Learning to compare two objects are essential in applications, such as digital forensics, face recognition, and brain network analysis, especially when labeled data is scarce and imbalanced. As these applications make high-stake decisions and involve societal values like fairness and transparency, it is critical to explain the learned models. We aim to study post-hoc explanations of Siamese networks (SN) widely used in learning to compare. We characterize the instability of gradient-based explanations due to the additional compared object in SN, in contrast to architectures with a single input instance. We propose an optimization framework that derives global invariance from unlabeled data using self-learning to promote the stability of local explanations tailored for specific query-reference pairs. The optimization problems can be solved using gradient descent-ascent (GDA) for constrained optimization, or SGD for KL-divergence regularized unconstrained optimization, with convergence proofs, especially when the objective functions are nonconvex due to the Siamese architecture. Quantitative results and case studies on tabular and graph data from neuroscience and chemical engineering show that the framework respects the self-learned invariance while robustly optimizing the faithfulness and simplicity of the explanation. We further demonstrate the convergence of GDA experimentally.
We consider the problem of efficiently inferring interventional distributions in a causal Bayesian network from a finite number of observations. Let $\mathcal{P}$ be a causal model on a set $\mathbf{V}$ of observable variables on a given causal graph $G$. For sets $\mathbf{X},\mathbf{Y}\subseteq \mathbf{V}$, and setting ${\bf x}$ to $\mathbf{X}$, let $P_{\bf x}(\mathbf{Y})$ denote the interventional distribution on $\mathbf{Y}$ with respect to an intervention ${\bf x}$ to variables ${\bf x}$. Shpitser and Pearl (AAAI 2006), building on the work of Tian and Pearl (AAAI 2001), gave an exact characterization of the class of causal graphs for which the interventional distribution $P_{\bf x}({\mathbf{Y}})$ can be uniquely determined. We give the first efficient version of the Shpitser-Pearl algorithm. In particular, under natural assumptions, we give a polynomial-time algorithm that on input a causal graph $G$ on observable variables $\mathbf{V}$, a setting ${\bf x}$ of a set $\mathbf{X} \subseteq \mathbf{V}$ of bounded size, outputs succinct descriptions of both an evaluator and a generator for a distribution $\hat{P}$ that is $\varepsilon$-close (in total variation distance) to $P_{\bf x}({\mathbf{Y}})$ where $Y=\mathbf{V}\setminus \mathbf{X}$, if $P_{\bf x}(\mathbf{Y})$ is identifiable. We also show that when $\mathbf{Y}$ is an arbitrary set, there is no efficient algorithm that outputs an evaluator of a distribution that is $\varepsilon$-close to $P_{\bf x}({\mathbf{Y}})$ unless all problems that have statistical zero-knowledge proofs, including the Graph Isomorphism problem, have efficient randomized algorithms.
Graph neural networks (GNN) have been successful in many fields, and derived various researches and applications in real industries. However, in some privacy sensitive scenarios (like finance, healthcare), training a GNN model centrally faces challenges due to the distributed data silos. Federated learning (FL) is a an emerging technique that can collaboratively train a shared model while keeping the data decentralized, which is a rational solution for distributed GNN training. We term it as federated graph learning (FGL). Although FGL has received increasing attention recently, the definition and challenges of FGL is still up in the air. In this position paper, we present a categorization to clarify it. Considering how graph data are distributed among clients, we propose four types of FGL: inter-graph FL, intra-graph FL and graph-structured FL, where intra-graph is further divided into horizontal and vertical FGL. For each type of FGL, we make a detailed discussion about the formulation and applications, and propose some potential challenges.
Yuzhou Chen, Ignacio Segovia-Domínguez, Yulia R. Gel
There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.
