Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the relationship between evidence and hypothesis in a directed manner. Moreover, the direction in which evidence is stored is typically from evidence to hypothesis.

IDEAL (Influence Diagram Evaluation and Analysis in Lisp) is a software environment for creation and evaluation of belief networks and influence diagrams. IDEAL is primarily a research tool and provides an implementation of many of the latest developments in belief network and influence diagram evaluation in a unified framework. This paper describes IDEAL and some lessons learned during its development.

This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to implement them in expert systems. The Bayesian theory is well known; its main ideas go back to the work of Thomas Bayes (1702-1761). The theory of belief functions, often called the Dempster-Shafer theory in the artificial intelligence community, is less well known, but it has even older antecedents; belief-function arguments appear in the work of George Hooper (16401723) and James Bernoulli (1654-1705). For elementary expositions of the theory of belief functions, see Shafer (1976, 1985).

This paper shows that the common method used for making predictions under uncertainty in A1 and science is in error. This method is to use currently available data to select the best model from a given class of models-this process is called abduction-and then to use this model to make predictions about future data. The correct method requires averaging over all the models to make a prediction-we call this method transduction. Using transduction, an AI system will not give misleading results when basing predictions on small amounts of data, when no model is clearly best. For common classes of models we show that the optimal solution can be given in closed form.

This paper derives a formula for computing the conditional probability of a set of candidates, where a candidate is a set of disorders that explain a given set of positive findings. Such candidate sets are produced by a recent method for multidisorder diagnosis called symptom clustering. A symptom clustering represents a set of candidates compactly as a cartesian product of differential diagnoses. By evaluating the probability of a candidate set, then, a large set of candidates can be validated or pruned simultaneously. The probability of a candidate set is then specialized to obtain the probability of a single candidate. Unlike earlier results, the equation derived here allows the specification of positive, negative, and unknown symptoms and does not make assumptions about disorders not in the candidate.

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the compressed data is available analytically, speeding up computation by many orders of magnitude while also bypassing robustness issues due to convergence and mixing problems with MCMC. Model averaging is used to reduce sensitivity to the random projection matrix, while accommodating uncertainty in the subspace dimension. Strong theoretical support is provided for the approach by showing near parametric convergence rates for the predictive density in the large p small n asymptotic paradigm. Practical performance relative to competitors is illustrated in simulations and real data applications.

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.

Network detection is an important capability in many areas of applied research in which data can be represented as a graph of entities and relationships. Oftentimes the object of interest is a relatively small subgraph in an enormous, potentially uninteresting background. This aspect characterizes network detection as a "big data" problem. Graph partitioning and network discovery have been major research areas over the last ten years, driven by interest in internet search, cyber security, social networks, and criminal or terrorist activities. The specific problem of network discovery is addressed as a special case of graph partitioning in which membership in a small subgraph of interest must be determined. Algebraic graph theory is used as the basis to analyze and compare different network detection methods. A new Bayesian network detection framework is introduced that partitions the graph based on prior information and direct observations. The new approach, called space-time threat propagation, is proved to maximize the probability of detection and is therefore optimum in the Neyman-Pearson sense. This optimality criterion is compared to spectral community detection approaches which divide the global graph into subsets or communities with optimal connectivity properties. We also explore a new generative stochastic model for covert networks and analyze using receiver operating characteristics the detection performance of both classes of optimal detection techniques.

A new probabilistic network construction system, DYNASTY, is proposed for diagnostic reasoning given variables whose probabilities change over time. Diagnostic reasoning is formulated as a sequential stochastic process, and is modeled using influence diagrams. Given a set O of observations, DYNASTY creates an influence diagram in order to devise the best action given O. Sensitivity analyses are conducted to determine if the best network has been created, given the uncertainty in network parameters and topology. DYNASTY uses an equivalence class approach to provide decision thresholds for the sensitivity analysis. This equivalence-class approach to diagnostic reasoning differentiates diagnoses only if the required actions are different. A set of network-topology updating algorithms are proposed for dynamically updating the network when necessary.

The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural networks describing the associative dependency of variables. These networks have a probability distribution, which is a special case of the distribution generated by probabilistic inference networks. Hence both types of networks can be combined allowing to integrate probabilistic rules as well as unspecified associations in a sound way. The resulting network may have a number of interesting features including cycles of probabilistic rules, hidden 'unobservable' variables, and uncertain and contradictory evidence.