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Incomplete covariate vectors are known to be problematic for estimation and inferences on model parameters, but their impact on prediction performance is less understood. We develop an imputation-free method that builds on a random partition model admitting variable-dimension covariates. Cluster-specific response models further incorporate covariates via linear predictors, facilitating estimation of smooth prediction surfaces with relatively few clusters. We exploit marginalization techniques of Gaussian kernels to analytically project response distributions according to any pattern of missing covariates, yielding a local regression with internally consistent uncertainty propagation that utilizes only one set of coefficients per cluster. Aggressive shrinkage of these coefficients regulates uncertainty due to missing covariates. The method allows in- and out-of-sample prediction for any missingness pattern, even if the pattern in a new subject's incomplete covariate vector was not seen in the training data. We develop an MCMC algorithm for posterior sampling that improves a computationally expensive update for latent cluster allocation. Finally, we demonstrate the model's effectiveness for nonlinear point and density prediction under various circumstances by comparing with other recent methods for regression of variable dimensions on synthetic and real data.

Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural network approximation. We show that this is indeed possible for shape spaces with a special product structure, namely those smoothly approximable by a direct sum of low-dimensional manifolds. Our proposed architecture leverages this structure by separately learning approximations for the low-dimensional factors and a subsequent combination. After developing the approach as a general framework, we apply it to a shape space of triangular surfaces. Here, typical examples of data manifolds are given through datasets of articulated models and can be factorized, for example, by a Sparse Principal Geodesic Analysis (SPGA). We demonstrate the effectiveness of our proposed approach with experiments on synthetic data as well as manifolds extracted from data via SPGA.

Community Search (CS) is one of the fundamental graph analysis tasks, which is a building block of various real applications. Given any query nodes, CS aims to find cohesive subgraphs that query nodes belong to. Recently, a large number of CS algorithms are designed. These algorithms adopt predefined subgraph patterns to model the communities, which cannot find ground-truth communities that do not have such pre-defined patterns in real-world graphs. Thereby, machine learning (ML) and deep learning (DL) based approaches are proposed to capture flexible community structures by learning from ground-truth communities in a data-driven fashion. These approaches rely on sufficient training data to provide enough generalization for ML models, however, the ground-truth cannot be comprehensively collected beforehand. In this paper, we study ML/DL-based approaches for CS, under the circumstance of small training data. Instead of directly fitting the small data, we extract prior knowledge which is shared across multiple CS tasks via learning a meta model. Each CS task is a graph with several queries that possess corresponding partial ground-truth. The meta model can be swiftly adapted to a task to be predicted by feeding a few task-specific training data. We find that trivially applying multiple classical metalearning algorithms to CS suffers from problems regarding prediction effectiveness, generalization capability and efficiency. To address such problems, we propose a novel meta-learning based framework, Conditional Graph Neural Process (CGNP), to fulfill the prior extraction and adaptation procedure. A meta CGNP model is a task-common node embedding function for clustering, learned by metric-based graph learning, which fully exploits the characteristics of CS. We compare CGNP with CS algorithms and ML baselines on real graphs with ground-truth communities.

This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that simultaneously incorporates intra-image information to promote sparsity in each individual edge map with inter-image information to promote similarities in any unchanged regions. By treating both the edges as well as the similarity between adjacent images as random variables, there is no need to separately form regions of change. Thus we avoid both additional computational cost as well as any information loss resulting from pre-processing the image. Our numerical examples demonstrate that our new method compares favorably with more standard SBL approaches.

To deploy and operate deep neural models in production, the quality of their predictions, which might be contaminated benignly or manipulated maliciously by input distributional deviations, must be monitored and assessed. Specifically, we study the case of monitoring the healthy operation of a deep neural network (DNN) receiving a stream of data, with the aim of detecting input distributional deviations over which the quality of the network's predictions is potentially damaged. Using selective prediction principles, we propose a distribution deviation detection method for DNNs. The proposed method is derived from a tight coverage generalization bound computed over a sample of instances drawn from the true underlying distribution. Based on this bound, our detector continuously monitors the operation of the network over a test window and fires off an alarm whenever a deviation is detected. This novel detection method consistently and significantly outperforms the state of the art with respect to the CIFAR-10 and ImageNet datasets, thus establishing a new performance bar for this task, while being substantially more efficient in time and space complexities.

Out-of-distribution (OOD) detection is concerned with identifying data points that do not belong to the same distribution as the model's training data. For the safe deployment of predictive models in a real-world environment, it is critical to avoid making confident predictions on OOD inputs as it can lead to potentially dangerous consequences. However, OOD detection largely remains an under-explored area in the audio (and speech) domain. This is despite the fact that audio is a central modality for many tasks, such as speaker diarization, automatic speech recognition, and sound event detection. To address this, we propose to leverage feature-space of the model with deep k-nearest neighbors to detect OOD samples. We show that this simple and flexible method effectively detects OOD inputs across a broad category of audio (and speech) datasets. Specifically, it improves the false positive rate (FPR@TPR95) by 17% and the AUROC score by 7% than other prior techniques.

Community detection is a fundamental task in social network analysis. Online social networks have dramatically increased the volume and speed of interactions among users, enabling advanced analysis of these dynamics. Despite a growing interest in tracking the evolution of groups of users in real-world social networks, most community detection efforts focus on communities within static networks. Here, we describe a framework for tracking communities over time in a dynamic network, where a series of significant events is identified for each community. To this end, a modularity-based strategy is proposed to effectively detect and track dynamic communities. The potential of our framework is shown by conducting extensive experiments on synthetic networks containing embedded events. Results indicate that our framework outperforms other state-of-the-art methods. In addition, we briefly explore how the proposed approach can identify dynamic communities in a Twitter network composed of more than 60,000 users, which posted over 5 million tweets throughout 2020. The proposed framework can be applied to different social network and provides a valuable tool to understand the evolution of communities in dynamic social networks.

Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.

This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both the mixing coefficients and the community distribution are parameterized by the low-dimensional representations of the nodes and communities. We designed an effective variational inference algorithm which regularizes the community membership of neighboring nodes to be similar in the latent space. Experimental results on multiple real-world graphs show that vGraph is very effective in both community detection and node representation learning, outperforming many competitive baselines in both tasks. We show that the framework of vGraph is quite flexible and can be easily extended to detect hierarchical communities.