Despite the advantages of Federated Learning (FL), such as devolving model training to intelligent devices and preserving data privacy, FL still faces the risk of the single point of failure and attack from malicious participants. Recently, blockchain is considered a promising solution that can transform FL training into a decentralized manner and improve security during training. However, traditional consensus mechanisms and architecture for blockchain can hardly handle the large-scale FL task due to the huge resource consumption, limited throughput, and high communication complexity. To this end, this paper proposes a two-layer blockchain-driven FL framework, called as ChainsFL, which is composed of multiple Raft-based shard networks (layer-l) and a Direct Acyclic Graph (DAG)-based main chain (layer-2) where layer-l limits the scale of each shard for a small range of information exchange, and layer-2 allows each shard to update and share the model in parallel and asynchronously. Furthermore, FL procedure in a blockchain manner is designed, and the refined DAG consensus mechanism to mitigate the effect of stale models is proposed. In order to provide a proof-of-concept implementation and evaluation, the shard blockchain base on Hyperledger Fabric is deployed on the self-made gateway as layer-l, and the self-developed DAG-based main chain is deployed on the personal computer as layer-2. The experimental results show that ChainsFL provides acceptable and sometimes better training efficiency and stronger robustness comparing with the typical existing FL systems.
Single- or multi-layer perceptrons, commonly known as neural networks, are universal approximators that can approximate any continuous functions arbitrarily well when the number of perceptrons is allowed to grow indefinitely. When prior knowledge about the target function is available, constraints can be imposed on the neural network to improve approximation accuracy. As an example, it is well known that convolutional neural networks (CNN) \cite{lecun1990handwritten} yield good performance on image classification. And its parameter-sharing scheme can also reduce the risk of overfitting. One of the key properties of image classification is that it is invariant to translation of input image. The translation invariance in CNN is achieved with two steps. On the one hand, the convolutional layer gives a translation equivariance as it is a linear time invariant system. The translation of the input image will be kept as a transformation of the output. On the other hand, the pooling layer will introduce local invariance. The stack of convolutional layers and pooling layers will then reach a receptive field the same size as input and also enforces global invariance. Inspired by the success of CNN on image related tasks, plenty of CNN generalizations \cite{gens2014deep, henaff2015deep, simonovsky2017dynamic, cohen2018spherical,chidester2018rotation} have been studied in other tasks. \emph{Domain invariance}, which refers to the property that the output is invariant to certain transformation of the input features is a crucial property which can help to generalize CNN to other machine learning applications. The works which introduce domain invariance fall into two categories. One of the categories introduces the invariance by injecting invariant constrains. The other category builds the equivariant network layer then achieves invariance by applying the pooling or normalization layer. In the equivariant network layer, the input is transformed by some group transformation the output is transformed correspondingly. As in the CNN example, the invariance can be achieved by first using equivariant layers then apply the pooling layer. In this dissertation, we will focus on the invariance and equivariance of neural networks and analyze the neural network architecture which can achieve invariance or equivariance. The main works can be summarized as following. \noindent\textbf{The Connections Between Convolutional Architecture and Equivariant Property} Convolutional neural networks have achieved great success in speech, image, and video signal processing tasks in recent years. There have been several attempts to justify the convolutional architecture and to generalize the convolution operation for treatment of other data types such as graphs and manifolds. Based on group representation theory and noncommutative harmonic analysis, it has recently been shown that the so-called group equivariance requirement of a feed-forward neural network necessitates the convolutional architectures. In our work, based on the familiar concepts of linear time-invariant systems, we develop an elementary proof of the same result. The nonlinear activation function, being a necessary components of practical deep neural networks, has been glossed over in previous analyses of the connection between equivariance and convolution. We identify sufficient conditions for the non-linear activation functions to preserve equivariance, and hence the necessity of the group convolution structure. Our analysis method is simple and intuitive, and holds the potential to be applied to more challenging scenarios such as non-transitive domains and multiple simultaneous equivariances. \noindent\textbf{Characteristics of Generalized Convolutional Neural Networks} Based on the analysis method above, a theoretical support for details of network architecture design is then provided in our work. We first analyze the necessary and sufficient condition for a neural network to be group equivariant when the group acts on the sub-domain of input/output. This part gives a theoretical support for how should we combine channels in a neural network layer. Meanwhile, it also gives guidelines for designing neural networks with partial equivariance/invariance. To further investigate the characteristics of generalized convolutional neural networks, we then analyze the multiple