Quantifying uncertainty is important for actionable predictions in real-world applications.

Random walks are key components of many machine learning algorithms with applications in computing graph partitioning [ST04, GKL+21], spectral embeddings [CPS15, CKK+18], or network inference [HMMT18], as well as learning image segmentation [MS00], ranking nodes in a graph [AC07] and many other applications.

The excess risk bound achieves the so-called fast learning rate.

We can verify that all of above complexity (nearly) matches the corresponding lower bounds.