instruction:
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:
We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization of the empirical risk. We focus on problems without strong convexity, for which all previously known algorithms achieve a convergence rate for function values of O(1/ √
answer:
Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n)


question:
Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stable-model semantics. We define the notion of a DLP-function, where a well-defined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stable-model semantics for DLP-functions. The module theorem extends the well-known splitting-set theorem and enables the decomposition of DLP-functions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLP-functions using a generalization of a translation-based verification method.
answer:
Modularity Aspects of Disjunctive Stable Models


question:
In this paper, we discuss how machine learning could be used to produce a systematic and more objective political discourse analysis. Political footprints are vector space models (VSMs) applied to political discourse. Each of their vectors represents a word, and is produced by training the English lexicon on large text corpora. This paper presents a simple implementation of political footprints, some heuristics on how to use them, and their application to four cases: the U.N. Kyoto Protocol and Paris Agreement, and two U.S. presidential elections. The reader will be offered a number of reasons to believe that political footprints produce meaningful results, along with some suggestions on how to improve their implementation.
answer:

Political Footprints: Political Discourse Analysis using Pre-Trained Word Vectors