Adaptive robust variable selection

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted $L_1$-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the $L_1$-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of the WR-Lasso. We show that only mild conditions on the model error distribution are needed. Our theoretical results also reveal that adaptive choice of the weight vector is essential for the WR-Lasso to enjoy these nice asymptotic properties. To make the WR-Lasso practically feasible, we propose a two-step procedure, called adaptive robust Lasso (AR-Lasso), in which the weight vector in the second step is constructed based on the $L_1$-penalized quantile regression estimate from the first step. This two-step procedure is justified theoretically to possess the oracle property and the asymptotic normality. Numerical studies demonstrate the favorable finite-sample performance of the AR-Lasso.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1191 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessment of Relation Between Subjectıve Memory Complaınts and Objective Cognitive Performance of Elderly Over 55 Years Old Age

ABSTRACT Introduction: This study investigated the frequency of forgetfulness in elderly individuals over 55 years of age and examined the association of subjective memory complaints (SMCs) with objective cognitive functions,, depression and other risk factors

Variable Selection and Prediction in High Dimensional Models

The aim of this thesis is to develop methods for variable selection and statistical prediction for high dimensional statistical problems. Along with proposing new and innovative procedures, this thesis also focuses on the theoretical properties of the proposed methods and establishes bounds on the statistical error of resulting estimators. The main body of the thesis is divided into three parts. In Chapter 1, a variable screening method for generalized linear models is discussed. The emphasis of the chapter is to provide a procedure to reduce the number of variables in a reliable and fast manner. Then, Chapter 2 considers the linear regression problem in high dimensions when the noise has heavy tails. To perform robust variable selection, a new method, called adaptive robust Lasso, is introduced. Finally, in Chapter 3, the subject is high dimensional classification problems. In this chapter, a robust approach for this problem is proposed and theoretical properties for this approach are established. Overall, the methods proposed in this thesis collectively attempt to solve many of the issues arising in high dimensional statistics, from screening to variable selection. In Chapter 1, we study the variable screening problem for generalized linear models. In many applications, researchers often have some prior knowledge that a certain set of variables is related to the response. In such a situation, a natural assessment on the relative importance of the other predictors is the conditional contributions of the individual predictors in presence of the known set of variables. This results in conditional sure independence screening (CSIS). We propose and study CSIS in the context of generalized linear models. For ultrahigh-dimensional statistical problems, we give conditions under which sure screening is possible and derive an upper bound on the number of selected variables. We also spell out the situation under which CSIS yields model selection consistency. In Chapter 2, we consider the heavy-tailed high dimensional linear regression problem. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of a quantile regression based method called WR-Lasso. We show that only mild conditions on the model error distribution are needed. Our theoretical results also reveal that adaptive choice of the weight vector is essential for the WR-Lasso to enjoy these nice asymptotic properties. To make the WR-Lasso practically feasible, we propose a two-step procedure, called adaptive robust Lasso (AR-Lasso), in which the weight vector in the second step is constructed based on the L_1 penalized quantile regression estimate from the first step. In Chapter 3, we provide an analysis about the issue of measurement errors in high dimensional linear classification problems. For such settings, we propose a new estimator called the robust sparse linear discriminant, that recovers the sparsity signal and adapts to the unknown noise level simultaneously. In contrast to the existing methods, we show that this new method has low risk properties even in the case of measurement errors. Moreover, we propose a new algorithm that recovers the solution paths for a continuum of regularization parameter values

Uncertainty Quantification in CNN Through the Bootstrap of Convex Neural Networks

Despite the popularity of Convolutional Neural Networks (CNN), the problem of uncertainty quantification (UQ) of CNN has been largely overlooked. Lack of efficient UQ tools severely limits the application of CNN in certain areas, such as medicine, where prediction uncertainty is critically important. Among the few existing UQ approaches that have been proposed for deep learning, none of them has theoretical consistency that can guarantee the uncertainty quality. To address this issue, we propose a novel bootstrap based framework for the estimation of prediction uncertainty. The inference procedure we use relies on convexified neural networks to establish the theoretical consistency of bootstrap. Our approach has a significantly less computational load than its competitors, as it relies on warm-starts at each bootstrap that avoids refitting the model from scratch. We further explore a novel transfer learning method so our framework can work on arbitrary neural networks. We experimentally demonstrate our approach has a much better performance compared to other baseline CNNs and state-of-the-art methods on various image datasets

Quantitative Assessment of Finger-Tapping Performance in Patients With Parkinson's Disease

WOS: 000312600000002Objective: The objective, quantitative assessment of patients with Parkinson's disease (PD) is essential for both the diagnosis and follow-up. To be of value in clinical trials and daily clinical practice, the method should be simple and easy, with minimal inter-rater observer variation. The finger-tapping (FT) test is an informative measure of upper-extremity motor skills as a part of the neurological assessment of patients with PD. Therefore, this study evaluated the motor skills of patients with PD by using a computer-based system that quantifies FT performance. Method: Software to measure FT performance was assessed in 25 patients with PD and 25 normal controls by using two FT testing procedures: single FT (SFT) and alternate FT (AFT). Confounding factors that had the potential to affect the performance were considered, including age, sex, education, and cognition. Results: The SFT and AFT scores for the affected side of patients with PD were significantly lower than the corresponding scores for the dominant side of control subjects. In PD patients, our method appeared to be adequate for evaluating bradykinesia independent of age, cognition and education. AFT was a more sensitive tool for determining the disease severity. Conclusion: This method is a sensitive, practical, and objective tool for evaluating upper-extremity motor skills in patients with PD. It also reflects the disease severity. We hope that this method might be useful in both daily practice and clinical studies

