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In this paper, we propose a system for automatic image annotation that has two main components. The first component consists of a novel semi-supervised possibilistic clustering and feature weighting algorithm based on robust modeling of the generalized Dirichlet (GD) finite mixture. This algorithm is used to group image regions into prototypical region clusters that summarize the training data and can be used as the basis of annotating new test images. The constraints consist of pairs of image regions that should not be included in the same cluster. These constraints are deduced from the irrelevance of all concepts annotating the training images to help in guiding the clustering process. The second component of our system consists of a probabilistic model that relies on the possibilistic membership degrees, generated by the clustering algorithm, to annotate unlabeled images. The proposed system was implemented and tested on a data set that include thousands of images using four-fold cross validation.

In this paper, a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of being both simple and realistic, and avoid the need for frequent re-calibration. The model prices of n options and a forward contract are expressed as time-varying functions of an (n + 1)-dimensional Brownian motion and it is investigated how the Brownian trajectory can be determined from the trajectories of the price processes. An approach based on particle filtering is presented for determining the location of the driving Brownian motion from option prices observed in discrete time. A simulation study and an empirical study of call options on the S&P 500 index illustrate that the model provides a good fit to option price data.

Using Gaussian mixture models for clustering is a statistically mature method for clustering in data science with numerous successful applications in science and engineering. The parameters for a Gaussian mixture model (GMM) are typically estimated from training data using the iterative expectation-maximization algorithm, which requires the number of Gaussian components a priori. In this study, we propose two algorithms rooted in numerical algebraic geometry (NAG), namely, an area-based algorithm and a local maxima algorithm, to identify the optimal number of components. The area-based algorithm transforms several GMM with varying number of components into sets of equivalent polynomial regression splines. Next, it uses homotopy continuation methods for evaluating the resulting splines to identify the number of components that is most compatible with the gradient data. The local maxima algorithm forms a set of polynomials by fitting a smoothing spline to a dataset. Next, it uses NAG to solve the system of the first derivatives for finding the local maxima of the resulting smoothing spline, which represent the number of mixture components. The local maxima algorithm also identifies the location of the centers of Gaussian components. Using a real-world case study in automotive manufacturing and extensive simulations, we demonstrate that the performance of the proposed algorithms is comparable with that of Akaike information criterion (AIC) and Bayesian information criterion (BIC), which are popular methods in the literature. We also show the proposed algorithms are more robust than AIC and BIC when the Gaussian assumption is violated.

Ribonucleic acid (RNA) molecules play important roles in a variety of biological processes. To properly function, RNA molecules usually have to fold to specific structures, and therefore understanding RNA structure is vital in comprehending how RNA functions. One approach to understanding and predicting biomolecular structure is to use knowledge-based potentials built from experimentally determined structures. These types of potentials have been shown to be effective for predicting both protein and RNA structures, but their utility is limited by their significantly rugged nature. This ruggedness (and hence the potential's usefulness) depends heavily on the choice of bin width to sort structural information (e.g. distances) but the appropriate bin width is not known a priori. To circumvent the binning problem, we compared knowledge-based potentials built from inter-atomic distances in RNA structures using different mixture models (Kernel Density Estimation, Expectation Minimization and Dirichlet Process). We show that the smooth knowledge-based potential built from Dirichlet process is successful in selecting native-like RNA models from different sets of structural decoys with comparable efficacy to a potential developed by spline-fitting — a commonly taken approach — to binned distance histograms. The less rugged nature of our potential suggests its applicability in diverse types of structural modeling.

Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have been proposed in which the distribution of gene expression values within each sub-group is assumed to be Gaussian. In the presence of noise and extreme observations, a mixture of Gaussian densities may over-fit and overestimate the true number of clusters. Moreover, commonly used model-based clustering algorithms do not generally provide a mechanism to quantify the relative contribution of each gene to the final partitioning of the data. We propose a penalized mixture of Student's t distributions for model-based clustering and gene ranking. Together with a resampling procedure, the proposed approach provides a means for ranking genes according to their contributions to the clustering process. Experimental results show that the algorithm performs well comparably to traditional Gaussian mixtures in the presence of outliers and longer tailed distributions. The algorithm also identifies the true informative genes with high sensitivity, and achieves improved model selection. An illustrative application to breast cancer data is also presented which confirms established tumor sub-classes.