equivariance case. The result shows the connection between model parameter sharing and equivariant property. In particular, we find that a model will have more parameter sharing if more equivariances are required. Meanwhile, we establish a universality result for shallow and deep generalized group convolutional neural networks as approximators of continuous group-equivariant functions. After choosing the network architecture, one common question we need to answer is that how many neurons do we want in our hidden layer? We show that the generalized convolution mapping to a quotient space is a projection of the image of a generalized convolution which maps to the maximum quotient space. This can be used to obtain guidelines for choosing the feature size of hidden layer. \noindent\textbf{Neural Networks with Invariant Properties} In the traditional convolutional neural networks, the spatial invariant properties are introduced by adding a global pooling layer after the convolutional layers. For some specific applications, there are still some potential for us to further reduce the model complexity by introduce invariant property in earlier layers. An partial permutation invariant model for learning graph node embedding is introduced based on the classical invariant theory. In the image processing application, an affine equivariant preprocessing method is proposed to build neural networks invariant to affine transformation. \noindent\textbf{Partially Permutation Invariant Graph Node Embedding Model} Graph node embedding aims at learning a vector representation for all nodes given a graph. It is a central problem in many machine learning tasks (e.g., node classification, recommendation, community detection). The key problem in graph node embedding lies in how to define the dependence to neighbors. Existing approaches specify (either explicitly or implicitly) certain dependencies on neighbors, which may lead to loss of subtle but important structural information within the graph and other dependencies among neighbors. This intrigues us to ask the question: can we design a model to give the maximal flexibility of dependencies to each node's neighborhood. In our recent work, we propose a novel graph node embedding method (named \textbf{\OM}) via a novel notion of \textit{partial permutation invariant set function}, to capture any possible dependence. The partial permutation invariant set function is designed based on the set of \textit{invariant basis} with respect to permutation group. Our method 1) can learn an \textit{arbitrary} form of the representation function from the neighborhood, without losing any potential dependence structures, and 2) is applicable to both homogeneous and heterogeneous graph embedding, the latter of which is challenged by the diversity of node types. Furthermore, we provide theoretical guarantee for the representation capability of our method for general homogeneous and heterogeneous graphs. Empirical evaluation results on benchmark data sets show that our proposed {\OM} method outperforms the state-of-the-art approaches on producing node vectors for various learning tasks of both homogeneous and heterogeneous graphs. \noindent\textbf{Learning Models Invariant to Affine Transformations for Image Processing} The way designing invariant/partial invariant neural networks with invariant basis is difficult to extend to groups other than permutation group. Because the invariant basis is expensive to calculate. Even if we get the set of invariant basis, it will be very large and is not helpful to reduce model complexity. An alternative which can introduce invariant property to neural network is adding an equivariant transformer as a pre-processing layer. This equivariant transformer will revert all the affine transformations happens in the input. Thus the model will be invariant to affine transformations. Invariance to affine transformations is desirable property for many computer vision tasks like image classification and motion tracking. Enforcing and taking advantage of such affine invariance property is an essential part for building efficient models for machine learning. However, it has been challenging to build models that are provably affine invariant. Previous works have achieved partial invariance, such as invariance to shifting and to rotation. We propose to build an affine-invariant model in two steps. First, we apply image normalization, which renders the density function represented by the image to have zero mean and identity covariance matrix. The resulting normalized image is then processed by a second stage neural network that is either an equivariant transformer network (ETN) or group convolution networks. We provide proof of invariance and demonstrate the performance improvement of such neural networks in processing images that have been affine transformed.
This chapter considers the contributions that may be made to the evolution of an ethical and compassionate form of artificial general intelligence (AGI) by integrating knowledge graphs for classical economics, education, health, and space science. Classical economics offers pathways to the evolution of a form of AGI characterised as moral, ethical, and providing a capacity for building trust-based social capital of societies. Pathways that can be elucidated by applications of machine and deep learning to knowledge graphs of the fields of classical economics, ethics, and social capital. A network platform based on the application of distributed ledger technology is proposed to provide the basis for eliciting insights from interdependences between an ever expanding digital-quantum cloud hosting similarly empowered knowledge graphs for an ever increasing myriad of advancing fields. Knowledge graph sketches for education, health, space science, and other fields germane to building social capital serve to illustrate this proposed process and attendant business opportunities.
