Composite Graph Neural Networks for Molecular Property Prediction.

Graph Neural Networks have proven to be very valuable models for the solution of a wide variety of problems on molecular graphs, as well as in many other research fields involving graph-structured data. Molecules are heterogeneous graphs composed of atoms of different species. Composite graph neural networks process heterogeneous graphs with multiple-state-updating networks, each one dedicated to a particular node type. This approach allows for the extraction of information from s graph more efficiently than standard graph neural networks that distinguish node types through a one-hot encoded type of vector. We carried out extensive experimentation on eight molecular graph datasets and on a large number of both classification and regression tasks. The results we obtained clearly show that composite graph neural networks are far more efficient in this setting than standard graph neural networks.

A topological description of loss surfaces based on Betti Numbers.

In the context of deep learning models, attention has recently been paid to studying the surface of the loss function in order to better understand training with methods based on gradient descent. This search for an appropriate description, both analytical and topological, has led to numerous efforts in identifying spurious minima and characterize gradient dynamics. Our work aims to contribute to this field by providing a topological measure for evaluating loss complexity in the case of multilayer neural networks. We compare deep and shallow architectures with common sigmoidal activation functions by deriving upper and lower bounds for the complexity of their respective loss functions and revealing how that complexity is influenced by the number of hidden units, training models, and the activation function used. Additionally, we found that certain variations in the loss function or model architecture, such as adding an ℓ2 regularization term or implementing skip connections in a feedforward network, do not affect loss topology in specific cases.

Weisfeiler-Lehman goes dynamic: An analysis of the expressive power of Graph Neural Networks for attributed and dynamic graphs.

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence. Moreover, the proof of the approximation capability is mostly constructive and allows us to deduce hints on the architecture of GNNs that can achieve the desired approximation.

Modular Multi-Source Prediction of Drug Side-Effects With DruGNN.

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.

On Inductive-Transductive Learning With Graph Neural Networks.

Many real-world domains involve information naturally represented by graphs, where nodes denote basic patterns while edges stand for relationships among them. The graph neural network (GNN) is a machine learning model capable of directly managing graph-structured data. In the original framework, GNNs are inductively trained, adapting their parameters based on a supervised learning environment. However, GNNs can also take advantage of transductive learning, thanks to the natural way they make information flow and spread across the graph, using relationships among patterns. In this paper, we propose a mixed inductive-transductive GNN model, study its properties and introduce an experimental strategy that allows us to understand and distinguish the role of inductive and transductive learning. The preliminary experimental results show interesting properties for the mixed model, highlighting how the peculiarities of the problems and the data can impact on the two learning strategies.

A new deep learning approach integrated with clinical data for the dermoscopic differentiation of early melanomas from atypical nevi.

BACKGROUND: Timely recognition of malignant melanoma (MM) is challenging for dermatologists worldwide and represents the main determinant for mortality. Dermoscopic examination is influenced by dermatologists' experience and fails to achieve adequate accuracy and reproducibility in discriminating atypical nevi (AN) from early melanomas (EM). OBJECTIVE: We aimed to develop a Deep Convolutional Neural Network (DCNN) model able to support dermatologists in the classification and management of atypical melanocytic skin lesions (aMSL). METHODS: A training set (630 images), a validation set (135) and a testing set (214) were derived from the idScore dataset of 979 challenging aMSL cases in which the dermoscopic image is integrated with clinical data (age, sex, body site and diameter) and associated with histological data. A DCNN_aMSL architecture was designed and then trained on both dermoscopic images of aMSL and the clinical/anamnestic data, resulting in the integrated "iDCNN_aMSL" model. Responses of 111 dermatologists with different experience levels on both aMSL classification (intuitive diagnosis) and management decisions (no/long follow-up; short follow-up; excision/preventive excision) were compared with the DCNNs models. RESULTS: In the lesion classification study, the iDCNN_aMSL achieved the best accuracy, reaching an AUC = 90.3 %, SE = 86.5 % and SP = 73.6 %, compared to DCNN_aMSL (SE = 89.2 %, SP = 65.7 %) and intuitive diagnosis of dermatologists (SE = 77.0 %; SP = 61.4 %). CONCLUSIONS: The iDCNN_aMSL proved to be the best support tool for management decisions reducing the ratio of inappropriate excision. The proposed iDCNN_aMSL model can represent a valid support for dermatologists in discriminating AN from EM with high accuracy and for medical decision making by reducing their rates of inappropriate excisions.

