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Register a new userGraph Convolutional Gaussian Processes
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Added by
Ben Glocker
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations are functions with domains on general graphs. The structure of these models allows for high dimensional inputs while retaining expressibility, as is the case with convolutional neural networks. We present applications of graph convolutional Gaussian processes to images and triangular meshes, demonstrating their versatility and effectiveness, comparing favorably to existing methods, despite being relatively simple models.
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Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural networks, e.g., fully connected and convolutional neural networks, with infinite hidden units have been proved to be equivalent to Gaussian processes~(GPs). To exploit both the powerful representational capacity of GCNs and the great expressive power of GPs, we investigate similar properties of infinitely wide GCNs. More specifically, we propose a GP regression model via GCNs~(GPGC) for graph-based semi-supervised learning. In the process, we formulate the kernel matrix computation of GPGC in an iterative analytical form. Finally, we derive a conditional distribution for the labels of unobserved nodes based on the graph structure, labels for the observed nodes, and the feature matrix of all the nodes. We conduct extensive experiments to evaluate the semi-supervised classification performance of GPGC and demonstrate that it outperforms other state-of-the-art methods by a clear margin on all the datasets while being efficient.
We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural networks in active learning experiments where labels are scarce. Furthermore, the model does not require a validation data set for early stopping to control over-fitting. Our model can be viewed as an instance of empirical distribution regression weighted locally by network connectivity. We further motivate the intuitive construction of the model with a Bayesian linear model interpretation where the node features are filtered by an operator related to the graph Laplacian. The method can be easily implemented by adapting off-the-shelf scalable variational inference algorithms for Gaussian processes.
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together with fast but accurate posterior inference. We investigate several variations of the convolutional kernel, and apply it to MNIST and CIFAR-10, which have both been known to be challenging for Gaussian processes. We also show how the marginal likelihood can be used to find an optimal weighting between convolutional and RBF kernels to further improve performance. We hope that this illustration of the usefulness of a marginal likelihood will help automate discovering architectures in larger models.
We present an end-to-end statistical framework for personalized, accurate, and minimally invasive modeling of female reproductive hormonal patterns. Reconstructing and forecasting the evolution of hormonal dynamics is a challenging task, but a critical one to improve general understanding of the menstrual cycle and personalized detection of potential health issues. Our goal is to infer and forecast individual hormone daily levels over time, while accommodating pragmatic and minimally invasive measurement settings. To that end, our approach combines the power of probabilistic generative models (i.e., multi-task Gaussian processes) with the flexibility of neural networks (i.e., a dilated convolutional architecture) to learn complex temporal mappings. To attain accurate hormone level reconstruction with as little data as possible, we propose a sampling mechanism for optimal reconstruction accuracy with limited sampling budget. Our results show the validity of our proposed hormonal dynamic modeling framework, as it provides accurate predictive performance across different realistic sampling budgets and outperforms baselines methods.
Graph convolution networks have recently garnered a lot of attention for representation learning on non-Euclidean feature spaces. Recent research has focused on stacking multiple layers like in convolutional neural networks for the increased expressive power of graph convolution networks. However, simply stacking multiple graph convolution layers lead to issues like vanishing gradient, over-fitting and over-smoothing. Such problems are much less when using shallower networks, even though the shallow networks have lower expressive power. In this work, we propose a novel Multipath Graph convolutional neural network that aggregates the output of multiple different shallow networks. We train and test our model on various benchmarks datasets for the task of node property prediction. Results show that the proposed method not only attains increased test accuracy but also requires fewer training epochs to converge. The full implementation is available at https://github.com/rangan2510/MultiPathGCN
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