The anonymity of blockchain has accelerated the growth of illegal activities and criminal behaviors on cryptocurrency platforms. Although decentralization is one of the typical characteristics of blockchain, we urgently call for effective regulation to detect these illegal behaviors to ensure the safety and stability of user transactions. Identity inference, which aims to make a preliminary inference about account identity, plays a significant role in blockchain security. As a common tool, graph mining technique can effectively represent the interactive information between accounts and be used for identity inference. However, existing methods cannot balance scalability and end-to-end architecture, resulting high computational consumption and weak feature representation. In this paper, we present a novel approach to analyze user's behavior from the perspective of the transaction subgraph, which naturally transforms the identity inference task into a graph classification pattern and effectively avoids computation in large-scale graph. Furthermore, we propose a generic end-to-end graph neural network model, named $\text{I}^2 \text{BGNN}$, which can accept subgraph as input and learn a function mapping the transaction subgraph pattern to account identity, achieving de-anonymization. Extensive experiments on EOSG and ETHG datasets demonstrate that the proposed method achieve the state-of-the-art performance in identity inference.
With the wide application of blockchain in the financial field, the rise of various types of cybercrimes has brought great challenges to the security of blockchain. In order to better understand this emerging market and explore more efficient countermeasures for effective supervision, it is imperative to track transactions on blockchain-based systems. Due to the openness of Ethereum, we can easily access the publicly available transaction records, model them as a complex network, and further study the problem of transaction tracking via link prediction, which provides a deeper understanding of Ethereum transactions from a network perspective. Specifically, we introduce an embedding based link prediction framework that is composed of temporal-amount snapshot multigraph (TASMG) and present temporal-amount walk (TAW). By taking the realistic rules and features of transaction networks into consideration, we propose TASMG to model Ethereum transaction records as a temporal-amount network and then present TAW to effectively embed accounts via their transaction records, which integrates temporal and amount information of the proposed network. Experimental results demonstrate the superiority of the proposed framework in learning more informative representations and could be an effective method for transaction tracking.
Blockchain technology and, in particular, blockchain-based transaction offers us information that has never been seen before in the financial world. In contrast to fiat currencies, transactions through virtual currencies like Bitcoin are completely public. And these transactions of cryptocurrencies are permanently recorded on Blockchain and are available at any time. Therefore, this allows us to build transaction networks (TN) to analyze illegal phenomenons such as phishing scams in blockchain from a network perspective. In this paper, we propose a Transaction SubGraph Network (TSGN) based classification model to identify phishing accounts in Ethereum. Firstly we extract transaction subgraphs for each address and then expand these subgraphs into corresponding TSGNs based on the different mapping mechanisms. We find that TSGNs can provide more potential information to benefit the identification of phishing accounts. Moreover, Directed-TSGNs, by introducing direction attributes, can retain the transaction flow information that captures the significant topological pattern of phishing scams. By comparing with the TSGN, Directed-TSGN indeed has much lower time complexity, benefiting the graph representation learning. Experimental results demonstrate that, combined with network representation algorithms, the TSGN model can capture more features to enhance the classification algorithm and improve phishing nodes' identification accuracy in the Ethereum networks.
Graph convolutional networks (GCNs) have been employed as a kind of significant tool on many graph-based applications recently. Inspired by convolutional neural networks (CNNs), GCNs generate the embeddings of nodes by aggregating the information of their neighbors layer by layer. However, the high computational and memory cost of GCNs due to the recursive neighborhood expansion across GCN layers makes it infeasible for training on large graphs. To tackle this issue, several sampling methods during the process of information aggregation have been proposed to train GCNs in a mini-batch Stochastic Gradient Descent (SGD) manner. Nevertheless, these sampling strategies sometimes bring concerns about insufficient information collection, which may hinder the learning performance in terms of accuracy and convergence. To tackle the dilemma between accuracy and efficiency, we propose to use aggregators with different granularities to gather neighborhood information in different layers. Then, a degree-based sampling strategy, which avoids the exponential complexity, is constructed for sampling a fixed number of nodes. Combining the above two mechanisms, the proposed model, named Mix-grained GCN (MG-GCN) achieves state-of-the-art performance in terms of accuracy, training speed, convergence speed, and memory cost through a comprehensive set of experiments on four commonly used benchmark datasets and a new Ethereum dataset.
