A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

Topics in Network Analysis with Applications to Brain Connectomics

Large complex network data have become common in many scientific domains, and require new statistical tools for discovering the underlying structures and features of interest. This thesis presents new methodology for network data analysis, with a focus on problems arising in the field of brain connectomics. Our overall goal is to learn parsimonious and interpretable network features, with computationally efficient and theoretically justified methods. The first project in the thesis focuses on prediction with network covariates. This setting is motivated by neuroimaging applications, in which each subject has an associated brain network constructed from fMRI data, and the goal is to derive interpretable prediction rules for a phenotype of interest or a clinical outcome. Existing approaches to this problem typically either reduce the data to a small set of global network summaries, losing a lot of local information, or treat network edges as a ``bag of features'' and use standard statistical tools without accounting for the network nature of the data. We develop a method that uses all edge weights, while still effectively incorporating network structure by using a penalty that encourages sparsity in both the number of edges and the number of nodes used. We develop efficient optimization algorithms for implementing this method and show it achieves state-of-the-art accuracy on a dataset of schizophrenic patients and healthy controls while using a smaller and more readily interpretable set of features than methods which ignore network structure. We also establish theoretical performance guarantees. Communities in networks are observed in many different domains, and in brain networks they typically correspond to regions of the brain responsible for different functions. In connectomic analyses, there are standard parcellations of the brain into such regions, typically obtained by applying clustering methods to brain connectomes of healthy subjects. However, there is now increasing evidence that these communities are dynamic, and when the goal is predicting a phenotype or distinguishing between different conditions, these static communities from an unrelated set of healthy subjects may not be the most useful for prediction. We present a method for supervised community detection, that is, a method that finds a partition of the network into communities that is most useful for predicting a particular response. We use a block-structured regularization and compute the solution with a combination of a spectral method and an ADMM optimization algorithm. The method performs well on both simulated and real brain networks, providing support for the idea of task-dependent brain regions. The last part of the thesis focuses on the problem of community detection in the general network setting. Unlike in neuroimaging, statistical network analysis is typically applied to a single network, motivated by datasets from the social sciences. While community detection has been well studied, in practice nodes in a network often belong to more than one community, leading to the much harder problem of overlapping community detection. We propose a new approach for overlapping community detection based on sparse principal component analysis, and develop efficient algorithms that are able to accurately recover community memberships, provided each node does not belong to too many communities at once. The method has a very low computational cost relative to other methods available for this problem. We show asymptotic consistency of recovering community memberships by the new method, and good empirical performance on both simulated and real-world networks.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145883/1/jarroyor_1.pd

A Survey of Statistical Network Models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active “network community” and a substantial liter- ature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning net- work literature in statistical physics and computer science. The growthof the World Wide Web and the emergence of online “networking com- munities” such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize for- mal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Statistic

Learning patterns from sequential and network data using probabilistic models

The focus of this thesis is on developing probabilistic models for data observed over temporal and graph domains, and the corresponding variational inference algorithms. In many real-world phenomena, sequential data points that are observed closer in time often exhibit higher degrees of dependency. Similarly, data points observed over a graph domain (e.g., user interests in a social network) may exhibit higher dependencies with lower degrees of separation over the graph. Furthermore, the connectivity structures that define the graph domain can also evolve temporally (i.e., temporal networks) and exhibit dependencies over time. The data sets observed over temporal and graph domains often (but not always) violate the independent and identically distributed (i.i.d.) assumption made by many mathematical models. The works presented in this dissertation address various challenges in modelling data sets that exhibit dependencies over temporal and graph domains. In Chapter 3, I present a stochastic variational inference algorithm that enables factorial hidden Markov models for sequential data to scale up to extremely long sequences. In Chapter 4, I propose a simple but powerful Gaussian process model that captures the dependencies of data points observed on a graph domain, and demonstrate its viability in graph-based semi-supervised learning problems. In Chapter 5, I present a dynamical model for graphs that captures the temporal evolution of the connectivity structures as well as the sparse connectivity structures often observed in temporal real network data sets. Finally, I summarise the contributions of the thesis and propose several directions for future works that can build on the proposed methods in Chapter 6

