{'fraction_non_alphanumeric': 0.015211267605633802, 'fraction_numerical': 0.0, 'mean_word_length': 5.166666666666667, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical Optimization Methods based on Discrete Structure for Text Summarization and Relational Learning

Numerical optimization problems have an important role in natural language processing (NLP) and many machine learning (ML) tasks, which are accomplished by first making a mathematical model, and then solving certain optimization problems based on the developed model. The difficulty in solving a numerical optimization problem affects the efficiency of a task, and it is therefore important to design a model such that it can formalize the task well, thereby making the optimization problem easy to solve. In this thesis, we propose novel numerical optimization methods for text summarization and relational learning, both of which are typical ML and NLP tasks that can be solved using numerical optimization methods. The key point to our methods is exploiting the discrete structure inherent to the problem domains for decomposing them into small subproblems. This approach has two merits. The first merit is efficiency, i.e., we can use a discrete structure inherent to a problem by decomposing the problem into small subproblems, thereby solving the original problem efficiently. The second merit is flexibility in the design of the optimization problems. We have to be careful when making a new optimization problem for a given NLP or ML task because an easy problem may become a far more difficult problem if we extend it by adding new constraints or objectives. Our technique is flexible from the viewpoint that it can extend existing optimization problems without making the new problem difficult to solve. In the thesis, we treat three different tasks for text summarization and relational learning, and present a concrete optimization method for each of them.