As a blockchain in the field of Internet of Things, Tangle network has received extensive attention from academia and industry. The Tangle network forms a distributed ledger structure through a Directed Acyclic Graph (DAG). Malicious nodes try to achieve the purpose of attack by preventing consensus or reducing the efficiency of consensus. Fast Probabilistic Consensus (FPC) is an important method for the Tangle network to deal with malicious nodes. However, FPC did not consider the situation in which nodes not affected by the attacking node reached a consensus. Based on this situation, this article proposes a new possible attack strategy and defense strategy. The attacking node balances the proportional relationship between the attacked node and the unattended node, and makes a malicious answer close to 1:1, thereby affecting the consensus. This article simulates the realization of this attack method and proposes a defense strategy.
Blockchain-as-a-service (BaaS) experienced a dramatical growth in recent years, making it a hot research topic. With the expanding scale of distributed services deployed on the blockchain system, it is increasingly urgent to evaluate quality of service (QoS) attributes of blockchain services and in-blockchain peers-clients connections. The complicated association of service invocation and network environment naturally form a graph, making it possible to extract features through graph neural networks (GNN). To incorporate graph-structured information in QoS prediction, we proposed a graph matrix factorization (GraphMF) take advantages of both GNNs and collaborative filtering to estimate missing QoS values in the data matrix. Experiment conducted on a real-world dataset demonstrated the effectiveness of our model.
Current cryptocurrencies, such as Bitcoin and Ethereum, enable anonymity by using public keys to represent user accounts. On the other hand, inferring blockchain account types (i.e., miners, smart contracts or exchanges), which are also referred to as blockchain identities, is significant in many scenarios, such as risk assessment and trade regulation. Existing work on blockchain deanonymization mainly focuses on Bitcoin that supports simple transactions of cryptocurrencies. As the popularity of decentralized application (DApp) platform blockchains with Turing-complete smart contracts, represented by Ethereum, identity inference in blockchain faces new challenges because of user diversity and complexity of activities enabled by smart contracts. In this paper, we propose I$^2$GL, an identify inference approach based on big graph analytics and learning to address these challenges. Specifically, I$^2$GL constructs a transaction graph and aims to infer the identity of nodes using the graph learning technique based on Graph Convolutional Networks. Furthermore, a series of enhancement has been proposed by exploiting unique features of blockchain transaction graph. The experimental results on Ethereum transaction records show that I$^2$GL significantly outperforms other state-of-the-art methods.
Bitcoin and its decentralized computing paradigm for digital currency trading are one of the most disruptive technology in the 21st century. This article presents a novel approach to developing a Bitcoin transaction forecast model, DLForecast, by leveraging deep neural networks for learning Bitcoin transaction network representations. DLForecast makes three original contributions. First, we explore three interesting properties between Bitcoin transaction accounts: topological connectivity pattern of Bitcoin accounts, transaction amount pattern, and transaction dynamics. Second, we construct a time-decaying reachability graph and a time-decaying transaction pattern graph, aiming at capturing different types of spatial-temporal Bitcoin transaction patterns. Third, we employ node embedding on both graphs and develop a Bitcoin transaction forecasting system between user accounts based on historical transactions with built-in time-decaying factor. To maintain an effective transaction forecasting performance, we leverage the multiplicative model update (MMU) ensemble to combine prediction models built on different transaction features extracted from each corresponding Bitcoin transaction graph. Evaluated on real-world Bitcoin transaction data, we show that our spatial-temporal forecasting model is efficient with fast runtime and effective with forecasting accuracy over 60 percent and improves the prediction performance by 50 percent when compared to forecasting model built on the static graph baseline.
