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Register a new userNetwork Inference by Learned Node-Specific Degree Prior
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We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by cross validation. Then we formulate network inference as a matrix completion problem regularized by our degree prior. Our theoretical analysis indicates that this prior favors a network following the learned degree distribution, and may lead to improved network recovery error bound than previous work. Experimental results on both simulated and real biological networks demonstrate the superior performance of our method in various settings.
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We introduce the adversarially learned inference (ALI) model, which jointly learns a generation network and an inference network using an adversarial process. The generation network maps samples from stochastic latent variables to the data space while the inference network maps training examples in data space to the space of latent variables. An adversarial game is cast between these two networks and a discriminative network is trained to distinguish between joint latent/data-space samples from the generative network and joint samples from the inference network. We illustrate the ability of the model to learn mutually coherent inference and generation networks through the inspections of model samples and reconstructions and confirm the usefulness of the learned representations by obtaining a performance competitive with state-of-the-art on the semi-supervised SVHN and CIFAR10 tasks.
We propose a novel hierarchical generative model with a simple Markovian structure and a corresponding inference model. Both the generative and inference model are trained using the adversarial learning paradigm. We demonstrate that the hierarchical structure supports the learning of progressively more abstract representations as well as providing semantically meaningful reconstructions with different levels of fidelity. Furthermore, we show that minimizing the Jensen-Shanon divergence between the generative and inference network is enough to minimize the reconstruction error. The resulting semantically meaningful hierarchical latent structure discovery is exemplified on the CelebA dataset. There, we show that the features learned by our model in an unsupervised way outperform the best handcrafted features. Furthermore, the extracted features remain competitive when compared to several recent deep supervised approaches on an attribute prediction task on CelebA. Finally, we leverage the models inference network to achieve state-of-the-art performance on a semi-supervised variant of the MNIST digit classification task.
Bayesian neural networks have shown great promise in many applications where calibrated uncertainty estimates are crucial and can often also lead to a higher predictive performance. However, it remains challenging to choose a good prior distribution over their weights. While isotropic Gaussian priors are often chosen in practice due to their simplicity, they do not reflect our true prior beliefs well and can lead to suboptimal performance. Our new library, BNNpriors, enables state-of-the-art Markov Chain Monte Carlo inference on Bayesian neural networks with a wide range of predefined priors, including heavy-tailed ones, hierarchical ones, and mixture priors. Moreover, it follows a modular approach that eases the design and implementation of new custom priors. It has facilitated foundational discoveries on the nature of the cold posterior effect in Bayesian neural networks and will hopefully catalyze future research as well as practical applications in this area.
This paper is concerned by the problem of selecting an optimal sampling set of sensors over a network of time series for the purpose of signal recovery at non-observed sensors with a minimal reconstruction error. The problem is motivated by applications where time-dependent graph signals are collected over redundant networks. In this setting, one may wish to only use a subset of sensors to predict data streams over the whole collection of nodes in the underlying graph. A typical application is the possibility to reduce the power consumption in a network of sensors that may have limited battery supplies. We propose and compare various data-driven strategies to turn off a fixed number of sensors or equivalently to select a sampling set of nodes. We also relate our approach to the existing literature on sensor selection from multivariate data with a (possibly) underlying graph structure. Our methodology combines tools from multivariate time series analysis, graph signal processing, statistical learning in high-dimension and deep learning. To illustrate the performances of our approach, we report numerical experiments on the analysis of real data from bike sharing networks in different cities.
The mining of graphs in terms of their local substructure is a well-established methodology to analyze networks. It was hypothesized that motifs - subgraph patterns which appear significantly more often than expected at random - play a key role for the ability of a system to perform its task. Yet the framework commonly used for motif-detection averages over the local environments of all nodes. Therefore, it remains unclear whether motifs are overrepresented in the whole system or only in certain regions. In this contribution, we overcome this limitation by mining node-specific triad patterns. For every vertex, the abundance of each triad pattern is considered only in triads it participates in. We investigate systems of various fields and find that motifs are distributed highly heterogeneously. In particular we focus on the feed-forward loop motif which has been alleged to play a key role in biological networks.
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