In the high-dimensional regression model a response variable is linearly related to p covariates, but the sample size n is smaller than p. We assume that only a small subset of covariates is ‘active’ (i.e., the corresponding coefficients are non-zero), and consider the model-selection problem of identifying the active covariates. A popular approach is to estimate the regression coefficients thr...

When considering low-dimensional gene-treatment or gene-environment interactions we might suspect groups of genes to interact with treatment or environment in a similar way. For example, genes associated with related biological processes might interact with an environmental factor or a clinical treatment in its effect on a phenotype correspondingly. We use the idea of a structured interaction m...

We consider an iterated Lasso approach for variable selection and estimation in sparse, high-dimensional logistic regression models. In this approach, we use the Lasso (Tibshirani 1996) to obtain an initial estimator and reduce the dimension of the model. We then use the Lasso as the initial estimator in the adaptive Lasso (Zou 2006) to obtain the final selection and estimation results. We prov...

Sparsity or parsimony of statistical models is crucial for their proper interpretations, as in sciences and social sciences. Model selection is a commonly used method to find such models, but usually involves a computationally heavy combinatorial search. Lasso (Tibshirani, 1996) is now being used as a computationally feasible alternative to model selection. Therefore it is important to study La...

High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which generalizes the classical basis approach, combined with a Lasso or a group-Lasso procedure. Selection depends on penalty weights that need to be calibrated. Standard ...

We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior information into the model. In addition to quadratic programming, we employ the alternating direction method of multipliers (ADMM) and also derive an efficient solu...

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of Lasso. In this paper we propose an alternative method improving for predictive models with general convex loss functions which encompass normal linear models, logistic regression, quantile support vector machines. For a given penalty order absolute values nonzero coefficients and then select final mode...

This paper proposes a new approach to solve the problem of lack information in rating data due users or items, there is too little user for items collaborative filtering recommendation models (CFR models). In this approach, we consider similarity between based on lasso regression build CFR models. commonly used models, results are built only feedback matrix users. The our model predicted two ca...