Supervised Nested PageRank

Learning Supervised PageRank with Gradient-Free Optimization Methods

“…We denote m = m 1 + m 2 and ϕ = (ϕ 1 , ϕ 2 ) T . Let us describe the random walk on the graph Γ, which was considered in [21]. The…”

“…If it is non-zero, then the position of the node i 1 according to our ranking algorithm is higher than the position of the node i 2 but j 1 > j 2 . We consider square loss with margins b j1j2 > 0, where 1 ≤ j 2 < j 1 ≤ k: h(j 1 , j 2 , x) = (min{x + b j1j2 , 0}) 2 as it was done in previous studies [12,21,22]. We minimize…”

“…In contrast, a number of approaches allows to account for different properties of nodes and edges between them by encoding them in restart and transition probabilities (see [3,4,6,10,12,20,21]). These properties may include, e.g., the statistics about users' interactions with the nodes (in web graphs [12] or graphs of social networks [2]), types of edges (such as URL redirecting in web graphs [20]) or histories of nodes' and edges' changes [22].…”

“…Particularly, the transition probabilities in BrowseRank algorithm [12] are proportional to weights of edges which are equal to numbers of users' transitions. In the general ranking framework called Supervised PageRank [21], weights of nodes and edges in a graph are linear combinations of their features with coefficients as the model parameters. The authors consider an optimization problem for learning the parameters and solve it by a gradient-based optimization method.…”

“…In our paper, we consider the optimization problem from [21] and propose a two-level method to solve it. On the lower level, we use the linearly convergent method from [17] to calculate an approximation to the stationary distribution of the Markov process.…”