Recommending Answers to Math Questions Based on KL-Divergence and Approximate XML Tree Matching

Math is the science and study of quality, structure, space, and change. It seeks out patterns, formulates new conjectures, and establishes the truth by rigorous deduction from appropriately chosen axioms and definitions. The study of math makes a person better at solving problems. It gives someone skills that can use across other subjects and apply in different job roles. In the modern world, builders use math every day to do their work, since construction workers add, subtract, divide, multiply, and work with fractions. It is obvious that math is a major contributor to many areas of study. For this reason, math information retrieval (Math IR) deserves attention and recognition, since a reliable Math IR system helps users find relevant answers to math questions and benefits all math learners whenever they need help solve a math problem, regardless of the time and place. Moreover, Math IR systems enhance the learning experience of their users. In this paper, we present MaRec, a recommender system that retrieves and ranks math answers based on their textual content and embedded formulas in answering a math question. MaRec ranks a potential answer A given a math question Q by computing the (i) KL-divergence score on A and Q using their textual contents, and (ii) the subtree matching score of the math formulas in Q and A represented as XML trees. The design of MaRec is simple and easy to understand, since it solely relies on a probability model and an elegant tree-matching approach in ranking math answers. Conducted empirical studies show that MaRec significantly outperforms (i) three existing state-of-the-art MathIR systems based on an offline evaluation, and (ii) two top-of-the-line machine learning systems based on an online analysis.