Exact inference of marginals in probabilistic graphical models (PGM) is known to be intractable, necessitating the use of approximate methods. Most of the existing variational techniques perform iterative message passing in loopy graphs which is slow to converge for many benchmarks. In this paper, we propose a new algorithm for marginal inference that is based on the incremental build-infer-approximate (IBIA) paradigm. Our algorithm converts the PGM into a sequence of linked clique tree forests (SLCTF) with bounded clique sizes, and then uses a heuristic belief update algorithm to infer the marginals. For the special case of Bayesian networks, we show that if the incremental build step in IBIA uses the topological order of variables then (a) the prior marginals are consistent in all CTFs in the SLCTF and (b) the posterior marginals are consistent once all evidence variables are added to the SLCTF. In our approach, the belief propagation step is non-iterative and the accuracy-complexity trade-off is controlled using user-defined clique size bounds. Results for several benchmark sets from recent UAI competitions show that our method gives either better or comparable accuracy than existing variational and sampling based methods, with smaller runtimes.

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do not have this limitation, they are not interpretable and are inherently unable to deal with causal structure in the input space. Our goal is to build neural networks that combine the advantages of both approaches. Motivated by the perspective to inject causal knowledge while training such neural networks, this work presents initial steps in that direction. We demonstrate how a neural network can be trained to output conditional probabilities, providing approximately the same functionality as a Bayesian Network. Additionally, we propose two training strategies that allow encoding the independence relations inferred from a given causal structure into the neural network.

Exact inference in Bayesian networks is intractable and has an exponential dependence on the size of the largest clique in the corresponding clique tree (CT), necessitating approximations. Factor based methods to bound clique sizes are more accurate than structure based methods, but expensive since they involve inference of beliefs in a large number of candidate structure or region graphs. We propose an alternative approach for approximate inference based on an incremental build-infer-approximate (IBIA) paradigm, which converts the Bayesian network into a data structure containing a sequence of linked clique tree forests (SLCTF), with clique sizes bounded by a user-specified value. In the incremental build stage of this approach, CTFs are constructed incrementally by adding variables to the CTFs as long as clique sizes are within the specified bound. Once the clique size constraint is reached, the CTs in the CTF are calibrated in the infer stage of IBIA. The resulting clique beliefs are used in the approximate phase to get an approximate CTF with reduced clique sizes. The approximate CTF forms the starting point for the next CTF in the sequence. These steps are repeated until all variables are added to a CTF in the sequence. We prove that our algorithm for incremental construction of clique trees always generates a valid CT and our approximation technique preserves the joint beliefs of the variables within a clique. Based on this, we show that the SLCTF data structure can be used for efficient approximate inference of partition function and prior and posterior marginals. More than 500 benchmarks were used to test the method and the results show a significant reduction in error when compared to other approximate methods, with competitive runtimes.

Various AI models are increasingly being considered as part of clinical decision-support tools. However, the trustworthiness of such models is rarely considered. Clinicians are more likely to use a model if they can understand and trust its predictions. Key to this is if its underlying reasoning can be explained. A Bayesian network (BN) model has the advantage that it is not a black-box and its reasoning can be explained. In this paper, we propose an incremental explanation of inference that can be applied to'hybrid' BNs, i.e. those that contain both discrete and continuous nodes. The key questions that we answer are: (1) which important evidence supports or contradicts the prediction, and (2) through which intermediate variables does the information flow. The explanation is illustrated using a real clinical case study. A small evaluation study is also conducted.

The biggest limitation of probabilistic graphical models is the complexity of inference, which is often intractable. An appealing alternative is to use tractable probabilistic models, such as arithmetic circuits (ACs) and sum-product networks (SPNs), in which marginal and conditional queries can be answered efficiently. In this paper, we present the first discriminative structure learning algorithm for ACs, DACLearn (Discriminative AC Learner), which optimizes conditional log-likelihood. Based on our experiments, DACLearn learns models that are more accurate and compact than other tractable generative and discriminative baselines.

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form decisions from incomplete data in diagnostic problems has highlighted probabilistic methods [5] which compute posterior probabilities from prior distributions in a way similar to Bayes Rule, and thus are called Bayesian methods. This paper documents the use of a Bayesian method in a real time problem which is similar to medical diagnosis in that there is a need to form decisions and take some action without complete knowledge of conditions in the problem domain. This particular method has a limitation which is discussed.

Explanation facilities are a particularly important feature of expert system frameworks. It is an area in which traditional rule-based expert system frameworks have had mixed results. While explanations about control are well handled, facilities are needed for generating better explanations concerning knowledge base content. This paper approaches the explanation problem by examining the effect an event has on a variable of interest within a symmetric Bayesian inferencing system. We argue that any effect measure operating in this context must satisfy certain properties. Such a measure is proposed. It forms the basis for an explanation facility which allows the user of the Generalized Bayesian Inferencing System to question the meaning of the knowledge base. That facility is described in detail.

During the ongoing debate over the representation of uncertainty in Artificial Intelligence, Cheeseman, Lemmer, Pearl, and others have argued that probability theory, and in particular the Bayesian theory, should be used as the basis for the inference mechanisms of Expert Systems dealing with uncertainty. In order to pursue the issue in a practical setting, sophisticated tools for knowledge engineering are needed that allow flexible and understandable interaction with the underlying knowledge representation schemes. This paper describes a Generalized Bayesian framework for building expert systems which function in uncertain domains, using algorithms proposed by Lemmer. It is neither rule-based nor frame-based, and requires a new system of knowledge engineering tools. The framework we describe provides a knowledge-based system architecture with an inference engine, explanation capability, and a unique aid for building consistent knowledge bases.

Any probabilistic model of a problem is based on assumptions which, if violated, invalidate the model. Users of probability based decision aids need to be alerted when cases arise that are not covered by the aid's model. Diagnosis of model failure is also necessary to control dynamic model construction and revision. This paper presents a set of decision theoretically motivated heuristics for diagnosing situations in which a model is likely to provide an inadequate representation of the process being modeled.