We study the prototypical problem of high-dimensional linear regression in a robust model where an ε-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are drawn from a Gaussian distribution N (0, Σ) on R d . We give nearly tight upper bounds and computational lower bounds for this problem. Specifically, our main contributions are as follows: *

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We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the distribution. The eigenvalues of the covariance of a distribution contain basic information about the distribution, including the presence or lack of structure in the distribution, the effective dimensionality of the distribution, and the applicability of higher-level machine learning and multivariate statistical tools. We consider this fundamental recovery problem in the regime where the number of samples is comparable, or even sublinear in the dimensionality of the distribution in question. First, we propose a theoretically optimal and computationally efficient algorithm for recovering the moments of the eigenvalues of the population covariance matrix. We then leverage this accurate moment recovery, via a Wasserstein distance argument, to show that the vector of eigenvalues can be accurately recovered. We provide finite-sample bounds on the expected error of the recovered eigenvalues, which imply that our estimator is asymptotically consistent as the dimensionality of the distribution and sample size tend towards infinity, even in the sublinear sample regime where the ratio of the sample size to the dimensionality tends to zero. In addition to our theoretical results, we show that our approach performs well in practice for a broad range of distributions and sample sizes.

Background. Acute pancreatitis (AP) is a life-threatening disease caused by a variety of factors, and once it progresses to severe acute pancreatitis, the prognosis is poor. The purpose of this study was to investigate the diagnostic value of the neutrophil-lymphocyte ratio (NLR) for predicting the severity of acute pancreatitis. Materials and Methods. We searched the databases of PubMed, EMBASE, Web of Science, and Cochrane Library to identify eligible studies using the NLR to predict the severity of AP. The sensitivity (SEN), specificity (SPE), negative likelihood ratio (NLR), positive likelihood ratio (PLR), diagnostic odds ratio (DOR), and area under the receiver operating characteristic curve (AUC) were combined using a bivariate mixed model. Results. A total of 10 articles containing 394 cases and 1319 controls were included in the study. The combined SEN, SPE, NLR, PLR, DOR, and AUC are 79% (73%-84%), 71% (59%-80%), 0.30 (0.21-0.41), 2.7 (1.8-4.0), 9 (5-18), and 0.82 (0.78-0.85), respectively. Conclusions. NLR has a moderately high diagnostic value in predicting the severity of acute pancreatitis.

BackgroundHippo‐Yes‐associated protein (YAP) pathway plays an important role in epithelial cell proliferation and development. However, its possible role in chronic rhinosinusitis with nasal polyps (CRSwNP) remains unknown. We aim to investigate it on nasal epithelial proliferation and remodeling in CRSwNP.MethodsThe expressions of hippo pathway components as well as Ki‐67 and E‐cadherin in the sinonasal mucosa and nasal epithelial cells were analyzed in 14 controls, 14 eosinophilic CRSwNP, and 14 noneosinophilic CRSwNP. Nasal epithelial cells from 6 controls, 6 eosinophilic CRSwNP, and 6 noneosinophilic CRSwNP were cultured and treated with lipopolysaccharide (LPS), Poly(I:C), or a selective YAP inhibitor verteporfin (VP).ResultsThe hippo pathway components MST1, LATS1/2, YAP, and TEAD1 were increased in both eosinophilic and noneosinophilic CRSwNP, particularly in nasal epithelial cells, along with upregulation of Ki‐67 and downregulation of E‐cadherin. The mRNA levels of YAP positively correlated with the Ki‐67 mRNA levels, and negatively associated with the E‐cadherin mRNA levels in polyp tissues and epithelial cells from nasal polyps (NPECs). LPS and Poly(I:C) upregulated the YAP expression in nasal epithelial cells accompanied by increased TEAD1 and Ki‐67 expression. Conversely, YAP inhibition by VP decreased TEAD1 and Ki‐67 expression in NPECs.ConclusionsHippo pathway components are abnormally upregulated in NPECs, and its effector YAP promotes nasal epithelial cells proliferation and remodeling in CRSwNP. It provides a rationale to explore inhibition of YAP as a novel therapeutic strategy for reducing the epithelial proliferation and remodeling in CRSwNP.