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 Q]: This paper deals with the problem of esti­ mating the probability that one event was a cause of another in a given scenario. Us­ ing structural-semantical definitions of the probabilities of necessary or sufficient cau­ sation (or both), we show how to optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by weakening the data-generation assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attribution-related problems of decision making.
[EX A]: Probabilities of Causation: Bounds and Identification

[EX Q]: 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.
[EX A]: Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

[EX Q]: 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.
[EX A]:
Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision (Short Version)