Cross-Lingual Adaptation using Structural Correspondence Learning

Cross-lingual adaptation, a special case of domain adaptation, refers to the transfer of classification knowledge between two languages. In this article we describe an extension of Structural Correspondence Learning (SCL), a recently proposed algorithm for domain adaptation, for cross-lingual adaptation. The proposed method uses unlabeled documents from both languages, along with a word translation oracle, to induce cross-lingual feature correspondences. From these correspondences a cross-lingual representation is created that enables the transfer of classification knowledge from the source to the target language. The main advantages of this approach over other approaches are its resource efficiency and task specificity. We conduct experiments in the area of cross-language topic and sentiment classification involving English as source language and German, French, and Japanese as target languages. The results show a significant improvement of the proposed method over a machine translation baseline, reducing the relative error due to cross-lingual adaptation by an average of 30% (topic classification) and 59% (sentiment classification). We further report on empirical analyses that reveal insights into the use of unlabeled data, the sensitivity with respect to important hyperparameters, and the nature of the induced cross-lingual correspondences

Automorphisms of Higher Rank Lamplighter Groups

Let $\Gamma_d(q)$ denote the group whose Cayley graph with respect to a particular generating set is the Diestel-Leader graph $DL_d(q)$, as described by Bartholdi, Neuhauser and Woess. We compute both $Aut(\Gamma_d(q))$ and $Out(\Gamma_d(q))$ for $d \geq 2$, and apply our results to count twisted conjugacy classes in these groups when $d \geq 3$. Specifically, we show that when $d \geq 3$, the groups $\Gamma_d(q)$ have property $R_{\infty}$, that is, every automorphism has an infinite number of twisted conjugacy classes. In contrast, when $d=2$ the lamplighter groups $\Gamma_2(q)=L_q = {\mathbb Z}_q \wr {\mathbb Z}$ have property $R_{\infty}$ if and only if $(q,6) \neq 1$.Comment: 28 page

On chvátal's conjecture related to a hereditary system

AbstractIt is shown that among the maximal intersecting systems, which are subsystems of a hereditary family F, there is a star, as claimed by a conjecture of Chvátal, if it is assumed, that the number of bases of F is n, but n-1 bases of F form a simple-star