Clustering as an exploratory technique has been a promising approach for performing data analysis. In this paper, we propose a non-parametric Bayesian inference to address clustering problem. This approach is based on infinite multivariate Beta mixture models constructed through the framework of Dirichlet process. We apply an accelerated variational method to learn the model. The motivation behind proposing this technique is that Dirichlet process mixture models are capable to fit the data where the number of components is unknown. For large-scale data, this approach is computationally expensive. We overcome this problem with the help of accelerated Dirichlet process mixture models. Moreover, the truncation is managed using kd-trees. The performance of the model is validated on real medical applications and compared to three other similar alternatives. The results show the outperformance of our proposed framework.

Biomechanical modeling of human and animal brain tissue is a growing field of research, whose applications currently include simulating, with a view to minimizing, head injuries in car impacts, generically modeling dynamic behavior in the surgical theater, such as brain shift, and increasingly, providing medical experts with clinical tools such as surgical simulators and predictive models for tumour growth. This chapter provides an overview of the literature on the biomechanics of the brain, with a particular emphasis on applications to intrasurgical brain shift estimation and to surgical simulation. Included is a discussion of the underlying continua, of numerical estimation techniques, and of related cutting and resection models.

Most approaches in forecasting merely try to predict the next value of the time series. In contrast, this paper presents a framework to predict the full probability distribution. It is expressed as a mixture model: the dynamics of the individual states is modeled with so-called "experts" (potentially non-linear neural networks), and the dynamics between the states is modeled using a hidden Markov approach. The full density predictions are obtained by a weighted superposition of the individual densities of each expert. This model class is called "hidden Markov experts".

Results are presented for daily S&P500 data. While the predictive accuracy of the mean does not improve over simpler models, evaluating the prediction of the full density shows a clear out-of-sample improvement both over a simple GARCH(1,1) model (which assumes Gaussian distributed returns) and over a "gated experts" model (which expresses the weighting for each state non-recursively as a function of external inputs). Several interpretations are given: the blending of supervised and unsupervised learning, the discovery of hidden states, the combination of forecasts, the specialization of experts, the removal of outliers, and the persistence of volatility.

High dimensional mixture models are very important in bioinformatics. One major area of application is to DNA microarray data. The most difficult part of inference is the estimation of the mixing distribution. Our goal is to estimate the prior/mixing density f based on data observed from the marginal/mixture density π_f(x) = ∫ p(x|θ)f(θ) dμ(θ). We discuss properties of two relatively new and very fast algorithms for a NP Empirical Bayes estimate by M. Newton. These estimates are compared in simulations to the NP Bayes estimate. We provide motivation through stochastic approximation and prove convergence.

This paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals. We note that there is heterogeneity in behaviour between individuals and within individuals. By ‘heterogeneity between individuals’ we mean that people are different, in terms of both their preference functionals and their parameters for these functionals. By ‘heterogeneity within individuals’ we mean that the behaviour may be different even by the same individual for the same choice problem. We propose methods of taking into account all forms of heterogeneity, concentrating particularly on using a Mixture Model to capture the heterogeneity of preference functionals.

The recent spate of theoretical models of behaviour under ambiguity can be partitioned into two sets: those involving multiple priors and those not involving multiple priors. This paper provides an experimental investigation into the first set. Using an appropriate experimental interface we examine the fitted and predictive power of the various theories. We first estimate subject-by-subject, and then estimate and predict using a mixture model over the contending theories. The individual estimates suggest that 24% of our 149 subjects have behaviour consistent with Expected Utility, 56% with the Smooth Model, 11% with Rank Dependent Expected Utility and 9% with the Alpha Model; these figures are close to the mixing proportions obtained from the mixture estimates where the respective posterior probabilities of each of them being of the various types are 25%, 50%, 20% and 5%; and using the predictions 22%, 53%, 22% and 3%. The Smooth model appears the best.