The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions to ensure efficient, polynomial time estimation of model parameters. For several combinatorial structures, including cycles, partially ordered sets, permutations and other graph classes, these assumptions do not hold. In this thesis, we address the problem of designing learning algorithms for predicting combinatorial structures by introducing two new assumptions: (i) The first assumption is that a particular counting problem can be solved efficiently. The consequence is a generalisation of the classical ridge regression for structured prediction. (ii) The second assumption is that a particular sampling problem can be solved efficiently. The consequence is a new technique for designing and analysing probabilistic structured prediction models. These results can be applied to solve several complex learning problems including but not limited to multi-label classification, multi-category hierarchical classification, and label ranking.

Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations in sparsely populated regions. We show that heavy-tailed stochastic processes (which we construct from Gaussian processes via a copula), can be used to improve robustness of regression and classification estimators to such outliers by selectively shrinking them more strongly in sparse regions than in dense regions. We carry out a theoretical analysis to show that selective shrinkage occurs, provided the marginals of the heavy-tailed process have sufficiently heavy tails. The analysis is complemented by experiments on biological data which indicate significant improvements of estimates in sparse regions while producing competitive results in dense regions.

Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the graph $G(x)$ of $Y$ conditioned on $X=x$ as ``graph-valued regression.'' In this paper, we propose a semiparametric method for estimating $G(x)$ that builds a tree on the $X$ space just as in CART (classification and regression trees), but at each leaf of the tree estimates a graph. We call the method ``Graph-optimized CART,'' or Go-CART. We study the theoretical properties of Go-CART using dyadic partitioning trees, establishing oracle inequalities on risk minimization and tree partition consistency. We also demonstrate the application of Go-CART to a meteorological dataset, showing how graph-valued regression can provide a useful tool for analyzing complex data.

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not suitable in high dimensional settings. In this paper, we present StARS: a new stability-based method for choosing the regularization parameter in high dimensional inference for undirected graphs. The method has a clear interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling. This interpretation requires essentially no conditions. Under mild conditions, we show that StARS is partially sparsistent in terms of graph estimation: i.e. with high probability, all the true edges will be included in the selected model even when the graph size diverges with the sample size. Empirically, the performance of StARS is compared with the state-of-the-art model selection procedures, including $K$-CV, AIC, and BIC, on both synthetic data and a real microarray dataset. StARS outperforms all these competing procedures.

The Dendritic Cell Algorithm (DCA) is an immune-inspired algorithm, developed for the purpose of anomaly detection. The algorithm performs multi-sensor data fusion and correlation which results in a 'context aware' detection system. Previous applications of the DCA have included the detection of potentially malicious port scanning activity, where it has produced high rates of true positives and low rates of false positives. In this work we aim to compare the performance of the DCA and of a Self-Organizing Map (SOM) when applied to the detection of SYN port scans, through experimental analysis. A SOM is an ideal candidate for comparison as it shares similarities with the DCA in terms of the data fusion method employed. It is shown that the results of the two systems are comparable, and both produce false positives for the same processes. This shows that the DCA can produce anomaly detection results to the same standard as an established technique.

The Lady Maisry ballads afford us a framework within which to segment a storyline into its major components. Segments and as a consequence nodal points are discussed for nine different variants of the Lady Maisry story of a (young) woman being burnt to death by her family, on account of her becoming pregnant by a foreign personage. We motivate the importance of nodal points in textual and literary analysis. We show too how the openings of the nine variants can be analyzed comparatively, and also the conclusions of the ballads.

Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called \emph{riffled independence}, encompassing a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the \emph{riffle shuffle}, common in card games, to combine the two permutations to form a single permutation. Within the context of ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. In this paper, we provide a formal introduction to riffled independence and present algorithms for using riffled independence within Fourier-theoretic frameworks which have been explored by a number of recent papers. Additionally, we propose an automated method for discovering sets of items which are riffle independent from a training set of rankings. We show that our clustering-like algorithms can be used to discover meaningful latent coalitions from real preference ranking datasets and to learn the structure of hierarchically decomposable models based on riffled independence.

Objectives: Text categorization has been used in biomedical informatics for identifying documents containing relevant topics of interest. We developed a simple method that uses a chi-square-based scoring function to determine the likelihood of MEDLINE citations containing genetic relevant topic. Methods: Our procedure requires construction of a genetic and a nongenetic domain document corpus. We used MeSH descriptors assigned to MEDLINE citations for this categorization task. We compared frequencies of MeSH descriptors between two corpora applying chi-square test. A MeSH descriptor was considered to be a positive indicator if its relative observed frequency in the genetic domain corpus was greater than its relative observed frequency in the nongenetic domain corpus. The output of the proposed method is a list of scores for all the citations, with the highest score given to those citations containing MeSH descriptors typical for the genetic domain. Results: Validation was done on a set of 734 manually annotated MEDLINE citations. It achieved predictive accuracy of 0.87 with 0.69 recall and 0.64 precision. We evaluated the method by comparing it to three machine learning algorithms (support vector machines, decision trees, na\"ive Bayes). Although the differences were not statistically significantly different, results showed that our chi-square scoring performs as good as compared machine learning algorithms. Conclusions: We suggest that the chi-square scoring is an effective solution to help categorize MEDLINE citations. The algorithm is implemented in the BITOLA literature-based discovery support system as a preprocessor for gene symbol disambiguation process.

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

Class prediction is an important application of microarray gene expression data analysis. The high-dimensionality of microarray data, where number of genes (variables) is very large compared to the number of samples (obser- vations), makes the application of many prediction techniques (e.g., logistic regression, discriminant analysis) difficult. An efficient way to solve this prob- lem is by using dimension reduction statistical techniques. Increasingly used in psychology-related applications, Rasch model (RM) provides an appealing framework for handling high-dimensional microarray data. In this paper, we study the potential of RM-based modeling in dimensionality reduction with binarized microarray gene expression data and investigate its prediction ac- curacy in the context of class prediction using linear discriminant analysis. Two different publicly available microarray data sets are used to illustrate a general framework of the approach. Performance of the proposed method is assessed by re-randomization scheme using principal component analysis (PCA) as a benchmark method. Our results show that RM-based dimension reduction is as effective as PCA-based dimension reduction. The method is general and can be applied to the other high-dimensional data problems.