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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 proba­ bility distribution, which is a special case of the distribution generated by proba­ bilistic inference networks. Hence both types of networks can be combined al­ lowing 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 'un­ observable' variables, and uncertain and contradictory evidence.
Integrating Probabilistic Rules into Neural Networks: A Stochastic EM Learning Algorithm

The Region Connection Calculus (RCC) [41] is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC5 and RCC8 (two fragments of RCC) as well as other qualitative spatial/temporal calculi has been investigated in depth in the literature. Most of these works focus on the consistency of qualitative constraint networks. In this paper, we consider the important problem of redundant qualitative constraints. For a set Γ of qualitative constraints, we say a constraint (xRy) in Γ is redundant if it is entailed by the rest of Γ. A prime subnetwork of Γ is a subset of Γ which contains no redundant constraints and has the same solution set as Γ. It is natural to ask how to compute such a prime subnetwork, and when it is unique. In this paper, we show that this problem is in general intractable, but becomes tractable if Γ is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of RCC5 or RCC8 in which weak composition distributes over nonempty intersections, then Γ has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from Γ. As a byproduct, we show that any path-consistent network over such a distributive subalgebra is weakly globally consistent and minimal. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant con∗Corresponding Author Email addresses: sanjiang.li@uts.edu.au (Sanjiang Li), zhiguo.long@student.uts.edu.au (Zhiguo Long), liuweiming@baidu.com (Weiming Liu), matt@duckham.org (Matt Duckham), aboth@student.unimelb.edu.au (Alan Both) Preprint submitted to Elsevier February 16, 2015 ar X iv :1 40 3. 06 13 v2 [ cs .A I] 1 3 Fe b 20 15 straints than previously proposed algorithms, especially in constraint networks with larger proportions of partial overlap relations.
On Redundant Topological Constraints

Multitask learning algorithms are typically designed assuming some fixed, a priori known latent structure shared by all the tasks. However, it is usually unclear what type of latent task structure is the most appropriate for a given multitask learning problem. Ideally, the “right” latent task structure should be learned in a data-driven manner. We present a flexible, nonparametric Bayesian model that posits a mixture of factor analyzers structure on the tasks. The nonparametric aspect makes the model expressive enough to subsume many existing models of latent task structures (e.g, meanregularized tasks, clustered tasks, low-rank or linear/non-linear subspace assumption on tasks, etc.). Moreover, it can also learn more general task structures, addressing the shortcomings of such models. We present a variational inference algorithm for our model. Experimental results on synthetic and realworld datasets, on both regression and classification problems, demonstrate the effectiveness of the proposed method.

Flexible Modeling of Latent Task Structures in Multitask Learning