vector RAG

Linear programming (LP) decoding for low-density parity-check codes (and related domains such as compressed sensing) has received increased attention over recent years because of its practical performance-coming close to that of iterative decoding algorithms-and its amenability to finite-blocklength analysis. Several works starting with the work of Feldman showed how to analyze LP decoding using properties of expander graphs. This line of analysis works for only low error rates, about a couple of orders of magnitude lower than the empirically observed performance. It is possible to do better for the case of random noise, as shown by Daskalakis and Koetter and Vontobel. Building on work of Koetter and Vontobel, we obtain a novel understanding of LP decoding, which allows us to establish a 0.05 fraction of correctable errors for rate-½ codes; this comes very close to the performance of iterative decoders and is significantly higher than the best previously noted correctable bit error rate for LP decoding. Our analysis exploits an explicit connection between LP decoding and message-passing algorithms and, unlike other techniques, directly works with the primal linear program. An interesting byproduct of our method is a notion of a “locally optimal” solution that we show to always be globally optimal (i.e., it is the nearest codeword). Such a solution can in fact be found in near-linear time by a “reweighted” version of the min-sum algorithm, obviating the need for LP. Our analysis implies, in particular, that this reweighted version of the min-sum decoder corrects up to a 0.05 fraction of errors.

Representations and Generalized Frequent Pattern Discovery . . . . . . 67 Eray Özkural On Hierarchical Compression and Power Laws in Nature. . . . . . . . . . . . . . . 77 Arthur Franz From First-Order Logic to Assertional Logic . . . . . . . . . . . . . . . . . . . . . . . 87 Yi Zhou

以我们在现实生活当中处理数据库的经验来看,为了从数据库中使用限制性的信息抽取方法得到有用的数据和信息,我们有必要使用"特点子集选择"的方法(Feature Subset Selection).而这种方法需要从多个相关的属性当中进行多次的试验从而找到某种特定的子集.在这种情况下,如何能够找到快速的、准确的同时又是简便的选择算法变得越来越关键.这篇文章对由Dr.Robert Holtes提出的"One-R"算法进行了适当的改进,通过"Chi"氏独立性检验和拜亚(Bayes Decision Theory)公式推导出的新方法,在试验的基础上表明,这种新的算法在某种程度上比原来的"One-R"算法要准确.