Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs that is differentiable and compatible with recent advances in link prediction algorithms. Informally, the Kolmogorov complexity of an object is the length of the shortest computer program that produces the object. Complex networks are often generated, in part, by simple mechanisms; for example, many citation networks and social networks are approximately scale-free and can be explained by preferential attachment. A preference for predicting graphs with simpler generating mechanisms motivates our choice of Kolmogorov complexity as a regularization term. In our experiments the regularization method shows good performance on many diverse real-world networks, however we determine that this is likely due to an aggregation method rather than any actual estimation of Kolmogorov complexity.
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