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

Towards Deeper Understanding in Neuroimaging

Neuroimaging is a growing domain of research, with advances in machine learning having tremendous potential to expand understanding in neuroscience and improve public health. Deep neural networks have recently and rapidly achieved historic success in numerous domains, and as a consequence have completely redefined the landscape of automated learners, giving promise of significant advances in numerous domains of research. Despite recent advances and advantages over traditional machine learning methods, deep neural networks have yet to have permeated significantly into neuroscience studies, particularly as a tool for discovery. This dissertation presents well-established and novel tools for unsupervised learning which aid in feature discovery, with relevant applications to neuroimaging. Through our works within, this dissertation presents strong evidence that deep learning is a viable and important tool for neuroimaging studies

Stochastic Gradient MCMC for Nonlinear State Space Models

State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with time, as in the linear case, but particle filters additionally suffer from increasing particle degeneracy with longer series. Stochastic gradient MCMC methods have been developed to scale inference for hidden Markov models (HMMs) and linear SSMs using buffered stochastic gradient estimates to account for temporal dependencies. We extend these stochastic gradient estimators to nonlinear SSMs using particle methods. We present error bounds that account for both buffering error and particle error in the case of nonlinear SSMs that are log-concave in the latent process. We evaluate our proposed particle buffered stochastic gradient using SGMCMC for inference on both long sequential synthetic and minute-resolution financial returns data, demonstrating the importance of this class of methods

A Normalized Autoencoder for LHC Triggers

Autoencoders are an effective analysis tool for the LHC, as they represent one of its main goal of finding physics beyond the Standard Model. The key challenge is that out-of-distribution anomaly searches based on the compressibility of features do not apply to the LHC, while existing density-based searches lack performance. We present the first autoencoder which identifies anomalous jets symmetrically in the directions of higher and lower complexity. The normalized autoencoder combines a standard bottleneck architecture with a well-defined probabilistic description. It works better than all available autoencoders for top vs QCD jets and reliably identifies different dark-jet signals.Comment: 26 pages, 11 figures; update based on referees repor