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: Finding inclusion-minimal hitting sets for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic literature focuses on the problem of recognizing the collection of minimal hitting sets; however, in many of the applications, it is more important to generate these hitting sets. We survey twenty algorithms from across a variety of domains, considering their history, classification, useful features, and computational performance on a variety of synthetic and real-world inputs. We also provide a suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.

Answer: The minimal hitting set generation problem: algorithms and computation


Question: We introduce a simple, general strategy to manipulate the behavior of a neural decoder that enables it to generate outputs that have specific properties of interest (e.g., sequences of a pre-specified length). The model can be thought of as a simple version of the actor-critic model that uses an interpolation of the actor (the MLE-based token generation policy) and the critic (a value function that estimates the future values of the desired property) for decision making. We demonstrate that the approach is able to incorporate a variety of properties that cannot be handled by standard neural sequence decoders, such as sequence length and backward probability (probability of sources given targets), in addition to yielding consistent improvements in abstractive summarization and machine translation when the property to be optimized is BLEU or ROUGE scores.

Answer: Learning to Decode for Future Success


Question: Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian optimization methods that enforce such constraints implicitly, leveraging the fact that the feasible parameter values form a manifold. While Riemannian methods exist for some specific problems, such as learning a single subspace, there are more general subspace constraints that offer additional flexibility when setting up an optimization problem but have not been formulated as a manifold. We propose the partitioned subspace (PS) manifold for optimizing matrices that are constrained to represent one or more subspaces. Each point on the manifold defines a partitioning of the input space into mutually orthogonal subspaces, where the number of partitions and their sizes are defined by the user. As a result, distinct groups of features can be learned by defining different objective functions for each partition. We illustrate the properties of the manifold through experiments on multiple dataset analysis and domain adaptation.

Answer:
A Manifold Approach to Learning Mutually Orthogonal Subspaces