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.

Ex Input:
Consider a setting where selfish agents are to be assigned to coalitions or projects from a set P. Each project k P is characterized by a valuation function; vk(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.

Ex Output:
Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Ex Input:
Ensembling is a well-known technique in neural machine translation (NMT) to improve system performance. Instead of a single neural net, multiple neural nets with the same topology are trained separately, and the decoder generates predictions by averaging over the individual models. Ensembling often improves the quality of the generated translations drastically. However, it is not suitable for production systems because it is cumbersome and slow. This work aims to reduce the runtime to be on par with a single system without compromising the translation quality. First, we show that the ensemble can be unfolded into a single large neural network which imitates the output of the ensemble system. We show that unfolding can already improve the runtime in practice since more work can be done on the GPU. We proceed by describing a set of techniques to shrink the unfolded network by reducing the dimensionality of layers. On JapaneseEnglish we report that the resulting network has the size and decoding speed of a single NMT network but performs on the level of a 3-ensemble system.

Ex Output:
Unfolding and Shrinking Neural Machine Translation Ensembles

Ex Input:
Conventional methods of estimating latent behaviour generally use attitudinal questions which are subjective and these survey questions may not always be available. We hypothesize that an alternative approach can be used for latent variable estimation through an undirected graphical models. For instance, non-parametric artificial neural networks. In this study, we explore the use of generative non-parametric modelling methods to estimate latent variables from prior choice distribution without the conventional use of measurement indicators. A restricted Boltzmann machine is used to represent latent behaviour factors by analyzing the relationship information between the observed choices and explanatory variables. The algorithm is adapted for latent behaviour analysis in discrete choice scenario and we use a graphical approach to evaluate and understand the semantic meaning from estimated parameter vector values. We illustrate our methodology on a financial instrument choice dataset and perform statistical analysis on parameter sensitivity and stability. Our findings show that through non-parametric statistical tests, we can extract useful latent information on the behaviour of latent constructs through machine learning methods and present strong and significant influence on the choice process. Furthermore, our modelling framework shows robustness in input variability through sampling and validation. Paper presented at International Choice Modelling Conference 2017 Laboratory of Innovations in Transportation (LITrans), Department of Civil Engineering, Ryerson University, Toronto, Canada, Email: melvin.wong@ryerson.ca Laboratory of Innovations in Transportation (LITrans), Department of Civil Engineering, Ryerson University, Toronto, Canada, Email: bilal.farooq@ryerson.ca Laboratoire d'Interpretation et de Traitement d'Images et Video (LITIV), Department of Computer and Software Engineering, Polytechnique Montreal, Montreal, Canada, Email: guillaume-alexandre.bilodeau@polymtl.ca ar X iv :1 70 6. 00 50 5v 1 [ cs .L G ] 1 J un 2 01 7

Ex Output:
Discriminative conditional restricted Boltzmann machine for discrete choice and latent variable modelling