Asymptotic properties of Lasso in high-dimensional partially linear models

We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.

A survey on distributed compressed sensing： theory and applications

The compressed sensing （CS） theory makes sample rate relate to signal structure and content. CS samples and compresses the signal with far below Nyquist sampling frequency simultaneously. However, CS only considers the intra-signal correlations, without taking the correlations of the multi-signals into account. Distributed compressed sensing （DCS） is an extension of CS that takes advantage of both the inter- and intra-signal correlations, which is wildly used as a powerful method for the multi-signals sensing and compression in many fields. In this paper, the characteristics and related works of DCS are reviewed. The framework of DCS is introduced. As DCS＇s main portions, sparse representation, measurement matrix selection, and joint reconstruction are classified and summarized. The applications of DCS are also categorized and discussed. Finally, the conclusion remarks and the further research works are provided.

Bayesian compressive principal component analysis

Principal component analysis(PCA)is a widely used method for multivariate data analysis that projects the original high-dimensional data onto a low-dimensional subspace with maximum variance.However,in practice,we would be more likely to obtain a few compressed sensing(CS)measurements than the complete high-dimensional data due to the high cost of data acquisition and storage.In this paper,we propose a novel Bayesian algorithm for learning the solutions of PCA for the original data just from these CS measurements.To this end,we utilize a generative latent variable model incorporated with a structure prior to model both sparsity of the original data and effective dimensionality of the latent space.The proposed algorithm enjoys two important advantages:1)The effective dimensionality of the latent space can be determined automatically with no need to be pre-specified;2)The sparsity modeling makes us unnecessary to employ multiple measurement matrices to maintain the original data space but a single one,thus being storage efficient.Experimental results on synthetic and real-world datasets show that the proposed algorithm can accurately learn the solutions of PCA for the original data,which can in turn be applied in reconstruction task with favorable results.