Liang Chen, Jiaying Peng, Yang Liu, Jintang Li · 6 authors
Blockchain has attracted an increasing amount of researches, and there are lots of refreshing implementations in different fields. Cryptocurrency as its representative implementation, suffers the economic loss due to phishing scams. In our work, accounts and transactions are treated as nodes and edges, thus detection of phishing accounts can be modeled as a node classification problem. Correspondingly, we propose a detecting method based on Graph Convolutional Network and autoencoder to precisely distinguish phishing accounts. Experiments on different large-scale real-world datasets from Ethereum show that our proposed model consistently performs promising results compared with related methods.
Graph networks are extensively used as an essential framework to analyse the interconnections between transactions and capture illicit behaviour in Bitcoin blockchain. Due to the complexity of Bitcoin transaction graph, the prediction of illicit transactions has become a challenging problem to unveil illicit services over the network. Graph Convolutional Network, a graph neural network based spectral approach, has recently emerged and gained much attention regarding graph-structured data. Previous research has highlighted the degraded performance of the latter approach to predict illicit transactions using, a Bitcoin transaction graph, so-called Elliptic data derived from Bitcoin blockchain. Motivated by the previous work, we seek to explore graph convolutions in a novel way. For this purpose, we present a novel approach that is modelled using the existing Graph Convolutional Network intertwined with linear layers. Concisely, we concatenate node embeddings obtained from graph convolutional layers with a single hidden layer derived from the linear transformation of the node feature matrix and followed by Multi-layer Perceptron. Our approach is evaluated using Elliptic data, wherein efficient accuracy is yielded. The proposed approach outperforms the original work of same data set.
Victor Ermolaev, Indrek Klangberg, Yash Madhwal, Silver Vapper · 6 authors
In modern and interconnected world, information is accumulatively stored digitally, making the process of exchanging, gathering and querying the information much easier. Continuously, it has introduced new challenges about how to ensure its consistency and reliability due to the sheer volume of data. A blockchain-based information system can provide an incorruptible record of history, enabling better auditing and data management practices. The paper describes how to combine an Exonum blockchain and a Neo4j graph database into a system that can provide a verifiable audit trail of data integrity and its modifications for information stored in a graph database.
As the largest public blockchain-based platform supporting smart contracts, Ethereum has accumulated a large number of user transaction records since its debut in 2014. Analysis of Ethereum transaction records, however, is still relatively unexplored till now. Modeling the transaction records as a static simple graph, existing methods are unable to accurately characterize the temporal and multiplex features of the edges. In this brief, we first model the Ethereum transaction records as a complex network by incorporating time and amount features of the transactions, and then design several flexible temporal walk strategies for random-walk based graph representation of this large-scale network. Experiments of temporal link prediction on real Ethereum data demonstrate that temporal information and multiplicity characteristic of edges are indispensable for accurate modeling and understanding of Ethereum transaction networks.
OBJECTIVE: To facilitate clinical/genomic/biomedical research, constructing generalizable predictive models using cross-institutional methods while protecting privacy is imperative. However, state-of-the-art methods assume a "flattened" topology, while real-world research networks may consist of "network-of-networks" which can imply practical issues including training on small data for rare diseases/conditions, prioritizing locally trained models, and maintaining models for each level of the hierarchy. In this study, we focus on developing a hierarchical approach to inherit the benefits of the privacy-preserving methods, retain the advantages of adopting blockchain, and address practical concerns on a research network-of-networks. MATERIALS AND METHODS: We propose a framework to combine level-wise model learning, blockchain-based model dissemination, and a novel hierarchical consensus algorithm for model ensemble. We developed an example implementation HierarchicalChain (hierarchical privacy-preserving modeling on blockchain), evaluated it on 3 healthcare/genomic datasets, as well as compared its predictive correctness, learning iteration, and execution time with a state-of-the-art method designed for flattened network topology. RESULTS: HierarchicalChain improves the predictive correctness for small training datasets and provides comparable correctness results with the competing method with higher learning iteration and similar per-iteration execution time, inherits the benefits of the privacy-preserving learning and advantages of blockchain technology, and immutable records models for each level. DISCUSSION: HierarchicalChain is independent of the core privacy-preserving learning method, as well as of the underlying blockchain platform. Further studies are warranted for various types of network topology, complex data, and privacy concerns. CONCLUSION: We demonstrated the potential of utilizing the information from the hierarchical network-of-networks topology to improve prediction.