We tackle the problem of inferring node labels in a partially labeled graph where each node in the graph has multiple label types and each label type has a large number of possible labels. Our primary example, and the focus of this paper, is the joint inference of label types such as hometown, current city, and employers, for users connected by a social network. Standard label propagation fails to consider the properties of the label types and the interactions between them. Our proposed method, called EdgeExplain, explicitly models these, while still enabling scalable inference under a distributed message-passing architecture. On a billion-node subset of the Facebook social network, EdgeExplain significantly outperforms label propagation for several label types, with lifts of up to 120 for recall@1 and 60 for recall@3.
Many graph-based approaches can be viewed as estimating a function over the nodes of the graph, with the function being close to the observed labels, and smooth (similar) at adjacent nodes. Label propagation @cite_24 @cite_0 uses a quadratic function, but other penalties are also possible @cite_23 @cite_21 @cite_8 . Other approaches modify the random walk interpretation of label propagation @cite_13 @cite_31 . In order to handle a large number of distinct label values, the label assignments can be summarized using count-min sketches @cite_2 . None of the approaches consider interactions between multiple label types, and hence fail to capture the edge formation process in graphs considered here.
@cite_8 @cite_21 @cite_24 @cite_0 @cite_23 @cite_2 @cite_31 @cite_13
2007477772 2030703286 2109524159 1590313574
Graph-based approaches have been most successful in semisupervised learning. In this paper, we focus on label propagation in graph-based semisupervised learning. One essential point of label propagation is that the performance is heavily affected by incorporating underlying manifold of given data into the input graph. The other more important point is that in many recent real-world applications, the same instances are represented by multiple heterogeneous data sources. A key challenge under this setting is to integrate different data representations automatically to achieve better predictive performance. In this paper, we address the issue of obtaining the optimal linear combination of multiple different graphs under the label propagation setting. For this problem, we propose a new formulation with the sparsity (in coefficients of graph combination) property which cannot be rightly achieved by any other existing methods. This unique feature provides two important advantages: 1) the improvement of prediction performance by eliminating irrelevant or noisy graphs and 2) the interpretability of results, i.e., easily identifying informative graphs on classification. We propose efficient optimization algorithms for the proposed approach, by which clear interpretations of the mechanism for sparsity is provided. Through various synthetic and two real-world data sets, we empirically demonstrate the advantages of our proposed approach not only in prediction performance but also in graph selection ability. Given a graph G, a function f:V(G)->Z, and an initial 0 1-vertex-labelling c"1:V(G)-> 0,1 , we study an iterative 0 1-vertex-labelling process on G where in each round every vertex v never changes its label from 1 to 0, and changes its label from 0 to 1 if at least f(v) neighbours have label 1. Such processes model opinion disease spreading or fault propagation and have been studied under names such as irreversible threshold majority processes in a large variety of contexts. Our contributions concern computational aspects related to the minimum cardinality irr"f(G) of sets of vertices with initial label 1 such that during the process on G all vertices eventually change their label to 1. Such sets are known as irreversible conversion sets, dynamic irreversible monopolies, or catastrophic fault patterns. Answering a question posed by Dreyer and Roberts [P.A. Dreyer Jr., F.S. Roberts, Irreversible k-threshold processes: graph-theoretical threshold models of the spread of disease and of opinion, Discrete Appl. Math. 157 (2009) 1615-1627], we prove a hardness result for irr"f(G) where f(v)=2 for every [email protected]?V(G). Furthermore, we describe a general reduction principle for irr"f(G), which leads to efficient algorithms for graphs with simply structured blocks such as trees and chordal graphs. Transductive inference on graphs such as label propagation algorithms is receiving a lot of attention. In this paper, we address a label propagation problem on multiple networks and present a new algorithm that automatically integrates structure information brought in by multiple networks. The proposed method is robust in that irrelevant networks are automatically deemphasized, which is an advantage over Tsuda's approach (2005). We also show that the proposed algorithm can be interpreted as an expectation-maximization (EM) algorithm with a student-t prior. Finally, we demonstrate the usefulness of our method in protein function prediction and digit classification, and show analytically and experimentally that our algorithm is much more efficient than existing algorithms. We study the problem of predicting the labelling of a graph. The graph is given and a trial sequence of (vertex,label) pairs is then incrementally revealed to the learner. On each trial a vertex is queried and the learner predicts a boolean label. The true label is then returned. The learner’s goal is to minimise mistaken predictions. We propose minimum p-seminorm interpolation to solve this problem. To this end we give a p-seminorm on the space of graph labellings. Thus on every trial we predict using the labelling which minimises the p-seminorm and is also consistent with the revealed (vertex, label) pairs. When p = 2 this is the harmonic energy minimisation procedure of [22], also called (Laplacian) interpolated regularisation in [1]. In the limit as p → 1 this is equivalent to predicting with a label-consistent mincut. We give mistake bounds relative to a label-consistent mincut and a resistive cover of the graph. We say an edge is cut with respect to a labelling if the connected vertices have disagreeing labels. We find that minimising the p-seminorm with p = 1 + where → 0 as the graph diameter D → ∞ gives a bound of O(Φ logD) versus a bound of O(ΦD) when p = 2 where Φ is the number of cut edges.