arXiv subjects
Publications and source records attributed to Maxim Zhukovskii.
In the paper we investigate power law for PageRank components for the Buckley-Osthus model for web graph. We compare different numerical methods for PageRank calculation. With the best method we do a lot of numerical experiments. These experiments confirm the hypothesis about power law. At the end we discuss real model of web-ranking based on the classical PageRank approach.
In this paper, we consider a non-convex loss-minimization problem of learning Supervised PageRank models, which can account for some properties not considered by classical approaches such as the classical PageRank model. We propose gradient-based and random gradient-free methods to solve this problem. Our algorithms are based on the concept of an inexact oracle and unlike the state state-of-the-art gradient-based method we manage to provide theoretically the convergence rate guarantees for both of them. In particular, under the assumption of local convexity of the loss function, our random gradient-free algorithm guarantees decrease of the loss function value expectation. At the same time, we theoretically justify that without convexity assumption for the loss function our gradient-based algorithm allows to find a point where the stationary condition is fulfilled with a given accuracy. For both proposed optimization algorithms, we find the settings of hyperparameters which give the lowest complexity (i.e., the number of arithmetic operations needed to achieve the given accuracy of the solution of the loss-minimization problem). The resulting estimates of the complexity are also provided. Finally, we apply proposed optimization algorithms to the web page ranking problem and compare proposed and state-of-the-art algorithms in terms of the considered loss function.
In this paper, we consider a problem of learning supervised PageRank models, which can account for some properties not considered by classical approaches such as the classical PageRank algorithm. Due to huge hidden dimension of the optimization problem we use random gradient-free methods to solve it. We prove a convergence theorem and estimate the number of arithmetic operations needed to solve it with a given accuracy. We find the best settings of the gradient-free optimization method in terms of the number of arithmetic operations needed to achieve given accuracy of the objective. In the paper, we apply our algorithm to the web page ranking problem. We consider a parametric graph model of users' behavior and evaluate web pages' relevance to queries by our algorithm. The experiments show that our optimization method outperforms the untuned gradient-free method in the ranking quality.