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.

In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in firstorder logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. Third, we present several properties of the algorithm. Finally, we discuss limitations of lifted inference for symmetric probabilistic databases (where the weights of ground literals depend only on the relation name, and not on the constants of the domain), and prove the impossibility of a dichotomy result for the complexity of probabilistic inference for the entire language FOL.
Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

Concept maps can be used to concisely represent important information and bring structure into large document collections. Therefore, we study a variant of multidocument summarization that produces summaries in the form of concept maps. However, suitable evaluation datasets for this task are currently missing. To close this gap, we present a newly created corpus of concept maps that summarize heterogeneous collections of web documents on educational topics. It was created using a novel crowdsourcing approach that allows us to efficiently determine important elements in large document collections. We release the corpus along with a baseline system and proposed evaluation protocol to enable further research on this variant of summarization.
Connecting the dots: Summarizing and Structuring Large Document Collections Using Concept Maps

For large, real-world inductive learning problems, the number of training examples often must be limited due to the costs associated with procuring, preparing, and storing the training examples and/or the computational costs associated with learning from them. In such circumstances, one question of practical importance is: if only n training examples can be selected, in what proportion should the classes be represented? In this article we help to answer this question by analyzing, for a fixed training-set size, the relationship between the class distribution of the training data and the performance of classification trees induced from these data. We study twenty-six data sets and, for each, determine the best class distribution for learning. The naturally occurring class distribution is shown to generally perform well when classifier performance is evaluated using undifferentiated error rate (0/1 loss). However, when the area under the ROC curve is used to evaluate classifier performance, a balanced distribution is shown to perform well. Since neither of these choices for class distribution always generates the best-performing classifier, we introduce a “budget-sensitive” progressive sampling algorithm for selecting training examples based on the class associated with each example. An empirical analysis of this algorithm shows that the class distribution of the resulting training set yields classifiers with good (nearly-optimal) classification performance.

Learning When Training Data are Costly: The Effect of Class Distribution on Tree Induction