大規模非構造データを用いた顧客エンゲージメント行動のためのマーケティングモデル

Tohoku University照井伸彦課

Socio-Cognitive and Affective Computing

Social cognition focuses on how people process, store, and apply information about other people and social situations. It focuses on the role that cognitive processes play in social interactions. On the other hand, the term cognitive computing is generally used to refer to new hardware and/or software that mimics the functioning of the human brain and helps to improve human decision-making. In this sense, it is a type of computing with the goal of discovering more accurate models of how the human brain/mind senses, reasons, and responds to stimuli. Socio-Cognitive Computing should be understood as a set of theoretical interdisciplinary frameworks, methodologies, methods and hardware/software tools to model how the human brain mediates social interactions. In addition, Affective Computing is the study and development of systems and devices that can recognize, interpret, process, and simulate human affects, a fundamental aspect of socio-cognitive neuroscience. It is an interdisciplinary field spanning computer science, electrical engineering, psychology, and cognitive science. Physiological Computing is a category of technology in which electrophysiological data recorded directly from human activity are used to interface with a computing device. This technology becomes even more relevant when computing can be integrated pervasively in everyday life environments. Thus, Socio-Cognitive and Affective Computing systems should be able to adapt their behavior according to the Physiological Computing paradigm. This book integrates proposals from researchers who use signals from the brain and/or body to infer people's intentions and psychological state in smart computing systems. The design of this kind of systems combines knowledge and methods of ubiquitous and pervasive computing, as well as physiological data measurement and processing, with those of socio-cognitive and affective computing

Women in Artificial intelligence (AI)

This Special Issue, entitled "Women in Artificial Intelligence" includes 17 papers from leading women scientists. The papers cover a broad scope of research areas within Artificial Intelligence, including machine learning, perception, reasoning or planning, among others. The papers have applications to relevant fields, such as human health, finance, or education. It is worth noting that the Issue includes three papers that deal with different aspects of gender bias in Artificial Intelligence. All the papers have a woman as the first author. We can proudly say that these women are from countries worldwide, such as France, Czech Republic, United Kingdom, Australia, Bangladesh, Yemen, Romania, India, Cuba, Bangladesh and Spain. In conclusion, apart from its intrinsic scientific value as a Special Issue, combining interesting research works, this Special Issue intends to increase the invisibility of women in AI, showing where they are, what they do, and how they contribute to developments in Artificial Intelligence from their different places, positions, research branches and application fields. We planned to issue this book on the on Ada Lovelace Day (11/10/2022), a date internationally dedicated to the first computer programmer, a woman who had to fight the gender difficulties of her times, in the XIX century. We also thank the publisher for making this possible, thus allowing for this book to become a part of the international activities dedicated to celebrating the value of women in ICT all over the world. With this book, we want to pay homage to all the women that contributed over the years to the field of AI

Bayesian stochastic blockmodels for community detection in networks and community-structured covariance selection

Networks have been widely used to describe interactions among objects in diverse fields. Given the interest in explaining a network by its structure, much attention has been drawn to finding clusters of nodes with dense connections within clusters but sparse connections between clusters. Such clusters are called communities, and identifying such clusters is known as community detection. Here, to perform community detection, I focus on stochastic blockmodels (SBM), a class of statistically-based generative models. I present a flexible SBM that represents different types of data as well as node attributes under a Bayesian framework. The proposed models explicitly capture community behavior by guaranteeing that connections are denser within communities than between communities. First, I present a degree-corrected SBM based on a logistic regression formulation to model binary networks. To fit the model, I obtain posterior samples via Gibbs sampling based on Polya-Gamma latent variables. I conduct inference based on a novel, canonically mapped centroid estimator that formally addresses label non-identifiability and captures representative community assignments. Next, to accommodate large-scale datasets, I further extend the degree-corrected SBM to a broader family of generalized linear models with group correction terms. To conduct exact inference efficiently, I develop an iteratively-reweighted least squares procedure that implicitly updates sufficient statistics on the network to obtain maximum a posteriori (MAP) estimators. I demonstrate the proposed model and estimation on simulated benchmark networks and various real-world datasets. Finally, I develop a Bayesian SBM for community-structured covariance selection. Here, I assume that the data at each node are Gaussian and a latent network where two nodes are not connected if their observations are conditionally independent given observations of other nodes. Under the context of biological and social applications, I expect that this latent network shows a block dependency structure that represents community behavior. Thus, to identify the latent network and detect communities, I propose a hierarchical prior in two levels: a spike-and-slab prior on off-diagonal entries of the concentration matrix for variable selection and a degree-corrected SBM to capture community behavior. I develop an efficient routine based on ridge regularization and MAP estimation to conduct inference