Abstract-We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same order as that of LP optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse, it can be shown that the mean squared error of the reconstruction is upper bounded by constant multiples of the measurement and signal perturbation energies.Index Terms-Compressive sensing, orthogonal matching pursuit, reconstruction algorithms, restricted isometry property, sparse signal reconstruction.

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In many real world applications, labeled data are in short supply. It often happens that obtaining labeled data in a new domain is expensive and time consuming, while there may be plenty of labeled data from a related but different domain. Traditional machine learning is not able to cope well with learning across different domains. In this paper, we address this problem for a text-mining task, where the labeled data are under one distribution in one domain known as in-domain data, while the unlabeled data are under a related but different domain known as out-of-domain data. Our general goal is to learn from the in-domain and apply the learned knowledge to out-of-domain. We propose a coclustering based classification (CoCC) algorithm to tackle this problem. Co-clustering is used as a bridge to propagate the class structure and knowledge from the in-domain to the out-of-domain. We present theoretical and empirical analysis to show that our algorithm is able to produce high quality classification results, even when the distributions between the two data are different. The experimental results show that our algorithm greatly improves the classification performance over the traditional learning algorithms.

Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New Background Postoperative delirium and postoperative cognitive dysfunction share risk factors and may co-occur, but their relationship is not well established. The primary goals of this study were to describe the prevalence of postoperative cognitive dysfunction and to investigate its association with in-hospital delirium. The authors hypothesized that delirium would be a significant risk factor for postoperative cognitive dysfunction during follow-up. Methods This study used data from an observational study of cognitive outcomes after major noncardiac surgery, the Successful Aging after Elective Surgery study. Postoperative delirium was evaluated each hospital day with confusion assessment method–based interviews supplemented by chart reviews. Postoperative cognitive dysfunction was determined using methods adapted from the International Study of Postoperative Cognitive Dysfunction. Associations between delirium and postoperative cognitive dysfunction were examined at 1, 2, and 6 months. Results One hundred thirty-four of 560 participants (24%) developed delirium during hospitalization. Slightly fewer than half (47%, 256 of 548) met the International Study of Postoperative Cognitive Dysfunction-defined threshold for postoperative cognitive dysfunction at 1 month, but this proportion decreased at 2 months (23%, 123 of 536) and 6 months (16%, 85 of 528). At each follow-up, the level of agreement between delirium and postoperative cognitive dysfunction was poor (kappa less than .08) and correlations were small (r less than .16). The relative risk of postoperative cognitive dysfunction was significantly elevated for patients with a history of postoperative delirium at 1 month (relative risk = 1.34; 95% CI, 1.07–1.67), but not 2 months (relative risk = 1.08; 95% CI, 0.72–1.64), or 6 months (relative risk = 1.21; 95% CI, 0.71–2.09). Conclusions Delirium significantly increased the risk of postoperative cognitive dysfunction in the first postoperative month; this relationship did not hold in longer-term follow-up. At each evaluation, postoperative cognitive dysfunction was more common among patients without delirium. Postoperative delirium and postoperative cognitive dysfunction may be distinct manifestations of perioperative neurocognitive deficits.

The varying-coefficient model is an important class of nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is large, the issue of variable selection arises. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in sparse ultra-high dimensional varying-coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order, and the dimensionality reduction of NIS is quantified. To enhance the practical utility and finite sample performance, two data-driven iterative NIS methods are proposed for selecting thresholding parameters and variables: conditional permutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS. The effectiveness and flexibility of the proposed methods are further illustrated by simulation studies and real data applications.