We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on the GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks.
DCNNs also share strong ties to probabilistic relational models (PRMs), a family of graphical models that are capable of representing distributions over relational data @cite_12 . In contrast to PRMs, DCNNs are deterministic, which allows them to avoid the exponential blowup in learning and inference that hampers PRMs.
@cite_12
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We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks. The formalism Probabilistic Relational Models (PRM) couples discrete Bayesian Networks with a modeling formalism similar to UML class diagrams and has been used for architecture analysis. PRMs are well-suited to perform architecture analysis with respect to system qualities since they support both modeling and analysis within the same formalism. A particular strength of PRMs is the ability to perform meaningful analysis of domains where there is a high level of uncertainty, as is often the case when performing system quality analysis. However, the use of discrete Bayesian networks in PRMs complicates the analysis of continuous phenomena. The main contribution of this paper is the Hybrid Probabilistic Relational Models (HPRM) formalism which extends PRMs to enable continuous analysis thus extending the applicability for architecture analysis and especially for trade-off analysis of system qualities. HPRMs use hybrid Bayesian networks which allow combinations of discrete and continuous variables. In addition to presenting the HPRM formalism, the paper contains an example which details the use of HPRMs for architecture trade-off analysis. a b s t r a c t Linear Proximal Support Vector Machines (LPSVMs), like decision trees, classic SVM, etc. are originally not equipped to handle drifting data streams that exhibit high and varying degrees of class imbalance. For online classification of data streams with imbalanced class distribution, we propose a dynamic class imbalance learning (DCIL) approach to incremental LPSVM (IncLPSVM) modeling. In doing so, we simplify a computationally non-renewable weighted LPSVM to several core matrices multiplying two simple weight coefficients. When data addition and or retirement occurs, the proposed DCIL-IncLPSVM 1 accommodates newly presented class imbalance by a simple matrix and coefficient updating, meanwhile ensures no discriminative information lost throughout the learning process. Experiments on benchmark datasets indicate that the proposed DCIL-IncLPSVM outperforms classic IncSVM and IncLPSVM in terms of F -measure and G-mean metrics. Moreover, our application to online face membership authentication shows that the proposed DCIL-IncLPSVM remains effective in the presence of highly dynamic class imbalance, which usually poses serious problems to previous approaches. A large portion of real-world data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with “flat” data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much of the relational structure present in our database. This paper builds on the recent work on probabilistic relational models (PRMs), and describes how to learn them from databases. PRMs allow the properties of an object to depend probabilistically both on other properties of that object and on properties of related objects. Although PRMs are significantly more expressive than standard models, such as Bayesian networks, we show how to extend well-known statistical methods for learning Bayesian networks to learn these models. We describe both parameter estimation and structure learning — the automatic induction of the dependency structure in a model. Moreover, we show how the learning procedure can exploit standard database retrieval techniques for efficient learning from large datasets. We present experimental results on both real and synthetic relational databases.