Stochastic partition processes for exchangeable graphs produce axis-aligned blocks on a product space. In relational modeling, the resulting blocks uncover the underlying interactions between two sets of entities of the relational data. Although some flexible axis-aligned partition processes, such as the Mondrian process, have been able to capture complex interacting patterns in a hierarchical fashion, they are still in short of capturing dependence between dimensions. To overcome this limitation, we propose the Ostomachion process (OP), which relaxes the cutting direction by allowing for oblique cuts. The partitions generated by an OP are convex polygons that can capture inter-dimensional dependence. The OP also exhibits interesting properties: 1) Along the time line the cutting times can be characterized by a homogeneous Poisson process, and 2) on the partition space the areas of the resulting components comply with a Dirichlet distribution. We can thus control the expected number of cuts and the expected areas of components through hyper-parameters. We adapt the reversible-jump MCMC algorithm for inferring OP partition structures. The experimental results on relational modeling and decision tree classification have validated the merit of the OP.

Water pipe failures can cause significant economic and social costs, hence have become the primary challenge to water utilities. In this paper, we propose a Bayesian nonparametric approach, namely the Dirichlet process mixture of hierarchical beta process model, for water pipe failure prediction. It can select high-risk pipes for physical condition assessment, thereby preventing disastrous failures proactively.

Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.

Many prevalent multi-class classification approaches can be unified and generalized by the output coding framework which usually consists of three phases: (1) coding, (2) learning binary classifiers, and (3) decoding. Most of these approaches focus on the first two phases and predefined distance function is used for decoding. In this paper, however, we propose to perform learning in coding space for more adaptive decoding, thereby improving overall performance. Ramp loss is exploited for measuring multi-class decoding error. The proposed algorithm has uniform stability. It is insensitive to data noises and scalable with large scale datasets. Generalization error bound and numerical results are given with promising outcomes.

A novel bayesian non-parametric method for tracking is proposed in this paper. The foreground appearance distribution is modeled by unbounded mixtures controlled through a Bayesian non-parametric process. Two posterior inference strategies are provided: Gibbs sampling and sequential importance sampling. Both of these two sampling strategy benefits from the conjugate prior/posterior pairs by factorizing the joint posterior distributions. Once the mixture model is obtained/updated, the similarities/probablity of each observations assigned to this mixture model could be easily calculated. In model matching/verification, the Kullback-Leibler divergence and texture information is adopted for verification purpose. The robustness of our methods is demonstrated by the experiments.