SHADOWCAST: CONTROLLABLE GRAPH GENERA-TION WITH EXPLAINABILITY

Abstract

We introduce the problem of explaining graph generation, formulated as controlling the generative process to produce desired graphs with explainable structures. By directing this generative process, we can explain the observed outcomes. We propose SHADOWCAST, a controllable generative model capable of mimicking networks and directing the generation, as an approach to this novel problem. The proposed model is based on a conditional generative adversarial network for graph data. We design it with the capability to control the conditions using a simple and transparent Markov model. Comprehensive experiments on three real-world network datasets demonstrate our model's competitive performance in the graph generation task. Furthermore, we control SHADOWCAST to generate graphs of different structures to show its effective controllability and explainability. As the first work to pose the problem of explaining generated graphs by controlling the generation, SHADOWCAST paves the way for future research in this exciting area.

1. INTRODUCTION

In many real-world networks, including but not limited to communication, financial, and social networks, graph generative models are applied to model relationships among actors. It is crucial that the models not only mimic the structure of observed networks but also generate graphs with desired properties because it allows for an increased understanding of these relationships. Currently, there are no such methods for explaining graph generation. Meaningful interactions between agents are often investigated under different what-if scenarios, which determines the feasibility of the interactions under abnormal and unforeseen circumstances. In such investigations, instead of using actual data, we can generate synthetic data to study and test the systems (Barse et al., 2003; Skopik et al., 2014) . However, there are many challenges. (1) Data is not accessible by direct measurement of the system. (2) Data is not available. (3) Data produced by generative models cannot be explained. To address these challenges, we have to answer a natural and meaningful question: Can we control the generative process to shape and explain the generated graphs? In this work, we introduce the novel problem of explaining graph generation. The goal is to generate graphs of desired shapes by learning to control the associated graph properties and structure to influence the generative process. We provide an illustrative case study of email communications in an organization with two departments (Figure 1 ), where interactions of the employees follow a regular pattern during normal operations. Due to limited data, previously observed network information may be missing scenarios of intra-department email surge within either the Human Resources or Accounting departments. When such situations are required for analyzing the system, an ideal model should generate graphs that reflect these scenarios (see box in Figure 1 ) while maintaining the organizational structure. By effectively controlling the generative process, SHADOWCAST allows users to generate designed graphs that meet conditions resembling a wide range of possibilities. Overall, this is a meaningful problem because controlling the generative process to explain generated networks proves to be valuable in many applications such as anomaly detection and data augmentation. Existing graph generative models aim to mimic the structure of given networks, but they cannot easily shape graphs into other desired states. These works either directly capture the graph structure (Cao & Kipf, 2018; Liu et al., 2017; Tavakoli et al., 2017; Zhou et al., 2019; Ma et al., 2018; You et al., 2018; Simonovsky & Komodakis, 2018; Bojchevski et al., 2018) or model node feature While there are no existing methods for explaining graph generation, studies of explainability in other AI methods are increasing in popularity. One family of work, proxy methods (Huysmans et al., 2011; Augasta & Kathirvalavakumar, 2011; Zilke et al., 2016; Lakkaraju et al., 2017) , learns to approximate model predictions with simpler surrogate models. Another line of work (Adadi & Berrada, 2018; Guidotti et al., 2018; Koh & Liang, 2017) treats models as black-boxes and carefully queries them for relevant information to form interpretations of the results. The works closest to our problem are in interpretable Graph Neural Network (GNN) models, where models predict and assign values to edges via attention mechanisms (Veličković et al., 2018; Neil et al., 2018; Xie & Grossman, 2018) . Notably, even the latest work (Ying et al., 2019) , which considers both graph structure and node feature information, still only explains predictions of individual nodes but cannot produce explanations for entire graphs. We propose SHADOWCAST, an approach for explaining graph generation, which addresses the challenge of generating graphs with user-desired structures. It is achieved by using easy-to-understand node properties that are intended to capture graph semantics in an explicable way. These properties form the shadow that we control in order to guide the graph generative process. The model architecture is essentially based on conditional GANs (Mirza & Osindero, 2014) . The model introduces control by leveraging the conditions, which we manage with a transparent Markov model, as a control vector to influence the generative process. It allows for user-specified parameters such as density distributions to generate designed graphs that are explainable. Finally, the generator captures essential graph structures while exploring a myriad of other possibilities in multifarious networks. We first evaluate SHADOWCAST on three real-world social and information networks to demonstrate its competitive performance against several state-of-the-art graph generation methods in mimicking given graphs. Our model achieves impressive results that are superior in most datasets. In addition, we demonstrate the capability of SHADOWCAST to produce customizable synthetic graphs through tunable parameters, which existing generative models are incapable of performing.

2. EXPLAINABLE GRAPH GENERATION

In this section, we describe the explainable graph generation problem. The core idea of the problem lies in generating graphs of desired structures through control of node properties as a form of explainability. We define these properties and its structure as a shadow and introduce our approach SHADOWCAST. Since it is a challenge to directly control the generation of graphs due to their complex interconnected nature, we model them through shadows, which can be manipulated to control the graph generation. We depict the problem and our approach in detail below (Sections 2.1 and 2.2).



Figure 1: Case study illustration of explaining controlled generation: Many times, data of various situations are not available in observed real-world networks. SHADOWCAST allows us to generate graphs of desired structures and provide explanations for the generations.

