In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
--------
Question: Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

Answer: Shortest path distance in random k-nearest neighbor graphs

Question: Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet our rigorous understanding of its performance is highly incomplete. Recently, work in Balakrishnan et al. (2014) has demonstrated that for an important class of problems, EM exhibits linear local convergence. In the high-dimensional setting, however, the M -step may not be well defined. We address precisely this setting through a unified treatment using regularization. While regularization for high-dimensional problems is by now well understood, the iterative EM algorithm requires a careful balancing of making progress towards the solution while identifying the right structure (e.g., sparsity or low-rank). In particular, regularizing the M -step using the state-of-the-art high-dimensional prescriptions (e.g., a la Wainwright (2014)) is not guaranteed to provide this balance. Our algorithm and analysis are linked in a way that reveals the balance between optimization and statistical errors. We specialize our general framework to sparse gaussian mixture models, high-dimensional mixed regression, and regression with missing variables, obtaining statistical guarantees for each of these examples.

Answer: Regularized EM Algorithms: A Unified Framework and Statistical Guarantees

Question: Question answering (QA) has been the subject of a resurgence over the past years. The said resurgence has led to a multitude of question answering (QA) systems being developed both by companies and research facilities. While a few components of QA systems get reused across implementations, most systems do not leverage the full potential of component reuse. Hence, the development of QA systems is currently still a tedious and time-consuming process. We address the challenge of accelerating the creation of novel or tailored QA systems by presenting a concept for a self-wiring approach to composing QA systems. Our approach will allow the reuse of existing, web-based QA systems or modules while developing new QA platforms. To this end, it will rely on QA modules being described using the Web Ontology Language. Based on these descriptions, our approach will be able to automatically compose QA systems using a data-driven approach automatically.

Answer:
Self-Wiring Question Answering Systems