Graph representation learning has been extensively studied in recent years. Despite its potential in generating continuous embeddings for various networks, both the effectiveness and efficiency to infer high-quality representations toward large corpus of nodes are still challenging. Sampling is a critical point to achieve the performance goals. Prior arts usually focus on sampling positive node pairs, while the strategy for negative sampling is left insufficiently explored. To bridge the gap, we systematically analyze the role of negative sampling from the perspectives of both objective and risk, theoretically demonstrating that negative sampling is as important as positive sampling in determining the optimization objective and the resulted variance. To the best of our knowledge, we are the first to derive the theory and quantify that the negative sampling distribution should be positively but sub-linearly correlated to their positive sampling distribution. With the guidance of the theory, we propose MCNS, approximating the positive distribution with self-contrast approximation and accelerating negative sampling by Metropolis-Hastings. We evaluate our method on 5 datasets that cover extensive downstream graph learning tasks, including link prediction, node classification and personalized recommendation, on a total of 19 experimental settings. These relatively comprehensive experimental results demonstrate its robustness and superiorities.
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