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On Pattern Recovery of The Fused Lasso
Confidence interval jackknife empirical likelihood risk measure
2016/1/25
Quantifying risks is of importance in insurance. In this paper, we employ the jackknife empirical likelihood method to construct confidence intervals for some risk measures and related quantities stud...
Vanilla Lasso for sparse classification under single index models
Vanilla Lasso sparse classification single index models
2016/1/20
This paper study sparse classification problems. We show that under single-index models, vanilla Lasso could give good estimate of unknown parameters. With this result, we see that even if the model i...
On Pattern Recovery of The Fused Lasso
Fused Lasso Non-asymptotic Pattern recovery Preconditioning
2016/1/20
We study the property of the Fused Lasso Signal Approximator(FLSA) for estimating a blocky signal sequence with additive noise.We transform the FLSA to an ordinary Lasso problem. By studying the prope...
The Lasso under Poisson-like Heteroscedasticity
Lasso Poisson-like Model Sign Consistency Heteroscedas- ticity
2016/1/19
The performance of the Lasso is well understood under the assumptions of the standard sparse linear model with homoscedastic noise. However, in several applications, the standard model does not descri...
For high dimensional supervised learning problems, often using problem specific assumptions can lead to greater accuracy. For problems with grouped covariates, which are believed to have sparse effect...
Learning interactions via hierarchical group-lasso regularization
hierarchical interaction computer intensive regression logistic
2015/8/21
We introduce a method for learning pairwise interactions in a linear regression or logistic regression model in a manner that satisfies strong hierarchy: whenever an interaction is estimated to be non...
Network Lasso: Clustering and Optimization in Large Graphs
Convex Optimization ADMM Network Lasso
2015/7/8
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimiza...
The lasso penalizes a least squares regression by the sum of the absolute values
(L1-norm) of the coefficients. The form of this penalty encourages sparse solutions (with many
coefficien...
A framework to characterize performance of LASSO algorithms
Noisy linear systems of equations LASSO SOCP ℓ 1 -optimization compressed sensing
2013/5/2
In this paper we consider solving \emph{noisy} under-determined systems of linear equations with sparse solutions. A noiseless equivalent attracted enormous attention in recent years, above all, due t...
The Lasso is a popular statistical tool invented by Robert Tibshirani for linear regression when the number of covariates is greater than or comparable to the number of observations. The validity of t...
An Equivalence between the Lasso and Support Vector Machines
Equivalence the Lasso Support Vector Machines
2013/4/28
We investigate the relation of two fundamental tools in machine learning, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resu...
Fused Multiple Graphical Lasso
Fused Multiple Graphical Lasso
2012/11/23
In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating ...
The Lasso for High-Dimensional Regression with a Possible Change-Point
Lasso oracleine qualities sample splitting sparsity threshold models
2012/11/23
We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter....
Lasso and probabilistic inequalities for multivariate point processes
Multivariate counting process Hawkes processes adaptive estimation Lasso procedure Bernstein-type inequalities.
2012/9/17
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an un...
Sequential Lasso for feature selection with ultra-high dimensional feature space
extended BIC feature selection selection consistency Sequential Lasso
2011/7/19
We propose a novel approach, Sequential Lasso, for feature selection in linear regression models with ultra-high dimensional feature spaces.