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.

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.

We derive generalization error bounds for traditional time-series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These non-asymptotic bounds need only weak assumptions on the data-generating process, yet allow forecasters to select among competing models and to guarantee, with high probability, that their chosen model will perform well. We motivate our techniques with and apply them to standard economic and financial forecasting tools---a GARCH model for predicting equity volatility and a dynamic stochastic general equilibrium model (DSGE), the standard tool in macroeconomic forecasting. We demonstrate in particular how our techniques can aid forecasters and policy makers in choosing models which behave well under uncertainty and mis-specification.

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.

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.

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.

In the IT world it is very important to get things exactly right, unless of course you are dealing with fuzzy logic. If your banking system, for example, is out by a decimal place, this can lead to some very unhappy customers or some very happy ones and a less than happy bank. There are many areas where calculations and units of measure are vital, just ask one of the Mars exploration landing teams. Not so obvious are making sure that things like translation services are accurate, as Microsoft found out recently. The Bing search engine saw some very red-faced Redmondites when Saudi Arabian users found that "Daesh" has been translated as "Saudi Arabia". For those not familiar with the term, Daesh is one name for Isis.

Hearing Aid (HA) algorithms need to be tuned ("fitted") to match the impairment of each specific patient. The lack of a fundamental HA fitting theory is a strong contributing factor to an unsatisfying sound experience for about 20% of hearing aid patients. This paper proposes a probabilistic modeling approach to the design of HA algorithms. The proposed method relies on a generative probabilistic model for the hearing loss problem and provides for automated inference of the corresponding (1) signal processing algorithm, (2) the fitting solution as well as a principled (3) performance evaluation metric. All three tasks are realized as message passing algorithms in a factor graph representation of the generative model, which in principle allows for fast implementation on hearing aid or mobile device hardware. The methods are theoretically worked out and simulated with a custom-built factor graph toolbox for a specific hearing loss model.

Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case basis; examples include robust linear regression, robust mixture models, and bursty topic models. In this paper we develop a general approach to robust Bayesian modeling. We show how to turn an existing Bayesian model into a robust model, and then develop a generic strategy for computing with it. We use our method to study robust variants of several models, including linear regression, Poisson regression, logistic regression, and probabilistic topic models. We discuss the connections between our methods and existing approaches, especially empirical Bayes and James-Stein estimation.