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:
Feature subset selection, as a special case of the general subset selection problem, has been the topic of a considerable number of studies due to the growing importance of data-mining applications. In the feature subset selection problem there are two main issues that need to be addressed: (i) Finding an appropriate measure function than can be fairly fast and robustly computed for high-dimensional data. (ii) A search strategy to optimize the measure over the subset space in a reasonable amount of time. In this article mutual information between features and class labels is considered to be the measure function. Two series expansions for mutual information are proposed, and it is shown that most heuristic criteria suggested in the literature are truncated approximations of these expansions. It is well-known that searching the whole subset space is an NP-hard problem. Here, instead of the conventional sequential search algorithms, we suggest a parallel search strategy based on semidefinite programming (SDP) that can search through the subset space in polynomial time. By exploiting the similarities between the proposed algorithm and an instance of the maximumcut problem in graph theory, the approximation ratio of this algorithm is derived and is compared with the approximation ratio of the backward elimination method. The experiments show that it can be misleading to judge the quality of a measure solely based on the classification accuracy, without taking the effect of the non-optimum search strategy into account.

Ex Output:
A Semidefinite Programming Based Search Strategy for Feature Selection with Mutual Information Measure

Ex Input:
Dawid, Kjrerulff & Lauritzen (1994) provided a preliminary description of a hybrid between Monte-Carlo sampling methods and exact lo cal computations in junction trees. Utiliz ing the strengths of both methods, such hy brid inference methods has the potential of expanding the class of problems which can be solved under bounded resources as well as solving problems which otherwise resist ex act solutions. The paper provides a detailed description of a particular instance of such a hybrid scheme; namely, combination of ex act inference and Gibbs sampling in discrete Bayesian networks. We argue that this com bination calls for an extension of the usual message passing scheme of ordinary junction trees.

Ex Output:
HUGS: Combining Exact Inference and Gibbs Sampling in Junction Trees

Ex Input:
We introduce a model for bidirectional retrieval of images and sentences through a multi-modal embedding of visual and natural language data. Unlike previous models that directly map images or sentences into a common embedding space, our model works on a finer level and embeds fragments of images (objects) and fragments of sentences (typed dependency tree relations) into a common space. In addition to a ranking objective seen in previous work, this allows us to add a new fragment alignment objective that learns to directly associate these fragments across modalities. Extensive experimental evaluation shows that reasoning on both the global level of images and sentences and the finer level of their respective fragments significantly improves performance on image-sentence retrieval tasks. Additionally, our model provides interpretable predictions since the inferred intermodal fragment alignment is explicit.

Ex Output:
Deep Fragment Embeddings for Bidirectional Image Sentence Mapping