Inductive–Transductive Learning with Graph Neural Networks

Rossi, Alberto; Tiezzi, Matteo; Dimitri, Giovanna Maria; Bianchini, Monica; Maggini, Marco; Scarselli, Franco

doi:10.1007/978-3-319-99978-4_16

Cited by 17 publications

(12 citation statements)

References 20 publications

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“…( 8) using the Adam optimizer [30]. For the comparison with the original GNN model, we exploited the GNN Tensorflow implementation 6 introduced in [31].…”

Section: Methodsmentioning

confidence: 99%

Deep Constraint-based Propagation in Graph Neural Networks

Tiezzi,

Marra,

Melacci

et al. 2020

Preprint

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Several real-world applications are characterized by data that exhibit a complex structure that can be represented using graphs. The popularity of deep learning techniques renewed the interest in neural architectures able to process these patterns, inspired by the Graph Neural Network (GNN) model. GNNs encode the state of the nodes of the graph by means of an iterative diffusion procedure that, during the learning stage, must be computed at every epoch, until the fixed point of a learnable state transition function is reached, propagating the information among the neighbouring nodes. We propose a novel approach to learning in GNNs, based on constrained optimization in the Lagrangian framework. Learning both the transition function and the node states is the outcome of a joint process, in which the state convergence procedure is implicitly expressed by a constraint satisfaction mechanism, avoiding iterative epoch-wise procedures and the network unfolding. Our computational structure searches for saddle points of the Lagrangian in the adjoint space composed of weights, nodes state variables and Lagrange multipliers. This process is further enhanced by multiple layers of constraints that accelerate the diffusion process. An experimental analysis shows that the proposed approach compares favourably with popular models on several benchmarks.

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“…( 8) using the Adam optimizer [30]. For the comparison with the original GNN model, we exploited the GNN Tensorflow implementation 6 introduced in [31].…”

Section: Methodsmentioning

confidence: 99%

Deep Constraint-based Propagation in Graph Neural Networks

Tiezzi,

Marra,

Melacci

et al. 2020

Preprint

Self Cite

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“…We compared our model with the equivalent GNN in [21], with the same number of hidden neurons of the fa and fr functions. For the comparison, we exploited the GNN Tensorflow implementation 5 introduced in [20]. Results are presented in Table 3.…”

Section: Artificial Tasksmentioning

confidence: 99%

“…Learning rate for parameters θ fa and θ fr is selected from the set {10 −5 , 10 −4 , 10 −3 }, and the learning rate for the variables xv and λv from the set {10 −4 , 10 −3 , 10 −2 }.We compared our model with the equivalent GNN in[21], with the same number of hidden neurons of the fa and fr functions. For the comparison, we exploited the GNN Tensorflow implementation5 introduced in[20]. Results are presented in Table3.Constraints characterized by unilateral functions usually offer better performances than equivalent bilateral constraints.…”

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confidence: 99%

A Lagrangian Approach to Information Propagation in Graph Neural Networks

Tiezzi,

Marra,

Melacci

et al. 2020

Preprint

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In many real world applications, data are characterized by a complex structure, that can be naturally encoded as a graph. In the last years, the popularity of deep learning techniques has renewed the interest in neural models able to process complex patterns. In particular, inspired by the Graph Neural Network (GNN) model, different architectures have been proposed to extend the original GNN scheme. GNNs exploit a set of state variables, each assigned to a graph node, and a diffusion mechanism of the states among neighbor nodes, to implement an iterative procedure to compute the fixed point of the (learnable) state transition function. In this paper, we propose a novel approach to the state computation and the learning algorithm for GNNs, based on a constraint optimisation task solved in the Lagrangian framework. The state convergence procedure is implicitly expressed by the constraint satisfaction mechanism and does not require a separate iterative phase for each epoch of the learning procedure. In fact, the computational structure is based on the search for saddle points of the Lagrangian in the adjoint space composed of weights, neural outputs (node states), and Lagrange multipliers. The proposed approach is compared experimentally with other popular models for processing graphs.

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“…The prediction is set up as a multi-class multi-label node classification problem (applied only to drug nodes, and not to gene nodes), in which each DSE corresponds to a class. We adopt a mixed inductivetransductive learning scheme [28], that exploits both the features of drugs and genes (induction path) and the information on the side-effects of known drugs (transduction path), in order to predict the side-effects of new drugs. The whole method is flexible, since the graph dataset can be easily extended to include other node features and further relationships without changing the machine learning framework [29].…”

Section: Introductionmentioning

confidence: 99%

Modular multi-source prediction of drug side-effects with DruGNN

Bongini¹,

Scarselli²,

Bianchini³

et al. 2022

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Drug Side-Effects (DSEs) have a high impact on public health, care system costs, and drug discovery processes. Predicting the probability of side-effects, before their occurrence, is fundamental to reduce this impact, in particular on drug discovery. Candidate molecules could be screened before undergoing clinical trials, reducing the costs in time, money, and health of the participants. Drug side-effects are triggered by complex biological processes involving many different entities, from drug structures to protein-protein interactions. To predict their occurrence, it is necessary to integrate data from heterogeneous sources. In this work, such heterogeneous data is integrated into a graph dataset, expressively representing the relational information between different entities, such as drug molecules and genes. The relational nature of the dataset represents an important novelty for drug side-effect predictors. Graph Neural Networks (GNNs) are exploited to predict DSEs on our dataset with very promising results. GNNs are deep learning models that can process graph-structured data, with minimal information loss, and have been applied on a wide variety of biological tasks. Our experimental results confirm the advantage of using relationships between data entities, suggesting interesting future developments in this scope. The experimentation also shows the importance of specific subsets of data in determining associations between drugs and side-effects.

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Inductive–Transductive Learning with Graph Neural Networks

Cited by 17 publications

References 20 publications

Deep Constraint-based Propagation in Graph Neural Networks

Deep Constraint-based Propagation in Graph Neural Networks

A Lagrangian Approach to Information Propagation in Graph Neural Networks

Modular multi-source prediction of drug side-effects with DruGNN

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