The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The sequence reconstruction problem that we take as our formulation of DNA sequence assembly is a variation of the shortest common superstring problem, complicated by the presence of sequencing errors and reverse complements of fragments. Since the simpler superstring problem is NP-hard, any efficient reconstruction procedure must resort to heuristics. In this paper, however, a four phase approach based on rigorous design criteria is presented, and has been found to be very accurate in practice. Our method is robust in the sense that it can accommodate high sequencing error rates and list a series of alternate solutions in the event that several appear equally good. Moreover it uses a limited form ...

In this thesis we develop a discriminative learning method for dependency parsing using online large-margin training combined with spanning tree inference algorithms. We will show that this method provides state-of-the-art accuracy, is extensible through the feature set and can be implemented efficiently. Furthermore, we display the language independent nature of the method by evaluating it on over a dozen diverse languages as well as show its practical applicability through integration into a sentence compression system. We start by presenting an online large-margin learning framework that is a generaliza- tion of the work of Crammer and Singer [34, 37] to structured outputs, such as sequences and parse trees. This will lead to the heart of this thesis – discriminative dependency pars- ing. Here we will formulate dependency parsing in a spanning tree framework, yielding efficient parsing algorithms for both projective and non-projective tree structures. We will then extend the parsing algorithm to incorporate features over larger substructures with- out an increase in computational complexity for the projective case. Unfortunately, the non-projective problem then becomes NP-hard so we provide structurally motivated ap- proximate algorithms. Having defined a set of parsing algorithms, we will also define a rich feature set and train various parsers using the online large-margin learning framework. We then compare our trained dependency parsers to other state-of-the-art parsers on 14 diverse languages: Arabic, Bulgarian, Chinese, Czech, Danish, Dutch, English, German, Japanese, Portuguese, Slovene, Spanish, Swedish and Turkish. Having built an efficient and accurate discriminative dependency parser, this thesis will then turn to improving and applying the parser. First we will show how additional re- sources can provide useful features to increase parsing accuracy and to adapt parsers to new domains. We will also argue that the robustness of discriminative inference-based learning algorithms lend themselves well to dependency parsing when feature representa- tions or structural constraints do not allow for tractable parsing algorithms. Finally, we integrate our parsing models into a state-of-the-art sentence compression system to show its applicability to a real world problem.

Cancer has complex patterns of progression that include converging as well as diverging progressional pathways. Vogelstein’s path model of colon cancer was a pioneering contribution to cancer research. Since then, several attempts have been made at obtaining mathematical models of cancer progression, devising learning algorithms, and applying these to cross-sectional data. Beerenwinkel et al. provided, what they coined, EM-like algorithms for Oncogenetic Trees (OTs) and mixtures of such. Given the small size of current and future data sets, it is important to minimize the number of parameters of a model. For this reason, we too focus on tree-based models and introduce Hidden-variable Oncogenetic Trees (HOTs). In contrast to OTs, HOTs allow for errors in the data and thereby provide more realistic modeling. We also design global structural EM algorithms for learning HOTs and mixtures of HOTs (HOT-mixtures). The algorithms are global in the sense that, during the M-step, they find a structure that yields a global maximum of the expected complete log-likelihood rather than merely one that improves it. The algorithm for single HOTs performs very well on reasonable-sized data sets, while that for HOT-mixtures requires data sets of sizes obtainable only with tomorrow’s more cost-efficient technologies. 1