Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

计量经济分析 = Econometric analysis

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications, where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on the existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this article, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art GNNs into four categories, namely, recurrent GNNs, convolutional GNNs, graph autoencoders, and spatial–temporal GNNs. We further discuss the applications of GNNs across various domains and summarize the open-source codes, benchmark data sets, and model evaluation of GNNs. Finally, we propose potential research directions in this rapidly growing field.

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A Comprehensive Survey on Graph Neural Networks

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

(NR) is the first interactive data repository with a web-based platform for visual interactive analytics. Unlike other data repositories (e.g., UCI ML Data Repository, and SNAP), the network data repository (networkrepository.com) allows users to not only download, but to interactively analyze and visualize such data using our web-based interactive graph analytics platform. Users can in real-time analyze, visualize, compare, and explore data along many different dimensions. The aim of NR is to make it easy to discover key insights into the data extremely fast with little effort while also providing a medium for users to share data, visualizations, and insights. Other key factors that differentiate NR from the current data repositories is the number of graph datasets, their size, and variety. While other data repositories are static, they also lack a means for users to collaboratively discuss a particular dataset, corrections, or challenges with using the data for certain applications. In contrast, NR incorporates many social and collaborative aspects that facilitate scientific research, e.g., users can discuss each graph, post observations, and visualizations.

/pdf/the-network-data-repository-with-interactive-graph-analytics-2c3ilhzf4y.pdf

The network data repository with interactive graph analytics and visualization

In this work we present a large scale comparison study for the major machine learning models for time series forecasting. Specifically, we apply the models on the monthly M3 time series competition data (around a thousand time series). There have been very few, if any, large scale comparison studies for machine learning models for the regression or the time series forecasting problems, so we hope this study would fill this gap. The models considered are multilayer perceptron, Bayesian neural networks, radial basis functions, generalized regression neural networks (also called kernel regression), K-nearest neighbor regression, CART regression trees, support vector regression, and Gaussian processes. The study reveals significant differences between the different methods. The best two methods turned out to be the multilayer perceptron and the Gaussian process regression. In addition to model comparisons, we have tested different preprocessing methods and have shown that they have different impacts on the pe...

An empirical comparison of machine learning models for time series forecasting

Networks evolve continuously over time with the addition, deletion, and changing of links and nodes. Although many networks contain this type of temporal information, the majority of research in network representation learning has focused on static snapshots of the graph and has largely ignored the temporal dynamics of the network. In this work, we describe a general framework for incorporating temporal information into network embedding methods. The framework gives rise to methods for learning time-respecting embeddings from continuous-time dynamic networks. Overall, the experiments demonstrate the effectiveness of the proposed framework and dynamic network embedding approach as it achieves an average gain of 11.9% across all methods and graphs. The results indicate that modeling temporal dependencies in graphs is important for learning appropriate and meaningful network representations.

Continuous-Time Dynamic Network Embeddings

From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a tremendous success and impact in a variety of domains, there has yet to be a fast and efficient approach for computing the frequencies of these subgraph patterns. However, existing methods are not scalable to large networks with millions of nodes and edges, which impedes the application of graphlets to new problems that require large-scale network analysis. To address these problems, we propose a fast, efficient, and parallel algorithm for counting graphlets of size k={3,4}-nodes that take only a fraction of the time to compute when compared with the current methods used. The proposed graphlet counting algorithms leverages a number of proven combinatorial arguments for different graphlets. For each edge, we count a few graphlets, and with these counts along with the combinatorial arguments, we obtain the exact counts of others in constant time. On a large collection of 300+ networks from a variety of domains, our graphlet counting strategies are on average 460x faster than current methods. This brings new opportunities to investigate the use of graphlets on much larger networks and newer applications as we show in the experiments. To the best of our knowledge, this paper provides the largest graphlet computations to date as well as the largest systematic investigation on over 300+ networks from a variety of domains.

/pdf/efficient-graphlet-counting-for-large-networks-31akjutmbl.pdf

Efficient Graphlet Counting for Large Networks

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete understanding of network sampling is critical to support the field of network science. In this paper, we outline a framework for the general problem of network sampling by highlighting the different objectives, population and units of interest, and classes of network sampling methods. In addition, we propose a spectrum of computational models for network sampling methods, ranging from the traditionally studied model based on the assumption of a static domain to a more challenging model that is appropriate for streaming domains. We design a family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs. Furthermore, we demonstrate how traditional static sampling algorithms can be modified for graph streams for each of the three main classes of sampling methods: node, edge, and topology-based sampling. Experimental results indicate that our proposed family of sampling methods more accurately preserve the underlying properties of the graph in both static and streaming domains. Finally, we study the impact of network sampling algorithms on the parameter estimation and performance evaluation of relational classification algorithms.

Nesreen K. Ahmed

Papers

The network data repository with interactive graph analytics and visualization

An empirical comparison of machine learning models for time series forecasting

Continuous-Time Dynamic Network Embeddings

Efficient Graphlet Counting for Large Networks

Network Sampling: From Static to Streaming Graphs