Given n noisy samples with p dimensions, where n " p, we show that the multi-step thresholding procedure based on the Lasso – we call it the Thresholded Lasso, can accurately estimate a sparse vector β ∈ R in a linear model Y = Xβ + ", where Xn×p is a design matrix normalized to have column #2-norm √ n, and " ∼ N(0,σIn). We show that under the restricted eigenvalue (RE) condition (BickelRitov-T...

In regression settings where explanatory variables have very low correlations and where thereare relatively few effects each of large magnitude, it is commonly believed that the Lasso shall beable to find the important variables with few errors—if any. In contrast, this paper shows thatthis is not the case even when the design variables are stochastically independent. In a regim...

Wheat plays a vital role in the food production as it fulfills 60% requirements of calories and proteins to the 35% of the world population. Owing to wheat importance in food, wheat demand is increasing continuously. Wheat yield is committed to the availability of water supply. Due to climatic and environmental variations of different countries, water supply is not available in constant and des...

It has been hypothesized that rare variants may hold the key to unraveling the genetic transmission mechanism of many common complex traits. Currently, there is a dearth of statistical methods that are powerful enough to detect association with rare haplotypes. One of the recently proposed methods is logistic Bayesian LASSO for case-control data. By penalizing the regression coefficients throug...

A randomsubsetmethod (RSM)with a newweighting scheme is proposed and investigated for linear regression with a large number of features. Weights of variables are defined as averages of squared values of pertaining t-statistics over fitted models with randomly chosen features. It is argued that such weighting is advisable as it incorporates two factors: a measure of importance of the variable wi...

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates....

We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of randomly selected covariates. A measure of importance is yielded from this step for each covariate. In step 2, a similar procedure to the first step is implem...

In this project, we perform an integrative analysis of 24 kinds of anti-cancer drug response on around 400 cancer patients. First, we use Lasso to build a prediction system for each individual drug response. Then a graph Lasso is employed to utilize the correlation between multiple tasks in order to build a more robust prediction system. Finally, we further perform supervised and unsupervised c...

Testing for association between multiple markers and a phenotype can not only capture untyped causal variants in weak linkage disequilibrium with nearby typed markers but also identify the effect of a combination of markers. We propose a sliding window approach that uses multimarker genotypes as variables in a penalized regression. We investigate a penalty with three separate components: (1) a ...

MOTIVATION Classification and feature selection of genomics or transcriptomics data is often hampered by the large number of features as compared with the small number of samples available. Moreover, features represented by probes that either have similar molecular functions (gene expression analysis) or genomic locations (DNA copy number analysis) are highly correlated. Classical model selecti...