Multi-Modal Siamese Network for Diagnostically Similar Lesion Retrieval in Prostate MRI.

Multi-parametric prostate MRI (mpMRI) is a powerful tool to diagnose prostate cancer, though difficult to interpret even for experienced radiologists. A common radiological procedure is to compare a magnetic resonance image with similarly diagnosed cases. To assist the radiological image interpretation process, computerized Content-Based Image Retrieval systems (CBIRs) can therefore be employed to improve the reporting workflow and increase its accuracy. In this article, we propose a new, supervised siamese deep learning architecture able to handle multi-modal and multi-view MR images with similar PIRADS score. An experimental comparison with well-established deep learning-based CBIRs (namely standard siamese networks and autoencoders) showed significantly improved performance with respect to both diagnostic (ROC-AUC), and information retrieval metrics (Precision-Recall, Discounted Cumulative Gain and Mean Average Precision). Finally, the new proposed multi-view siamese network is general in design, facilitating a broad use in diagnostic medical imaging retrieval.

Image generation by GAN and style transfer for agar plate image segmentation.

BACKGROUND AND OBJECTIVES: Deep learning models and specifically Convolutional Neural Networks (CNNs) are becoming the leading approach in many computer vision tasks, including medical image analysis. Nevertheless, the CNN training usually requires large sets of supervised data, which are often difficult and expensive to obtain in the medical field. To address the lack of annotated images, image generation is a promising method, which is becoming increasingly popular in the computer vision community. In this paper, we present a new approach to the semantic segmentation of bacterial colonies in agar plate images, based on deep learning and synthetic image generation, to increase the training set size. Indeed, semantic segmentation of bacterial colony is the basis for infection recognition and bacterial counting in Petri plate analysis. METHODS: A convolutional neural network (CNN) is used to separate the bacterial colonies from the background. To face the lack of annotated images, a novel engine is designed - which exploits a generative adversarial network to capture the typical distribution of the bacterial colonies on agar plates - to generate synthetic data. Then, bacterial colony patches are superimposed on existing background images, taking into account both the local appearance of the background and the intrinsic opacity of the bacterial colonies, and a style transfer algorithm is used for further improve visual realism. RESULTS: The proposed deep learning approach has been tested on the only public dataset available with pixel-level annotations for bacterial colony semantic segmentation in agar plates. The role of including synthetic data in the training of a segmentation CNN has been evaluated, showing how comparable performances can be obtained with respect to the use of real images. Qualitative results are also reported for a second public dataset in which the segmentation annotations are not provided. CONCLUSIONS: The use of a small set of real data, together with synthetic images, allows obtaining comparable results with respect to using a complete set of real images. Therefore, the proposed synthetic data generator is able to address the scarcity of biomedical data and provides a scalable and cheap alternative to human ground-truth supervision.

The Vapnik-Chervonenkis dimension of graph and recursive neural networks.

The Vapnik-Chervonenkis dimension (VC-dim) characterizes the sample learning complexity of a classification model and it is often used as an indicator for the generalization capability of a learning method. The VC-dim has been studied on common feed-forward neural networks, but it has yet to be studied on Graph Neural Networks (GNNs) and Recursive Neural Networks (RecNNs). This paper provides upper bounds on the order of growth of the VC-dim of GNNs and RecNNs. GNNs and RecNNs are from a new class of neural network models which are capable of processing inputs that are given as graphs. A graph is a data structure that generalizes the representational power of vectors and sequences, via the ability to represent dependencies or relationships between feature vectors. It was shown previously that the ability of recurrent neural networks to process sequences increases the VC-dim when compared to the VC-dim of Neural Networks, which are limited to processing vectors. Since graphs are a more general form than sequences, the question arises how this will affect the VC-dimension of GNNs and RecNNs. A main finding in this paper is that the upper bounds on the VC-dim for GNNs and RecNNs are comparable to the upper bounds for recurrent neural networks. The result also suggests that the generalization capability of such models increases with the number of connected nodes.

On the complexity of neural network classifiers: a comparison between shallow and deep architectures.

