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Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to many supervised learning problems such as link prediction and node classification and have demonstrated state-of-the-art performance. Yet, their properties remain poorly understood. This paper studies properties of random walk based node embeddings in the unsupervised setting of discovering hidden block structure in the network, i.e., learning node representations whose cluster structure in Euclidean space reflects their adjacency structure within the network. We characterize the ergodic limits of the embedding objective, its generalization, and related convex relaxations to derive corresponding non-randomiz
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while preserving relevan
Random-walk based network embedding algorithms like node2vec and DeepWalk are widely used to obtain Euclidean representation of the nodes in a network prior to performing down-stream network inference tasks. Nevertheless, despite their impressive emp
A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte Carlo techniq
Sorting input objects is an important step in many machine learning pipelines. However, the sorting operator is non-differentiable with respect to its inputs, which prohibits end-to-end gradient-based optimization. In this work, we propose NeuralSort
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learn