Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We present an alternative notion of exchangeability for random graphs, which we call edge exchangeability, in which the distribution of a graph sequence is invariant to the order of the edges. We demonstrate that edge-exchangeable models, unlike models that are traditionally vertex exchangeable, can exhibit sparsity. To do so, we outline a general framework for graph generative models; by contrast to the pioneering work of Caron and Fox (2015), models within our framework are stationary across steps of the graph sequence. In particular, our model grows the graph by instantiating more latent atoms of a single random measure as the dataset size increases, rather than adding new atoms to the measure.

In statistics, making decisions always involves some amount of uncertainties. This could be due to the unknown parameters or quantities. For example if a company is releasing a product in the market, the population who will be activity seeking the product and the amount of market the product will capture compared to other products are uncertainties. Bayesian analysis can be applied in statistics when probability has uncertainty in the statistical model. Bayesian analysis can also be applied as an elastic augmentation of maximum likelihood.

Artificial intelligence (AI) developed by a University of Cincinnati doctoral graduate was recently assessed by subject-matter expert and retired United States Air Force Colonel Gene Lee - who holds extensive aerial combat experience as an instructor and Air Battle Manager with considerable fighter aircraft expertise - in a high-fidelity air combat simulator. The artificial intelligence, dubbed ALPHA, was the victor in that simulated scenario, and according to Lee, is "the most aggressive, responsive, dynamic and credible AI I've seen to date." Details on ALPHA - a significant breakthrough in the application of what's called genetic-fuzzy systems are published in the most-recent issue of the Journal of Defense Management, as this application is specifically designed for use with Unmanned Combat Aerial Vehicles (UCAVs) in simulated air-combat missions for research purposes. The tools used to create ALPHA as well as the ALPHA project have been developed by Psibernetix, Inc., recently founded by UC College of Engineering and Applied Science 2015 doctoral graduate Nick Ernest, now president and CEO of the firm; as well as David Carroll, programming lead, Psibernetix, Inc.; with supporting technologies and research from Gene Lee; Kelly Cohen, UC aerospace professor; Tim Arnett, UC aerospace doctoral student; and Air Force Research Laboratory sponsors. ALPHA is currently viewed as a research tool for manned and unmanned teaming in a simulation environment.

Morever, these algorithms are robust, so don't require problem-specific hand-tuning. One powerful example is sampling from an arbitrary probability distribution, which we need to do often (and efficiently!) when doing inference. The brute force approach, rejection sampling, is problematic because acceptance rates are low: as only a tiny fraction of attempts generate successful samples, the algorithms are slow and inefficient. See this post by Jeremey Kun for further details. Until recently, the main alternative to this naive approach was Markov Chain Monte Carlo sampling (of which Metropolis Hastings and Gibbs sampling are well-known examples). If you used Bayesian inference in the 90s or early 2000s, you may remember BUGS (and WinBUGS) or JAGS, which used these methods. These remain popular teaching tools (see e.g.

Search in an environment with an uncertain distribution of resources involves a trade-off between exploitation of past discoveries and further exploration. This extends to information foraging, where a knowledge-seeker shifts between reading in depth and studying new domains. To study this decision-making process, we examine the reading choices made by one of the most celebrated scientists of the modern era: Charles Darwin. From the full-text of books listed in his chronologically-organized reading journals, we generate topic models to quantify his local (text-to-text) and global (text-to-past) reading decisions using Kullback-Liebler Divergence, a cognitively-validated, information-theoretic measure of relative surprise. Rather than a pattern of surprise-minimization, corresponding to a pure exploitation strategy, Darwin's behavior shifts from early exploitation to later exploration, seeking unusually high levels of cognitive surprise relative to previous eras. These shifts, detected by an unsupervised Bayesian model, correlate with major intellectual epochs of his career as identified both by qualitative scholarship and Darwin's own self-commentary. Our methods allow us to compare his consumption of texts with their publication order. We find Darwin's consumption more exploratory than the culture's production, suggesting that underneath gradual societal changes are the explorations of individual synthesis and discovery. Our quantitative methods advance the study of cognitive search through a framework for testing interactions between individual and collective behavior and between short- and long-term consumption choices. This novel application of topic modeling to characterize individual reading complements widespread studies of collective scientific behavior.

Probabilistic modeling is a powerful approach for analyzing empirical information. We describe Edward, a library for probabilistic modeling. Edward's design reflects an iterative process pioneered by George Box: build a model of a phenomenon, make inferences about the model given data, and criticize the model's fit to the data. Edward supports a broad class of probabilistic models, efficient algorithms for inference, and many techniques for model criticism. The library builds on top of TensorFlow to support distributed training and hardware such as GPUs. Edward enables the development of complex probabilistic models and their algorithms at a massive scale.

The telecommunications industry is highly competitive, which means that the mobile providers need a business intelligence model that can be used to achieve an optimal level of churners, as well as a minimal level of cost in marketing activities. Machine learning applications can be used to provide guidance on marketing strategies. Furthermore, data mining techniques can be used in the process of customer segmentation. The purpose of this paper is to provide a detailed analysis of the C.5 algorithm, within naive Bayesian modelling for the task of segmenting telecommunication customers behavioural profiling according to their billing and socio-demographic aspects. Results have been experimentally implemented.

This paper provides a quantitative method for estimating the risk associated with candidate transportation technology, before it is developed and deployed. The proposed solution extends previous methods that rely exclusively on low-fidelity human-in-the-loop experimental data, or high-fidelity traffic data, by adopting a multifidelity approach that leverages data from both low- and high-fidelity sources. The multifidelity method overcomes limitations inherent to existing approaches by allowing a model to be trained inexpensively, while still assuring that its predictions generalize to the real-world. This allows for candidate technologies to be evaluated at the stage of conception, and enables a mechanism for only the safest and most effective technology to be developed and released.

The mixture models have become widely used in clustering, given its probabilistic framework in which its based, however, for modern databases that are characterized by their large size, these models behave disappointingly in setting out the model, making essential the selection of relevant variables for this type of clustering. After recalling the basics of clustering based on a model, this article will examine the variable selection methods for model-based clustering, as well as presenting opportunities for improvement of these methods.

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular these two models have the same dimension. The nested Markov model is therefore the best possible description of the latent variable model that avoids consideration of inequalities, which are extremely complicated in general. A consequence of this is that the constraint finding algorithm of Tian and Pearl (UAI 2002, pp519-527) is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and non-regular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.