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.

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.

Mining companies typically process all the material extracted from a mine site using processes which are extremely consumptive of energy and chemicals. Sorting the good material from the bad would effectively reduce required resources by leaving behind the bad material and only transporting and processing the good material. We use a relational influence diagram with an explicit utility model applied to the scenario in which an unknown number of rocks in unknown positions with unknown mineral compositions pass over 7 sensors toward 7 diverters on a high-throughput rock-sorting machine developed by MineSense Technologies Ltd. After receiving noisy sensor data, the system has 400 ms to decide whether to activate diverters which will divert the rocks into either a keep or discard bin. We learn the model offline and do online inference. Our result improves over the current state-of-the-art.

We study the problem of reasoning in the probabilistic Description Logic BEL. Using a novel structure, we show that probabilistic reasoning in this logic can be reduced in polynomial time to standard inferences over a Bayesian network. This reduction provides tight complexity bounds for probabilistic reasoning in BEL.

Crowdsourcing has been proven to be an effective and efficient tool to annotate large datasets. User annotations are often noisy, so methods to combine the annotations to produce reliable estimates of the ground truth are necessary. We claim that considering the existence of clusters of users in this combination step can improve the performance. This is especially important in early stages of crowdsourcing implementations, where the number of annotations is low. At this stage there is not enough information to accurately estimate the bias introduced by each annotator separately, so we have to resort to models that consider the statistical links among them. In addition, finding these clusters is interesting in itself as knowing the behavior of the pool of annotators allows implementing efficient active learning strategies. Based on this, we propose in this paper two new fully unsupervised models based on a Chinese Restaurant Process (CRP) prior and a hierarchical structure that allows inferring these groups jointly with the ground truth and the properties of the users. Efficient inference algorithms based on Gibbs sampling with auxiliary variables are proposed. Finally, we perform experiments, both on synthetic and real databases, to show the advantages of our models over state-of-the-art algorithms.

Neural connectomics has begun producing massive amounts of data, necessitating new analysis methods to discover the biological and computational structure. It has long been assumed that discovering neuron types and their relation to microcircuitry is crucial to understanding neural function. Here we developed a nonparametric Bayesian technique that identifies neuron types and microcircuitry patterns in connectomics data. It combines the information traditionally used by biologists, including connectivity, cell body location and the spatial distribution of synapses, in a principled and probabilistically-coherent manner. We show that the approach recovers known neuron types in the retina and enables predictions of connectivity, better than simpler algorithms. It also can reveal interesting structure in the nervous system of C. elegans, and automatically discovers the structure of a microprocessor. Our approach extracts structural meaning from connectomics, enabling new approaches of automatically deriving anatomical insights from these emerging datasets.

We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms of evaluation histories and conditional distributions on such histories. Church also includes a novel language construct, the stochastic memoizer, which enables simple description of many complex non-parametric models. We illustrate language features through several examples, including: a generalized Bayes net in which parameters cluster over trials, infinite PCFGs, planning by inference, and various non-parametric clustering models. Finally, we show how to implement query on any Church program, exactly and approximately, using Monte Carlo techniques.