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.

Example Input: We develop a new semantics for defeasible infer­ ence based on extended probability measures al­ lowed to take infinitesimal values, on the inter­ pretation of defaults as generalized conditional probability constraints and on a preferred-model implementation of entropy-maximization.
Example Output: Defaults and lnfinitesimals Defeasible Inference by Nonarchimedean Entropy Maximization

Example Input: In natural-language discourse, related events tend to appear near each other to describe a larger scenario. Such structures can be formalized by the notion of a frame (a.k.a. template), which comprises a set of related events and prototypical participants and event transitions. Identifying frames is a prerequisite for information extraction and natural language generation, and is usually done manually. Methods for inducing frames have been proposed recently, but they typically use ad hoc procedures and are difficult to diagnose or extend. In this paper, we propose the first probabilistic approach to frame induction, which incorporates frames, events, participants as latent topics and learns those frame and event transitions that best explain the text. The number of frames is inferred by a novel application of a split-merge method from syntactic parsing. In end-to-end evaluations from text to induced frames and extracted facts, our method produced state-of-the-art results while substantially reducing engineering effort.
Example Output: Probabilistic Frame Induction∗

Example Input: 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., à 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.
Example Output:
Regularized EM Algorithms: A Unified Framework and Statistical Guarantees