Measurement Error in Lasso: Impact and Correction

Regression with the lasso penalty is a popular tool for performing dimension reduction when the number of covariates is large. In many applications of the lasso, like in genomics, covariates are subject to measurement error. We study the impact of measurement error on linear regression with the lasso penalty, both analytically and in simulation experiments. A simple method of correction for measurement error in the lasso is then considered. In the large sample limit, the corrected lasso yields sign consistent covariate selection under conditions very similar to the lasso with perfect measurements, whereas the uncorrected lasso requires much more stringent conditions on the covariance structure of the data. Finally, we suggest methods to correct for measurement error in generalized linear models with the lasso penalty, which we study empirically in simulation experiments with logistic regression, and also apply to a classification problem with microarray data. We see that the corrected lasso selects less false positives than the standard lasso, at a similar level of true positives. The corrected lasso can therefore be used to obtain more conservative covariate selection in genomic analysis

Robust sure independence screening for nonpolynomial dimensional generalized linear models

We consider the problem of variable screening in ultra-high-dimensional generalized linear models (GLMs) of nonpolynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs well under pure and contaminated data scenarios. We provide a theoretical motivation for the use of marginal MDPDEs for variable screening from both population as well as sample aspects; in particular, we prove that the marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. Finally, we propose an appropriate MDPDE-based extension for robust conditional screening in GLMs along with the derivation of its sure screening property. Our proposed methods are illustrated through extensive numerical studies along with an interesting real data application

Robust Sure Independence Screening for Non-polynomial dimensional Generalized Linear Models

We consider the problem of variable screening in ultra-high dimensional (of non-polynomial order) generalized linear models (GLMs). Since the popular SIS approach is extremely unstable in the presence of contamination and noises, which may frequently arise in the large scale sample data (e.g., Omics data), we discuss a new robust screening procedure based on the minimum density power divergence estimator (MDPDE) of the marginal regression coefficients. Our proposed screening procedure performs extremely well both under pure and contaminated data scenarios. We also theoretically justify the use of this marginal MDPDEs for variable screening from the population as well as sample aspects; in particular, we prove that these marginal MDPDEs are uniformly consistent leading to the sure screening property of our proposed algorithm. We have also proposed an appropriate MDPDE based extension for robust conditional screening in the GLMs along with the derivation of its sure screening property.Comment: Work in Progres

Is the association between acne and mental distress influenced by diet? Results from a cross-sectional population study among 3775 late adolescents in Oslo, Norway

Background Several studies with conflicting findings have investigated the association between acne and mental health problems. Acne usually starts in adolescents, as does an increase in the prevalence of depression and anxiety. Recently, there has been more focus on the link between diet and acne and diet and mental health problems. The objective of this study is to investigate the association between acne and mental distress and to explore a possible influence of dietary factors on the relation. Methods A population-based cross-sectional study in Oslo of 18 or 19 year old adolescents. The participation rate was 80%. Acne was self-reported. To measure mental distress, the Hopkins Symptom Checklist 10 was used. Diet and lifestyle variables were also collected by questionnaire and socio-demographic variables were obtained from Statistics Norway. Results The prevalence of acne was 14.4% among the males and 12.8% among the females. The mean score of mental distress increased when the severity of acne increased. In the crude analyses, the significant associations with acne among the males were: mental distress OR = 1.63, frequent consumption of chocolate/sweets OR = 1.40, frequent consumption of potato chips OR = 1.54. The significant crude associations with acne among the females were: mental distress OR = 2.16, infrequent consumption of raw vegetables OR = 1.41, non-Western background OR = 1.77 and low family income OR = 2.14. No crude associations with acne were identified in either gender for the consumption of sugary soft drinks, fatty fish, cigarette smoking or alcohol. In adjusted models which included diet and socio-demographic variables, the association between acne and mental distress was unchanged for both males (OR = 1.68) and females (OR = 2.04), and between acne and infrequent consumption of raw vegetables among the females (OR = 1.38). Conclusion Among late adolescents in Oslo, self-reported acne is significantly associated with mental distress and, among girls, with infrequent consumption of raw vegetables. Our finding does not support the hypothesis that dietary factors alter the relationship between acne and mental distress