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:
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:
This paper studies theoretically and empirically a method of turning machinelearning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The price to pay for perfect calibration is that these probabilistic predictors produce imprecise (in practice, almost precise for large data sets) probabilities. When these imprecise probabilities are merged into precise probabilities, the resulting predictors, while losing the theoretical property of perfect calibration, are consistently more accurate than the existing methods in empirical studies. The conference version of this paper is to appear in Advances in Neural Information Processing Systems 28, 2015.
answer:
Large-scale probabilistic prediction with and without validity guarantees

question:
Extending the success of deep neural networks to natural language understanding and symbolic reasoning requires complex operations and external memory. Recent neural program induction approaches have attempted to address this problem, but are typically limited to differentiable memory, and consequently cannot scale beyond small synthetic tasks. In this work, we propose the Manager-ProgrammerComputer framework, which integrates neural networks with non-differentiable memory to support abstract, scalable and precise operations through a friendly neural computer interface. Specifically, we introduce a Neural Symbolic Machine, which contains a sequence-to-sequence neural "programmer", and a nondifferentiable "computer" that is a Lisp interpreter with code assist. To successfully apply REINFORCE for training, we augment it with approximate gold programs found by an iterative maximum likelihood training process. NSM is able to learn a semantic parser from weak supervision over a large knowledge base. It achieves new state-of-the-art performance on WEBQUESTIONSSP, a challenging semantic parsing dataset. Compared to previous approaches, NSM is end-to-end, therefore does not rely on feature engineering or domain specific knowledge.
answer:
Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision (Short Version)