we aim at learning continuous low-dimensional embeddings for first-order logic from scratch. In particular, we first consider a structural gradient based structure learning approach to generate plausible inference formulas from facts; then, we build grounded proof graphs using background facts, training examples, and these inference formulas. To learn embeddings for formulas, we map the training examples into the rows of a binary matrix, and inference formulas into the columns. Using a scalable matrix factorization approach, we then learn the latent continuous representations of examples and logical formulas via a low-rank approximation method. In experiments, we demonstrate the effectiveness of reasoning with first-order logic embeddings by comparing with several state-of-the-art baselines on two datasets in the task of knowledge base completion.