Related papers: A path algorithm for the Fused Lasso Signal Approx…
L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…
Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…
The fused lasso is an important method for signal processing when the hidden signals are sparse and blocky. It is often used in combination with the squared loss function. However, the squared loss is not suitable for heavy tail error…
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…
We present a path algorithm for the generalized lasso problem. This problem penalizes the $\ell_1$ norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on…
We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but…
Inferring network structures remains an interesting question for its importance on the understanding and controlling collective dynamics of complex systems. The existing shrinking methods such as Lasso-type estimation can not suitably…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
The ordinary least squares estimate in linear regression is sensitive to the influence of errors with large variance, which reduces its robustness, especially when dealing with heavy-tailed errors or outliers frequently encountered in…
We study a class of fused lasso problems where the estimated parameters in a sequence are regressed toward their respective observed values (fidelity loss), with $\ell_1$ norm penalty (regularization loss) on the differences between…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…
We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order…
We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical algorithms for Lasso, our quantum…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
We study tools for inference conditioned on model selection events that are defined by the generalized lasso regularization path. The generalized lasso estimate is given by the solution of a penalized least squares regression problem, where…
We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number…