Consistency Property of Finite FC-Normal Logic Programs

Marek＇s forward-chaining construction is one of the important techniques for investigating the non-monotonic reasoning. By introduction of consistency property over a logic program, they proposed a class of logic programs, FC-normal programs, each of which has at least one stable model. However, it is not clear how to choose one appropriate consistency property for deciding whether or not a logic program is FC-normal. In this paper, we firstly discover that, for any finite logic programⅡ, there exists the least consistency property LCon（Ⅱ） overⅡ, which just depends onⅡitself, such that, Ⅱ is FC-normal if and only ifⅡ is FC-normal with respect to （w.r.t.） LCon（Ⅱ）. Actually, in order to determine the FC-normality of a logic program, it is sufficient to check the monotonic closed sets in LCon（Ⅱ） for all non-monotonic rules, that is LFC（Ⅱ）. Secondly, we present an algorithm for computing LFC（Ⅱ）. Finally, we reveal that the brave reasoning task and cautious reasoning task for FC-normal logic programs are of the same difficulty as that of normal logic programs.

Censored Composite Conditional Quantile Screening for High-Dimensional Survival Data

In this paper,we introduce the censored composite conditional quantile coefficient(cC-CQC)to rank the relative importance of each predictor in high-dimensional censored regression.The cCCQC takes advantage of all useful information across quantiles and can detect nonlinear effects including interactions and heterogeneity,effectively.Furthermore,the proposed screening method based on cCCQC is robust to the existence of outliers and enjoys the sure screening property.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors,particularly when the variables are highly correlated.

Property （ω） and topological uniform descent

We give the necessary and sufficient condition for a bounded linear operator with property （ω） by means of the induced spectrum of topological uniform descent, and investigate the permanence of property （ω） under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators.

Feature Screening for High-Dimensional Survival Data via Censored Quantile Correlation

This paper proposes a new sure independence screening procedure for high-dimensional survival data based on censored quantile correlation(CQC).This framework has two distinctive features:1)Via incorporating a weighting scheme,our metric is a natural extension of quantile correlation(QC),considered by Li(2015),to handle high-dimensional survival data;2)The proposed method not only is robust against outliers,but also can discover the nonlinear relationship between independent variables and censored dependent variable.Additionally,the proposed method enjoys the sure screening property under certain technical conditions.Simulation results demonstrate that the proposed method performs competitively on survival datasets of high-dimensional predictors.

Penalized least squares estimation with weakly dependent data

In statistics and machine learning communities, the last fifteen years have witnessed a surge of high-dimensional models backed by penalized methods and other state-of-the-art variable selection techniques.The high-dimensional models we refer to differ from conventional models in that the number of all parameters p and number of significant parameters s are both allowed to grow with the sample size T. When the field-specific knowledge is preliminary and in view of recent and potential affluence of data from genetics, finance and on-line social networks, etc., such（s, T, p）-triply diverging models enjoy ultimate flexibility in terms of modeling, and they can be used as a data-guided first step of investigation. However, model selection consistency and other theoretical properties were addressed only for independent data, leaving time series largely uncovered. On a simple linear regression model endowed with a weakly dependent sequence, this paper applies a penalized least squares（PLS） approach. Under regularity conditions, we show sign consistency, derive finite sample bound with high probability for estimation error, and prove that PLS estimate is consistent in L_2 norm with rate （s log s/T）～1/2.