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.

Input: Consider Input: Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.

Output: Stable Model Counting and Its Application in Probabilistic Logic Programming


Input: Consider 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.

Output: Distributed Tree Kernels


Input: Consider Input: Kernel-based approaches for sequence classification have been successfully applied to a variety of domains, including the text categorization, image classification, speech analysis, biological sequence analysis, time series and music classification, where they show some of the most accurate results. Typical kernel functions for sequences in these domains (e.g., bag-of-words, mismatch, or subsequence kernels) are restricted to discrete univariate (i.e. one-dimensional) string data, such as sequences of words in the text analysis, codeword sequences in the image analysis, or nucleotide or amino acid sequences in the DNA and protein sequence analysis. However, original sequence data are often of real-valued multivariate nature, i.e. are not univariate and discrete as required by typical k-mer based sequence kernel functions. In this work, we consider the problem of the multivariate sequence classification (e.g., classification of multivariate music sequences, or multidimensional protein sequence representations). To this end, we extend univariate kernel functions typically used in sequence domains and propose efficient multivariate similarity kernel method (MVDFQ-SK) based on (1) a direct feature quantization (DFQ) of each sequence dimension in the original real-valued multivariate sequences and (2) applying novel multivariate discrete kernel measures on these multivariate discrete DFQ sequence representations to more accurately capture similarity relationships among sequences and improve classification performance. Experiments using the proposed MVDFQ-SK kernel method show excellent classification performance on three challenging music classification tasks as well as protein sequence classification with significant 25-40% improvements over univariate kernel methods and existing state-of-the-art sequence classification methods.


Output: Efficient multivariate kernels for sequence classification