Quantitative assessment of finger-tapping performance in patients with parkinson's disease [Parkinson hastalarında parmakvuru performansının kantitatif degerlendirilmesi özet]

Objective: The objective, quantitative assessment of patients with Parkinson's disease (PD) is essential for both the diagnosis and follow-up. To be of value in clinical trials and daily clinical practice, the method should be simple and easy, with minimal inter-rater observer variation. The finger-tapping (FT) test is an informative measure of upper-extremity motor skills as a part of the neurological assessment of patients with PD. Therefore, this study evaluated the motor skills of patients with PD by using a computer-based system that quantifies FT performance. Method: Software to measure FT performance was assessed in 25 patients with PD and 25 normal controls by using two FT testing procedures: single FT (SFT) and alternate FT (AFT). Confounding factors that had the potential to affect the performance were considered, including age, sex, education, and cognition. Results: The SFT and AFT scores for the affected side of patients with PD were significantly lower than the corresponding scores for the dominant side of control subjects. In PD patients, our method appeared to be adequate for evaluating bradykinesia independent of age, cognition and education. AFT was a more sensitive tool for determining the disease severity. Conclusion: This method is a sensitive, practical, and objective tool for evaluating upperextremity motor skills in patients with PD. It also reflects the disease severity. We hope that this method might be useful in both daily practice and clinical studies

Parkinson Hastalarında Parmakvuru Performansının Kantitatif Değerlendirilmesi

Amaç: Parkinson hastalarında motor semptomların kantitatif yöntemlerle objektif olarak değerlendirilmesi hem tanı hem de hastaların takipleri aşamasında önemlidir. Bu amaca yönelik yöntemlerin, günlük pratikte ya da klinik araştırmalarda rutin olarak kullanılabilmesi için, basit ve kolay kullanabilen bir yöntem olması ve ölçüm yapan kişiler arasında minimum farklılıkla uygulanabilmesi gerekmektedir. Parmak vuru testi Parkinson hastalarında nörolojik muayenenin bir parçası olarak, üst ekstremite motor becerileri hakkında oldukça iyi bilgi vermektedir. Bu çalışmada Parkinson hastalarının motor becerilerini değerlendiren parmak vuru hızı, bilgisayar destekli bir yöntemle kantitatif olarak ölçülmüştür. Yöntem: 25 Parkinson hastası ve 25 kontrol olgusunda parmak vuru hızı bir software yardımı ve bir klavye kullanılarak ölçülmüştür. Parmak vuru performansını değerlendirmek amacı ile tek parmak (TP) ve çift parmak alternan (AP) hareket hızı ölçülmüş ve parmak vuru hızını etkileyebilecek yaş, cinsiyet, eğitim ve kognisyon gibi faktörler değerlendirilmiştir. Bulgular: Parkinson hastalarında, hastalığın belirgin olduğu tarafta hem TP hem de AP vuru hızları anlamlı olarak yavaş bulunmuştur. Parkinson hastalarında kullandığımız bu yöntemin yaş, eğitim ve kognisyondan bağımsız olarak bradikineziyi değerlendirmede yeterli olduğu belirlenmiştir. AP vuru hızının hastalık derecesinin belirlenmesinde daha hassas olduğu gözlenmiştir. Sonuç: Bilgisayar yardımı ile değerlendirilen parmak vuru hızının Parkinson hastalarında üst ekstremite becerilerinin ve hastalık şiddetinin değerlendirilmesinde kullanılabilecek hassas, pratik ve objektif bir yöntem olduğu düşünülmektedir. Sonuç olarak bu yöntemin günlük pratik ve klinik araştırmalarda PH'nın değerlendirilmesinde faydalı olabileceği sonucuna varılmıştır.Objective: The objective, quantitative assessment of patients with Parkinson's disease (PD) is essential for both the diagnosis and follow-up. To be of value in clinical trials and daily clinical practice, the method should be simple and easy, with minimal inter-rater observer variation. The finger-tapping (FT) test is an informative measure of upper-extremity motor skills as a part of the neurological assessment of patients with PD. Therefore, this study evaluated the motor skills of patients with PD by using a computer-based system that quantifies FT performance. Method: Software to measure FT performance was assessed in 25 patients with PD and 25 normal controls by using two FT testing procedures: single FT (SFT) and alternate FT (AFT). Confounding factors that had the potential to affect the performance were considered, including age, sex, education, and cognition. Results: The SFT and AFT scores for the affected side of patients with PD were significantly lower than the corresponding scores for the dominant side of control subjects. In PD patients, our method appeared to be adequate for evaluating bradykinesia independent of age, cognition and education. AFT was a more sensitive tool for determining the disease severity. Conclusion: This method is a sensitive, practical, and objective tool for evaluating upper- extremity motor skills in patients with PD. It also reflects the disease severity. We hope that this method might be useful in both daily practice and clinical studies