We introduce the nested stochastic block model (NSBM) to cluster a collection of networks while simultaneously detecting communities within each network.
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred.
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information.
Bayesian methods for GOF can be appealing due to their ability to incorporate expert knowledge through prior distributions.
We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds.
The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and algorithms.
Adversarial examples can easily degrade the classification performance in neural networks.
In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity.
One of the key challenges for optimization on manifolds is the difficulty of verifying the complexity of the objective function, e. g., whether the objective function is convex or non-convex, and the degree of non-convexity.
Also based on the topological space structure of hypergraph data introduced in our paper, we introduce a modified nearest neighbors methods which is a generalization of the classical nearest neighbors methods from machine learning.
Inspired by the traditional finite difference and finite elements methods and emerging advancements in machine learning, we propose a sequence-to-sequence learning (Seq2Seq) framework called Neural-PDE, which allows one to automatically learn governing rules of any time-dependent PDE system from existing data by using a bidirectional LSTM encoder, and predict the solutions in next $n$ time steps.
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering.
In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks.
Ranked #1 on Node Classification on Cora
While the study of a single network is well-established, technological advances now allow for the collection of multiple networks with relative ease.
Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples).
Our work aims to fill a critical gap in the literature by generalizing parallel inference algorithms to optimization on manifolds.
in-GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces.
Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community.
We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods.