As examples such as the Monty Hall puzzle show, applying conditioning to update a probability distribution on a ``naive space', which does not take into account the protocol used, can often lead to counterintuitive results. Here we examine why. A criterion known as CAR (coarsening at random) in the statistical literature characterizes when ``naive' conditioning in a naive space works. We show that the CAR condition holds rather infrequently. We then consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE). We give a generalization of the CAR condition that characterizes when Jeffrey conditioning leads to appropriate answers, but show that there are no such conditions for MRE. This generalizes and interconnects previous results obtained in the literature on CAR and MRE.

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures. It is shown that the technology of Bayesian networks can be applied to algebraic conditional plausibility measures.

In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' one. In such circumstances, selection of this best model is achieved using a model selection criterion, most often the Bayesian information criterion. Rather than throw away all but the best model, we average multiple models that are in some sense close to the best one, thereby producing a weighted average of clustering results. Two (weighted) averaging approaches are considered: averaging the component membership probabilities and averaging models. In both cases, Occam's window is used to determine closeness to the best model and weights are computed within a Bayesian model averaging paradigm. In some cases, we need to merge components before averaging; we introduce a method for merging mixture components based on the adjusted Rand index. The effectiveness of our model-based clustering averaging approaches is illustrated using a family of Gaussian mixture models on real and simulated data.

This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer latent structure, and cope with large numbers of observed processes. A further novel contribution enables the model to work effectively in higher dimensional spaces. Using this method, we achieve vastly improved predictive performance on both 2D and 1D real data, validating our structured approach.

How to forecast next year's portfolio-wide credit default rate based on last year's default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year's portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fix. From this observation we can conclude that the standard default rate forecast based on last year's conditional default rates will always be located between last year's portfolio-wide default rate and the ML forecast for next year. As an application example, then cost quantification is discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.

Building large-scale knowledge bases from a variety of data sources is a longstanding goal of AI research. However, existing approaches either ignore the uncertainty inherent to knowledge extracted from text, the web, and other sources, or lack a consistent probabilistic semantics with tractable inference. To address this problem, we present a framework for tractable probabilistic knowledge bases (TPKBs). TPKBs consist of a hierarchy of classes of objects and a hierarchy of classes of object pairs such that attributes and relations are independent conditioned on those classes. These characteristics facilitate both tractable probabilistic reasoning and tractable maximum-likelihood parameter learning. TPKBs feature a rich query language that allows one to express and infer complex relationships between classes, relations, objects, and their attributes. The queries are translated to sequences of operations in a relational database facilitating query execution times in the sub-second range. We demonstrate the power of TPKBs by leveraging large data sets extracted from Wikipedia to learn their structure and parameters. The resulting TPKB models a distribution over millions of objects and billions of parameters. We apply the TPKB to entity resolution and object linking problems and show that the TPKB can accurately align large knowledge bases and integrate triples from open IE projects.

Over the last couple of years, the interest in combining probability and logic has grown strongly. This led to the development of different software packages like PRISM, ProbLog and Alchemy, which offer a variety of exact and approximate algorithms to perform inference and learning. What is lacking, however, are algorithms to perform efficient inference in relational temporal models by systematically exploiting temporal and local structure. Since many real-world problems require temporal models, we argue that more research is necessary to use this structure to obtain more efficient inference and learning. While existing relational representations of dynamic domains focus rather on approximate inference techniques we propose an exact algorithm.

Hierarchical representations are common in many artificial intelligence tasks, such as classification of satellites in orbit. Representing and reasoning on hierarchies is difficult, however, as they can be large, deep and constantly evolving. Although probabilistic programming provides the flexibility to model many situations, current probabilistic programming languages (PPL) do not adequately support hierarchical reasoning. We present a novel PPL approach to representing and reasoning about hierarchies that utilizes references, enabling unambiguous access and referral to hierarchical objects and their properties.

Probabilistic soft logic (PSL) is a probabilistic modeling framework which uses first-order logic and soft truth values in the interval[0;1] for reasoning in relational domains. PSL uses the Łukasiewicz t-norm and t-conorm from fuzzy logic to model respectively conjunction and disjunction. A PSL rule such as Trusts(A;X)^Trusts(X;B)->Trusts(A;B) models that “A trusts B” is true to the degree to which there is a trusted third party X. In the current version of PSL there is no way to express that A should trust B if most trusted friends of A trust B. In this work, we propose an extension of PSL with fuzzy quantifiers to address this limitation.

Complex decision making scenarios require maintaining high level of concentration and acquiring knowledge about the context of the task in hand. Focus of attention is not only affected by contextual factors but also by the way operators interact with the information. Conversely, determining optimal ways to interact with this information can augment operators’ cognition. However, challenges exist for determining efficient mathematical frameworks and sound metrics to infer, reason and assess the level of attention during spatio-temporal complex problem solving in hybrid human-machine systems. This paper proposes a computational framework based on a Bayesian approach (BAN) to infer users’ focus of attention based on physical expression generated from embodied interaction and further support decision-making in an unobtrusive manner. Experiments involving five interaction modalities (vision-based gesture interaction, glove-based gesture interaction, speech, feet, and body balance) were conducted to assess the proposed framework’s feasibility including the likelihood of assessed attention from enhanced BAN and task performance. Results confirm that physical expressions have a determining effect in the quality of the solutions in spatio-navigational type of problems.