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:
We develop a new semantics for defeasible infer­ ence based on extended probability measures al­ lowed to take infinitesimal values, on the inter­ pretation of defaults as generalized conditional probability constraints and on a preferred-model implementation of entropy-maximization.

Ex Output:
Defaults and lnfinitesimals Defeasible Inference by Nonarchimedean Entropy Maximization


Ex Input:
In this paper, we propose the distributed tree kernels (DTK) as a novel method to reduce time and space complexity of tree kernels. Using a linear complexity algorithm to compute vectors for trees, we embed feature spaces of tree fragments in low-dimensional spaces where the kernel computation is directly done with dot product. We show that DTKs are faster, correlate with tree kernels, and obtain a statistically similar performance in two natural language processing tasks.

Ex Output:
Distributed Tree Kernels


Ex Input:
Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a fam­ ily of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic low-discrepancy se­ quences. We first outline several theoreti­ cal aspects of deterministic low-discrepancy sequences, show three examples of such se­ quences, and then discuss practical issues re­ lated to applying them to belief updating in Bayesian networks. We propose an algorithm for selecting direction numbers for Sobol se­ quence. Our experimental results show that low-discrepancy sequences (especially Sobol sequence) significantly improve the perfor­ mance of simulation algorithms in Bayesian networks compared to Monte Carlo sampling.

Ex Output:

Computational Investigation of Low-Discrepancy Sequences in Simulation Algorithms for Bayesian Networks