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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Personalized PageRank to a Target Node
Peter Lofgren, Ashish Goel · 2013-04-17 · via cs.DS updates on arXiv.org

Personalalized PageRank uses random walks to determine the importance or authority of nodes in a graph from the point of view of a given source node. Much past work has considered how to compute personalized PageRank from a given source node to other nodes. In this work we consider the problem of computing personalized PageRanks to a given target node from all source nodes. This problem can be interpreted as finding who supports the target or who is interested in the target. We present an efficient algorithm for computing personalized PageRank to a given target up to any given accuracy. We give a simple analysis of our algorithm's running time in both the average case and the parameterized worst-case. We show that for any graph with $n$ nodes and $m$ edges, if the target node is randomly chosen and the teleport probability $α$ is given, the algorithm will compute a result with $ε$ error in time $O\left(\frac{1}{αε} \left(\frac{m}{n} + \log(n)\right)\right)$. This is much faster than the previously proposed method of computing personalized PageRank separately from every source node, and it is comparable to the cost of computing personalized PageRank from a single source. We present results from experiments on the Twitter graph which show that the constant factors in our running time analysis are small and our algorithm is efficient in practice.