We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal distribution. The selection method is based on testing conditional variances obtained for small subsets of process components. This allows to cope with the high-dimensional regime, where the sample size can be (drastically) smaller than the process dimension. We characterize the required sample size such that the proposed selection method is successful with high probability.

Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a general class of noisy matrix completion tasks where the underlying matrix is following an IMC model i.e., it is formed by a mixing matrix (a priori unknown) sandwiched between two known feature matrices. The mixing matrix here is assumed to be well approximated by the product of two sparse matrices---referred here to as "sparse factor models." We leverage the main theorem of Soni:2016:NMC and extend it to provide theoretical error bounds for the sparsity-regularized maximum likelihood estimators for the class of problems discussed in this paper. The main result is general in the sense that it can be used to derive error bounds for various noise models. In this paper, we instantiate our main result for the case of Gaussian noise and provide corresponding error bounds in terms of squared loss.

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and classification. It is well-known that solving for the sparse coefficient vector to maximize these priors results in a hard non-convex and mixed integer programming problem. Most existing solutions to this optimization problem either involve simplifying assumptions/relaxations or are computationally expensive. We propose a new greedy and adaptive matching pursuit (AMP) algorithm to directly solve this hard problem. Essentially, in each step of the algorithm, the set of active elements would be updated by either adding or removing one index, whichever results in better improvement. In addition, the intermediate steps of the algorithm are calculated via an inexpensive Cholesky decomposition which makes the algorithm much faster. Results on simulated data sets as well as real-world image recovery challenges confirm the benefits of the proposed AMP, particularly in providing a superior cost-quality trade-off over existing alternatives.

Two of today's major business and intellectual trends offer complementary insights about the challenge of making forecasts in a complex and rapidly changing world. Forty years of behavioral science research into the psychology of probabilistic reasoning have revealed the surprising extent to which people routinely base judgments and forecasts on systematically biased mental heuristics rather than careful assessments of evidence. These findings have fundamental implications for decision making, ranging from the quotidian (scouting baseball players and underwriting insurance contracts) to the strategic (estimating the time, expense, and likely success of a project or business initiative) to the existential (estimating security and terrorism risks). The bottom line: Unaided judgment is an unreliable guide to action. Consider psychologist Philip Tetlock's celebrated multiyear study concluding that even top journalists, historians, and political experts do little better than random chance at forecasting such political events as revolutions and regime changes.1 The second trend is the increasing ubiquity of data-driven decision making and artificial intelligence applications. Once again, an important lesson comes from behavioral science: A body of research dating back to the 1950s has established that even simple predictive models outperform human experts' ability to make predictions and forecasts. This implies that judiciously constructed predictive models can augment human intelligence by helping humans avoid common cognitive traps.

PsiberLogic is a completely free, open-source fuzzy logic controller package for Python 3. Psibernetix proudly supports the amazing Python community, and is happy to contribute to Python's open-source movement. This package is for anyone seeking a high-performance, python3-callable package for creating fuzzy logic controllers. 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.

ABSTRACT We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover that their operation corresponds to the assumption of a fixed posterior covariance that follows a simple parametric model. Interestingly, several well-known KLMS algorithms correspond to specific cases of this model. The probabilistic perspective allows us to understand how each of them handles uncertainty, which could explain some of their performance differences. Index Terms-- online learning, regression, Gaussian processes, kernel least-mean squares 1. INTRODUCTION Gaussian Process (GP) regression is a state-of-the-art Bayesian technique for nonlinear regression [1].

Generalization error bounds are probabilistically valid, non-asymptotic tools for characterizing the predictive ability of forecasting models. This methodology is fundamentally about choosing particular prediction functions out of some class of plausible alternatives so that, with high reliability, the resulting predictions will be nearly as accurate as possible ("probably approximately correct"). While many of these results are aimed at classification problems with independent and identically distributed (i.i.d.) data, this paper adapts and extends these methods to time-series models, so that economic and financial forecasting techniques can be evaluated rigorously. In particular, these methods control the expected accuracy of future predictions from mis-specified models based on finite samples. This allows for immediate model comparisons which neither appeal to asymptotics nor make strong assumptions about the data-generating process, in stark contrast to such popular model-selection tools as AIC.

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the multipoint expected improvement criterion. In turn, the latter relies on intermediate results that could be of independent interest concerning moments of truncated Gaussian vectors. The obtained expansion of the criterion enables studying its differentiability with respect to point batches and calculating the corresponding gradient in closed form. Furthermore , we derive fast numerical approximations of this gradient and propose efficient batch optimization strategies. Numerical experiments illustrate that the proposed approaches enable computational savings of between one and two order of magnitudes, hence enabling derivative-based batch-sequential acquisition function maximization to become a practically implementable and efficient standard.

Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood estimator and standard Bayesian procedures do not admit the root-$n$ parametric rate of convergence. We propose a general framework for the identification of singularity structures of the parameter space of finite mixtures, and study the impacts of the singularity levels on minimax lower bounds and rates of convergence for the maximum likelihood estimator over a compact parameter space. Our study makes explicit the deep links between model singularities, parameter estimation convergence rates and minimax lower bounds, and the algebraic geometry of the parameter space for mixtures of continuous distributions. The theory is applied to establish concrete convergence rates of parameter estimation for finite mixture of skewnormal distributions. This rich and increasingly popular mixture model is shown to exhibit a remarkably complex range of asymptotic behaviors which have not been hitherto reported in the literature.

Accurately determining dependency structure is critical to discovering a system's causal organization. We recently showed that the transfer entropy fails in a key aspect of this---measuring information flow---due to its conflation of dyadic and polyadic relationships. We extend this observation to demonstrate that this is true of all such Shannon information measures when used to analyze multivariate dependencies. This has broad implications, particularly when employing information to express the organization and mechanisms embedded in complex systems, including the burgeoning efforts to combine complex network theory with information theory. Here, we do not suggest that any aspect of information theory is wrong. Rather, the vast majority of its informational measures are simply inadequate for determining the meaningful dependency structure within joint probability distributions. Therefore, such information measures are inadequate for discovering intrinsic causal relations. We close by demonstrating that such distributions exist across an arbitrary set of variables.