Recently, researchers in the artificial neural network field have focused their attention on connectionist models composed by several hidden layers. In fact, experimental results and heuristic considerations suggest that deep architectures are more suitable than shallow ones for modern applications, facing very complex problems, e.g., vision and human language understanding. However, the actual theoretical results supporting such a claim are still few and incomplete. In this paper, we propose a new approach to study how the depth of feedforward neural networks impacts on their ability in implementing high complexity functions. First, a new measure based on topological concepts is introduced, aimed at evaluating the complexity of the function implemented by a neural network, used for classification purposes. Then, deep and shallow neural architectures with common sigmoidal activation functions are compared, by deriving upper and lower bounds on their complexity, and studying how the complexity depends on the number of hidden units and the used activation function. The obtained results seem to support the idea that deep networks actually implements functions of higher complexity, so that they are able, with the same number of resources, to address more difficult problems.

Solving graph data issues using a layered architecture approach with applications to web spam detection.

This paper proposes the combination of two state-of-the-art algorithms for processing graph input data, viz., the probabilistic mapping graph self organizing map, an unsupervised learning approach, and the graph neural network, a supervised learning approach. We organize these two algorithms in a cascade architecture containing a probabilistic mapping graph self organizing map, and a graph neural network. We show that this combined approach helps us to limit the long-term dependency problem that exists when training the graph neural network resulting in an overall improvement in performance. This is demonstrated in an application to a benchmark problem requiring the detection of spam in a relatively large set of web sites. It is found that the proposed method produces results which reach the state of the art when compared with some of the best results obtained by others using quite different approaches. A particular strength of our method is its applicability towards any input domain which can be represented as a graph.

SortNet: learning to rank by a neural preference function.

Relevance ranking consists in sorting a set of objects with respect to a given criterion. However, in personalized retrieval systems, the relevance criteria may usually vary among different users and may not be predefined. In this case, ranking algorithms that adapt their behavior from users' feedbacks must be devised. Two main approaches are proposed in the literature for learning to rank: the use of a scoring function, learned by examples, that evaluates a feature-based representation of each object yielding an absolute relevance score, a pairwise approach, where a preference function is learned to determine the object that has to be ranked first in a given pair. In this paper, we present a preference learning method for learning to rank. A neural network, the comparative neural network (CmpNN), is trained from examples to approximate the comparison function for a pair of objects. The CmpNN adopts a particular architecture designed to implement the symmetries naturally present in a preference function. The learned preference function can be embedded as the comparator into a classical sorting algorithm to provide a global ranking of a set of objects. To improve the ranking performances, an active-learning procedure is devised, that aims at selecting the most informative patterns in the training set. The proposed algorithm is evaluated on the LETOR dataset showing promising performances in comparison with other state-of-the-art algorithms.

Computational capabilities of graph neural networks.

In this paper, we will consider the approximation properties of a recently introduced neural network model called graph neural network (GNN), which can be used to process-structured data inputs, e.g., acyclic graphs, cyclic graphs, and directed or undirected graphs. This class of neural networks implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n onto an m-dimensional Euclidean space. We characterize the functions that can be approximated by GNNs, in probability, up to any prescribed degree of precision. This set contains the maps that satisfy a property called preservation of the unfolding equivalence, and includes most of the practically useful functions on graphs; the only known exception is when the input graph contains particular patterns of symmetries when unfolding equivalence may not be preserved. The result can be considered an extension of the universal approximation property established for the classic feedforward neural networks (FNNs). Some experimental examples are used to show the computational capabilities of the proposed model.

The graph neural network model.

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

Recursive processing of cyclic graphs.

Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically cyclic. In this paper, a methodology is proposed, which allows us to process any cyclic directed graph. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model.

Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods, and Some New Results.

In this paper, we present a review of some recent works on approximation by feedforward neural networks. A particular emphasis is placed on the computational aspects of the problem, i.e. we discuss the possibility of realizing a feedforward neural network which achieves a prescribed degree of accuracy of approximation, and the determination of the number of hidden layer neurons required to achieve this accuracy. Furthermore, a unifying framework is introduced to understand existing approaches to investigate the universal approximation problem using feedforward neural networks. Some new results are also presented. Finally, two training algorithms are introduced which can determine the weights of feedforward neural networks, with sigmoidal activation neurons, to any degree of prescribed accuracy. These training algorithms are designed so that they do not suffer from the problems of local minima which commonly affect neural network learning algorithms.