The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to engineering their knowledge bases. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.

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This article describes a theory of reasoning about uncertainty, baaed on a representation of states of certainty called endorsements The theory of endorsements is an alternative to numerical methods for reasoning about uncertainty, such as subjective Bayesian methods (Shortliffe and Buchanan, 1975; Duda, Hart, and Nilsson, 1976) and the Shafer-Dempster theory (Shafer, 1976). The fundamental concern with numerical representations of certainty is that they hide the reasoning that produces them and thus limit one's reasoning about uncertainty While numbers are easy to propagate over inferences, what the numbers mean is unclear The theory of endorsements provides a richer representation of the factors that affect certainty and supports multiple strategies for dealing with uncertainty. People's certainty of the past is limited by the fidelity of the devices that record it, their knowledge of the present is always incomplete, and their knowledge of the future is but speculation. Even though nothing is certain, people behave as if almost nothing is uncertain. They are adept at discounting uncertainty - making it go away.

The emergence of expert systems as one of the major areas of activity within AI has resulted in a rapid growth of interest within the AI community in issues relating to the management of uncertainty and evidential reasoning. During the past two years, in particular, the Dempster-Shafer theory of evidence has att,ract,ed considerable attention as a promising method of dealing with some of the basic problems arising in combination of evidence and data fusion. To develop an adequate understanding of this theory requires considerable effort and a good background in probability theory. There is, however, a simple way of approaching the Dempster-Shafer theory that only requires a minimal familiarity with relational models of data. For someone with a background in AI or database management, this approach has the advantage of relating in a natural way to the familiar framework of AI and databases.

The recent article by Roger C. Schank ("Where's the AI", AI Magazine, Winter, 1991) brought a broad nostalgic smile to my face. I believe that I am the unnamed Yale junior faculty member to whose work Prof. Schank alluded. Perhaps the intervening years have eradicated his memory of my name or, more likely, he wished to spare me the ignominy of serving as one of his principal strawmen. I, however, fully mindful of Oscar Wilde's observation that the only thing worse than being talked about is not being talked about, would not have been insulted by being identified. But, my purpose in writing is neither to defend my scientific integrity nor to dispel my anonymity.

Such problems are generally notoriously difficult. In this article, we review the recently discovered notion of adaptive submodularity, an intuitive diminishing returns condition that generalizes the classical notion of submodular set functions to sequential decision problems. Problems exhibiting the adaptive submodularity property can be efficiently and provably nearoptimally solved using simple myopic policies. We illustrate this concept in several case studies of interest in computational sustainability: First, we demonstrate how it can be used to efficiently plan for resolving uncertainty in adaptive management scenarios. Then, we show how it applies to dynamic conservation planning for protecting endangered species, a case study carried out in collaboration with the U.S. Geological Survey and the U.S. Fish and Wildlife Service.

In this work we introduce PHOENICS, a probabilistic global optimization algorithm combining ideas from Bayesian optimization with concepts from Bayesian kernel density estimation. We propose an inexpensive acquisition function balancing the explorative and exploitative behavior of the algorithm. This acquisition function enables intuitive sampling strategies for an efficient parallel search of global minima. The performance of PHOENICS is assessed via an exhaustive benchmark study on a set of 15 discrete, quasi-discrete and continuous multidimensional functions. Unlike optimization methods based on Gaussian processes (GP) and random forests (RF), we show that PHOENICS is less sensitive to the nature of the co-domain, and outperforms GP and RF optimizations. We illustrate the performance of PHOENICS on the Oregonator, a difficult case-study describing a complex chemical reaction network. We demonstrate that only PHOENICS was able to reproduce qualitatively and quantitatively the target dynamic behavior of this nonlinear reaction dynamics. We recommend PHOENICS for rapid optimization of scalar, possibly non-convex, black-box unknown objective functions.

Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples are parking a car, driving in city traffic, playing golf, cooking a meal, and summarizing a story. In performing such tasks, humans use perceptions of time, direction, speed, shape, possibility, likelihood, truth, and other attributes of physical and mental objects. Reflecting the bounded ability of the human brain to resolve detail, perceptions are intrinsically imprecise. In more concrete terms, perceptions are f-granular, meaning that (1) the boundaries of perceived classes are unsharp and (2) the values of attributes are granulated, with a granule being a clump of values (points, objects) drawn together by indistinguishability, similarity, proximity, and function.

Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data and their hidden generation process, respectively. It has been pointed out that conventional statistical analysis is not applicable to these models, because redundancy of the latent variable produces singularities in the parameter space. In recent years, a method based on algebraic geometry has allowed us to analyze the accuracy of predicting observable variables when using Bayesian estimation. However, how to analyze latent variables has not been sufficiently studied, even though one of the main issues in unsupervised learning is to determine how accurately the latent variable is estimated. A previous study proposed a method that can be used when the range of the latent variable is redundant compared with the model generating data. The present paper extends that method to the situation in which the latent variables have redundant dimensions. We formulate new error functions and derive their asymptotic forms. Calculation of the error functions is demonstrated in two-layered Bayesian networks.

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explicit density which makes quantitative evaluations challenging. To bridge this gap, we propose Flow-GANs, a generative adversarial network for which we can perform exact likelihood evaluation, thus supporting both adversarial and maximum likelihood training. When trained adversarially, Flow-GANs generate high-quality samples but attain extremely poor log-likelihood scores, inferior even to a mixture model memorizing the training data; the opposite is true when trained by maximum likelihood. Results on MNIST and CIFAR-10 demonstrate that hybrid training can attain high held-out likelihoods while retaining visual fidelity in the generated samples.