We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference. We then show how the approximation can be extended to a wide class of discrete-state Markov jump pro- cesses by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.

We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is stable with respect to the specified noise model; we call the resulting procedure a stable autoencoder. In the simplest case, with an isotropic noise model, our method is equivalent to a classical singular value shrinkage estimator. For non-isotropic noise models, e.g., Poisson noise, the method does not reduce to singular value shrinkage, and instead yields new estimators that perform well in experiments. Moreover, by iterating our stable autoencoding scheme, we can automatically generate low-rank estimates without specifying the target rank as a tuning parameter.

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.

Data mining is everywhere, but its story starts many years before Moneyball and Edward Snowden. The following are major milestones and "firsts" in the history of data mining plus how it's evolved and blended with data science and big data. Data mining is the computational process of exploring and uncovering patterns in large data sets a.k.a. It is fundamental to data mining and probability, since it allows understanding of complex realities based on estimated probabilities. The goal of regression analysis is to estimate the relationships among variables, and the specific method they used in this case is the method of least squares.

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.

This book is very easy to read and understand. Unlike Hastie's Statistical Learning book, it is not geared towards those with an expert level knowledge of statistics, and instead takes time to explain functions and formulas for the person with a decent but not extrordinary understanding of statistical/math concepts. For example, their description of a Gaussian was the clearest I've seen. On the other hand, if you're math/statistics background is considerable, you may find this book somewhat simplistic or tedious. The book has a good coverage of techniques and algorithms, although I was somewhat disappointed that they do not mention Influence Diagrams, considering the amount of coverage of both decision trees and Bayesian techniques.

Relational logistic regression (RLR) is a representation of conditional probability in terms of weighted formulae for modelling multi-relational data. In this paper, we develop a learning algorithm for RLR models. Learning an RLR model from data consists of two steps: 1- learning the set of formulae to be used in the model (a.k.a. structure learning) and learning the weight of each formula (a.k.a. parameter learning). For structure learning, we deploy Schmidt and Murphy's hierarchical assumption: first we learn a model with simple formulae, then more complex formulae are added iteratively only if all their sub-formulae have proven effective in previous learned models. For parameter learning, we convert the problem into a non-relational learning problem and use an off-the-shelf logistic regression learning algorithm from Weka, an open-source machine learning tool, to learn the weights. We also indicate how hidden features about the individuals can be incorporated into RLR to boost the learning performance. We compare our learning algorithm to other structure and parameter learning algorithms in the literature, and compare the performance of RLR models to standard logistic regression and RDN-Boost on a modified version of the MovieLens data-set.

This paper proposes a novel dynamic Hierarchical Dirichlet Process topic model that considers the dependence between successive observations. Conventional posterior inference algorithms for this kind of models require processing of the whole data through several passes. It is computationally intractable for massive or sequential data. We design the batch and online inference algorithms, based on the Gibbs sampling, for the proposed model. It allows to process sequential data, incrementally updating the model by a new observation. The model is applied to abnormal behaviour detection in video sequences. A new abnormality measure is proposed for decision making. The proposed method is compared with the method based on the non- dynamic Hierarchical Dirichlet Process, for which we also derive the online Gibbs sampler and the abnormality measure. The results with synthetic and real data show that the consideration of the dynamics in a topic model improves the classification performance for abnormal behaviour detection.

Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction fifty years ago, and is now commonly utilized within the family setting. Families of mixture models arise when the component parameters, usually the component covariance matrices, are decomposed and a number of constraints are imposed. Within the family setting, we need to choose the member of the family, i.e., the appropriate covariance structure, in addition to the number of mixture components. To date, the Bayesian information criterion (BIC) has proved most effective for model selection, and the expectation-maximization (EM) algorithm is usually used for parameter estimation. To date, this EM-BIC rubric has monopolized the literature on families of mixture models. We deviate from this rubric, using variational Bayes approximations for parameter estimation and the deviance information criterion for model selection. The variational Bayes approach alleviates some of the computational complexities associated with the EM algorithm by constructing a tight lower bound on the complex marginal likelihood and maximizing this lower bound by minimizing the associated Kullback-Leibler divergence. We use this approach on the most famous family of Gaussian mixture models within the literature and real and simulated data are used to compare our approach to the EM-BIC rubric.

When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the posterior distribution are shared amongst groups, and hence groups can borrow information from each other. When normalized dependent random measures prior with independent increments are applied, we can derive appropriate exchangeable probability partition function (EPPF), and subsequently also deduce its inference algorithm given any mixture model likelihood. We provide all necessary derivation and solution to this framework. For demonstration, we used mixture of Gaussians likelihood in combination with a dependent structure constructed by linear combinations of CRMs. Our experiments show superior performance when using this framework, where the inferred values including the mixing weights and the number of clusters both respond appropriately to the number of completely random measure used.