Combining models in appropriate ways to achieve high performance is commonly seen in machine learning fields today. Although a large amount of combinatorial models have been created, little attention is drawn to the commons in different models and their connections. A general modelling technique is thus worth studying to understand model combination deeply and shed light on creating new models. Prediction markets show a promise of becoming such a generic, flexible combinatorial model. By reviewing on several popular combinatorial models and prediction market models, this paper aims to show how the market models can generalise different combinatorial stuctures and how they implement these popular combinatorial models in specific conditions. Besides, we will see among different market models, Storkey's \emph{Machine Learning Markets} provide more fundamental, generic modelling mechanisms than the others, and it has a significant appeal for both theoretical study and application.

This paper is the continuation of our research work about linguistic truth-valued concept lattice. In order to provide a mathematical tool for mining tacit knowledge, we establish a concrete model of 6-ary linguistic truth-valued concept lattice and introduce a mining algorithm through the structure consistency. Specifically, we utilize the attributes to depict knowledge, propose the 6-ary linguistic truth-valued attribute extended context and congener context to characterize tacit knowledge, and research the necessary and sufficient conditions of forming tacit knowledge. We respectively give the algorithms of generating the linguistic truth-valued congener context and constructing the linguistic truth-valued concept lattice.

The existence of a non-algorithmic side of the mind, conjectured by Penrose on the basis of G\"odel's first incompleteness theorem, is investigated here in terms of a quantum metalanguage. We suggest that, besides human ordinary thought, which can be formalized in a computable, logical language, there is another important kind of human thought, which is Turing-non-computable. This is methatought, the process of thinking about ordinary thought. Metathought can be formalized as a metalanguage, which speaks about and controls the logical language of ordinary thought. Ordinary thought has two computational modes, the quantum mode and the classical mode, the latter deriving from decoherence of the former. In order to control the logical language of the quantum mode, one needs to introduce a quantum metalanguage, which in turn requires a quantum version of Tarski Convention T.

For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.

Fuzzy rule based models have a capability to approximate any continuous function to any degree of accuracy on a compact domain. The majority of FLC design process relies on heuristic knowledge of experience operators. In order to make the design process automatic we present a genetic approach to learn fuzzy rules as well as membership function parameters. Moreover, several statistical information criteria such as the Akaike information criterion (AIC), the Bhansali-Downham information criterion (BDIC), and the Schwarz-Rissanen information criterion (SRIC) are used to construct optimal fuzzy models by reducing fuzzy rules. A genetic scheme is used to design Takagi-Sugeno-Kang (TSK) model for identification of the antecedent rule parameters and the identification of the consequent parameters. Computer simulations are presented confirming the performance of the constructed fuzzy logic controller.

The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is determined by the data. As for most Bayesian nonparametric models, exact posterior inference is intractable---practitioners use Markov chain Monte Carlo (MCMC) or variational inference. Inspired by the split-merge MCMC algorithm for the Dirichlet process (DP) mixture model, we describe a novel split-merge MCMC sampling algorithm for posterior inference in the HDP. We study its properties on both synthetic data and text corpora. We find that split-merge MCMC for the HDP can provide significant improvements over traditional Gibbs sampling, and we give some understanding of the data properties that give rise to larger improvements.

This work is motivated by the problem of image mis-registration in remote sensing and we are interested in determining the resulting loss in the accuracy of pattern classification. A statistical formulation is given where we propose to use data contamination to model and understand the phenomenon of image mis-registration. This model is widely applicable to many other types of errors as well, for example, measurement errors and gross errors etc. The impact of data contamination on classification is studied under a statistical learning theoretical framework. A closed-form asymptotic bound is established for the resulting loss in classification accuracy, which is less than $\epsilon/(1-\epsilon)$ for data contamination of an amount of $\epsilon$. Our bound is sharper than similar bounds in the domain adaptation literature and, unlike such bounds, it applies to classifiers with an infinite Vapnik-Chervonekis (VC) dimension. Extensive simulations have been conducted on both synthetic and real datasets under various types of data contamination, including label flipping, feature swapping and the replacement of feature values with data generated from a random source such as a Gaussian or Cauchy distribution. Our simulation results show that the bound we derive is fairly tight.

n order for robots to engage in dialog with human teammates, they must have the ability to map between words in the language and aspects of the external world. A solution to this symbol grounding problem (Harnad, 1990) would enable a robot to interpret commands such as “Drive over to receiving and pick up the tire pallet.” In this article we describe several of our results that use probabilistic inference to address the symbol grounding problem. Our specific approach is to develop models that factor according to the linguistic structure of a command. We first describe an early result, a generative model that factors according to the sequential structure of language, and then discuss our new framework, generalized grounding graphs (G3). The G3 framework dynamically instantiates a probabilistic graphical model for a natural language input, enabling a mapping between words in language and concrete objects, places, paths and events in the external world. We report on corpus-based experiments where the robot is able to learn and use word meanings in three real-world tasks: indoor navigation, spatial language video retrieval, and mobile manipulation.

Probabilistic logics are receiving a lot of attention today because of their expressive power for knowledge representation and learning. However, this expressivity is detrimental to the tractability of inference, when done at the propositional level. To solve this problem, various lifted inference algorithms have been proposed that reason at the first-order level, about groups of objects as a whole. Despite the existence of various lifted inference approaches, there are currently no completeness results about these algorithms. The key contribution of this paper is that we introduce a formal definition of lifted inference that allows us to reason about the completeness of lifted inference algorithms relative to a particular class of probabilistic models. We then show how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables.

We present a joint image segmentation and labeling model (JSL) which, given a bag of figure-ground segment hypotheses extracted at multiple image locations and scales, constructs a joint probability distribution over both the compatible image interpretations (tilings or image segmentations) composed from those segments, andover their labeling into categories. The process of drawing samples from the joint distribution can be interpreted as first sampling tilings, modeled as maximal cliques, from a graph connecting spatially non-overlapping segments in the bag [1], followed by sampling labels for those segments, conditioned on the choice of a particular tiling. We learn the segmentation and labeling parameters jointly,based on Maximum Likelihood with a novel Incremental Saddle Point estimation procedure. The partition function over tilings and labelings is increasingly moreaccurately approximated by including incorrect configurations that a not-yet-competent model rates probable during learning. We show that the proposed methodologymatches the current state of the art in the Stanford dataset [2], as well as in VOC2010, where 41.7% accuracy on the test set is achieved.