The Genetic Analysis Workshop 15 Problem 3 simulated rheumatoid arthritis data set provided 100 replicates of simulated single-nucleotide polymorphism (SNP) and covariate data sets for 1500 families with an affected sib pair and 2000 controls, modeled after real rheumatoid arthritis data. The data generation model included nine unobserved trait loci, most of which have one or more of the genera...

During an electron-microscopic survey with the aim of identifying the parvovirus MVM transcription template, we observed previously unidentified structures of MVM DNA in lysates of virus-infected cells. These included double-stranded "lasso"-like structures and relaxed circles. Both structures were of unit length MVM DNA, indicating that they were not intermediates formed during replication; th...

This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by the lasso. We present the Condition-onSelection method that allows for valid selective inference, and study its application to the lasso, and several other ...

Abstract: We revisit the adaptive Lasso as well as the thresholded Lasso with refitting, in a high-dimensional linear model, and study prediction error, lq-error (q ∈ {1, 2}), and number of false positive selections. Our theoretical results for the two methods are, at a rather fine scale, comparable. The differences only show up in terms of the (minimal) restricted and sparse eigenvalues, favor...

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...

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-lin...

We consider variable selection problems in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping variables and then pursuing model fitting is widely accepted. When the dimension is very high, finding an appropriate group structure is as difficult as the original problem. We propose to use Elastic-net a...

In this paper, we propose a two-stage variable selection procedure for high dimensional quantile varying coefficient models. The proposed method is based on basis function approximation and LASSO-type penalties.We show that the first stage penalized estimator with LASSO penalty reduces the model from ultra-high dimensional to a model that has size close to the true model, but contains the true ...

We propose the use of the Least Absolute Shrinkage and Selection Operator (LASSO) regression method in order to predict the Cumulative Mean Squared Error (CMSE), incurred by the loss of individual slices in video transmission. We extract a number of quality-relevant features from the H.264/AVC video sequences, which are given as input to the LASSO. This method has the benefit of not only keepin...

We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering...