Optimal inference with local expressions

Probabilistic inference using Bayesian networks is now a well-established approach for reasoning under uncertainty. Among many e ciency-driven tech- niques which have been developed, the Optimal Factoring Problem (OFP) is distinguished for presenting a combinatorial optimization point of view on the problem. The contribution of this thesis is to extend OFP into a theoretical frame- work that not only covers the standard Bayesian networks but also includes non-standard Bayesian networks. A non-standard Bayesian network has struc- tures within its local distributions that are signi cant to the problem. This thesis presents value sets algebra as a coherent framework that facilitates formal treatments of inference in both standard and non-standard Bayesian networks as a combinatorial optimization problem. Parallel to value sets algebra theory local expression languages allow one to symbolically encode Bayesian network distributions. Such symbolic encod- ings allow all the structural and numerical information in distributions to be represented in the most compact form. However, the symbolic and syntactic exibilities in local expression languages have the usual drawback of allow- ing possible incoherent expressions. Value sets algebra leads us to an e cient coherency veri cation on such expressions. This thesis views optimal inference with local expressions as an optimal search problem. The search space for this problem is shown to be so large that it renders any exhaustive search impractical. Hence it is necessary to turn to heuristic solutions. Using A* heuristic framework and ideas from OFP, which is the counterpart of this problem for standard Bayesian networks, a heuris- tic algorithm for the problem is developed. As a key feature, this algorithm di erentiates between symbolic combinations of expressions and arithmetic op- erations in the expressions. Cost bearing arithmetic operations are performed only when su cient information is available to guarantee that no saving oppor- tunities are lost. On the other hand, expressions are combined in a way that quickly provides maximum opportunity for e cient arithmetic operations. This thesis also explores the representation of Intercausal Independencies (ICI) in Bayesian networks and de nes some new operators in local expression language which are shown to facilitate more e cient ICI representations

On the 3D point cloud for human-pose estimation

This thesis aims at investigating methodologies for estimating a human pose from a 3D point cloud that is captured by a static depth sensor. Human-pose estimation (HPE) is important for a range of applications, such as human-robot interaction, healthcare, surveillance, and so forth. Yet, HPE is challenging because of the uncertainty in sensor measurements and the complexity of human poses. In this research, we focus on addressing challenges related to two crucial components in the estimation process, namely, human-pose feature extraction and human-pose modeling. In feature extraction, the main challenge involves reducing feature ambiguity. We propose a 3D-point-cloud feature called viewpoint and shape feature histogram (VISH) to reduce feature ambiguity by capturing geometric properties of the 3D point cloud of a human. The feature extraction consists of three steps: 3D-point-cloud pre-processing, hierarchical structuring, and feature extraction. In the pre-processing step, 3D points corresponding to a human are extracted and outliers from the environment are removed to retain the 3D points of interest. This step is important because it allows us to reduce the number of 3D points by keeping only those points that correspond to the human body for further processing. In the hierarchical structuring, the pre-processed 3D point cloud is partitioned and replicated into a tree structure as nodes. Viewpoint feature histogram (VFH) and shape features are extracted from each node in the tree to provide a descriptor to represent each node. As the features are obtained based on histograms, coarse-level details are highlighted in large regions and fine-level details are highlighted in small regions. Therefore, the features from the point cloud in the tree can capture coarse level to fine level information to reduce feature ambiguity. In human-pose modeling, the main challenges involve reducing the dimensionality of human-pose space and designing appropriate factors that represent the underlying probability distributions for estimating human poses. To reduce the dimensionality, we propose a non-parametric action-mixture model (AMM). It represents high-dimensional human-pose space using low-dimensional manifolds in searching human poses. In each manifold, a probability distribution is estimated based on feature similarity. The distributions in the manifolds are then redistributed according to the stationary distribution of a Markov chain that models the frequency of human actions. After the redistribution, the manifolds are combined according to a probability distribution determined by action classification. Experiments were conducted using VISH features as input to the AMM. The results showed that the overall error and standard deviation of the AMM were reduced by about 7.9% and 7.1%, respectively, compared with a model without action classification. To design appropriate factors, we consider the AMM as a Bayesian network and propose a mapping that converts the Bayesian network to a neural network called NN-AMM. The proposed mapping consists of two steps: structure identification and parameter learning. In structure identification, we have developed a bottom-up approach to build a neural network while preserving the Bayesian-network structure. In parameter learning, we have created a part-based approach to learn synaptic weights by decomposing a neural network into parts. Based on the concept of distributed representation, the NN-AMM is further modified into a scalable neural network called NND-AMM. A neural-network-based system is then built by using VISH features to represent 3D-point-cloud input and the NND-AMM to estimate 3D human poses. The results showed that the proposed mapping can be utilized to design AMM factors automatically. The NND-AMM can provide more accurate human-pose estimates with fewer hidden neurons than both the AMM and NN-AMM can. Both the NN-AMM and NND-AMM can adapt to different types of input, showing the advantage of using neural networks to design factors

On CARICOM and the Varying Levels of and Motives for Integration Among the Member States

In an era of rapid transport and communication, spectators have come to expect a bridging of the classic political, social, and economic divide between states. It is taken for granted that states have more to work together than to strive independently for. CARICOM is the Caribbean\u27s experiment at regional integration and it member states have pledged their ostensible support. This study is aimed at gauging the true levels of enthusiasm of the member states, which have varied among them and over time. By analysing the trade pattern of the Members with each other in comparison with the rest of the world, the commitment of the member states was ascertained. The study explores various issues and characteristics of the region that help to bolster or threaten increased cooperation among the Members. Among these, external dependency, social peculiarities, and the vulnerability of the Members makes for an interesting and uncertain prediction for the group\u27s future. Using various indicators and indices from such sources as the World Bank, International Monetary Fund, and the Commonwealth Secretariat the states were compared and their various situations analysed to give reason for their varied levels of commitment to regionalisation through CARICOM. Certainly possessing more in common than not, the Members prove an exception, or perhaps a refutation to the idea of international cooperation being positively affected or catalysed by commonality