Sparse Model Identification and Learning for Ultra-high-dimensional Additive Partially Linear Models

The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the "curse of dimensionality". A natural question raised in practice is the choice of structure in the nonparametric part, that is, whether the continuous covariates enter into the model in linear or nonparametric form. In this paper, we present a comprehensive framework for simultaneous sparse model identification and learning for ultra-high-dimensional APLMs where both the linear and nonparametric components are possibly larger than the sample size. We propose a fast and efficient two-stage procedure. In the first stage, we decompose the nonparametric functions into a linear part and a nonlinear part. The nonlinear functions are approximated by constant spline bases, and a triple penalization procedure is proposed to select nonzero components using adaptive group LASSO. In the second stage, we refit data with selected covariates using higher order polynomial splines, and apply spline-backfitted local-linear smoothing to obtain asymptotic normality for the estimators. The procedure is shown to be consistent for model structure identification. It can identify zero, linear, and nonlinear components correctly and efficiently. Inference can be made on both linear coefficients and nonparametric functions. We conduct simulation studies to evaluate the performance of the method and apply the proposed method to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes for illustration

Pure Annihilation Type B→K0∗±(1430)K(∗)∓B \to K_0^{*\pm}(1430)K^{(*)\mp} Decays in the Family Non-universal Z′Z^\prime Model

By assuming that the scalar meson $K_0^*(1430)$ belongs to the first excited states or the lowest lying ground states, we study the pure annihilation-type decays $B \to K_0^{*\pm}(1430)K^{(*)\mp}$ in the QCD factorization approach. Within the standard model, the branching fractions are at the order of $10^{-8}-10^{-7}$, which is possible to be measured in the ongoing LHCb experiment or forthcoming Belle-II experiment. We also study these decays in the family non-universal $Z^\prime$ model. The results show that if $m_{Z^\prime}\approx 600\mathrm{GeV}$ ($\zeta=0.02$), both the branching fractions and $CP$ asymmetries of $\overline B^0\to K_0^{*+}(1430)K^-$ could be changed remarkably, which provides us a place for probing the effect of new physics. These results could be used to constrain the parameters of $Z^\prime$ model.Comment: 9 pages, 18 figure

Active Sampling for Large-scale Information Retrieval Evaluation

Evaluation is crucial in Information Retrieval. The development of models, tools and methods has significantly benefited from the availability of reusable test collections formed through a standardized and thoroughly tested methodology, known as the Cranfield paradigm. Constructing these collections requires obtaining relevance judgments for a pool of documents, retrieved by systems participating in an evaluation task; thus involves immense human labor. To alleviate this effort different methods for constructing collections have been proposed in the literature, falling under two broad categories: (a) sampling, and (b) active selection of documents. The former devises a smart sampling strategy by choosing only a subset of documents to be assessed and inferring evaluation measure on the basis of the obtained sample; the sampling distribution is being fixed at the beginning of the process. The latter recognizes that systems contributing documents to be judged vary in quality, and actively selects documents from good systems. The quality of systems is measured every time a new document is being judged. In this paper we seek to solve the problem of large-scale retrieval evaluation combining the two approaches. We devise an active sampling method that avoids the bias of the active selection methods towards good systems, and at the same time reduces the variance of the current sampling approaches by placing a distribution over systems, which varies as judgments become available. We validate the proposed method using TREC data and demonstrate the advantages of this new method compared to past approaches

Laplace transforms and valuations

It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform