arXiv research

This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the corr…

Paper proposes ASCCA for sparse CCA with trace Lasso regularization.

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, ca…

Study evaluates scikit-learn regularization frameworks for machine learning models.

Proposes MM-DUST for efficient generalized lasso solution paths.

A new method solves sparse regularization problems efficiently and robustly.

CAST improves spectral clustering for multi-scale data by integrating reachability similarity.

Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.

Paper analyzes multi-attribute data to estimate differences in Gaussian graphical models.

SDAMI enhances interpretable high-dimensional regression with sparse deep learning and footprint principle.

Paper relaxes factor analysis for noisy data, improving robustness.

Paper estimates differences in conditional independence graphs from time-dependent data.

PLS-Lasso integrates dimension reduction into regression for financial index tracking.

The paper examines Adaptive Lasso and Transfer Lasso, highlighting their differences and proposing a new method.

DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.

Unified approach for robust low rank matrix estimation with adversaries.

A fast method for Lasso and Logistic Lasso problems.

We leverage recent advances in high-dimensional statistics to derive new L2 estimation upper bounds for Lasso and Group Lasso in high-dimensions. For Lasso, our bounds scale as $(k^*/n) \log(p/k^*)$---$n\times p$ is the size of the design matrix and $k^*$ the dimension of the ground truth $\boldsymbolβ^*$---and match t…

We introduce an application of the group lasso to design of experiments. Note that we are NOT trying to explain experimental design for the group lasso. Conversely, we explain how we can use the idea of the group lasso in experimental design, showing that the problem of constructing an optimal design matrix can be tran…

New method for tuning Graphical Lasso hyperparameters.

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main differenc…

LLM-Lasso uses LLMs to improve feature selection in Lasso regression.

The solution path of the 1D fused lasso for an $n$-dimensional input is piecewise linear with $\mathcal{O}(n)$ segments (Hoefling et al. 2010 and Tibshirani et al 2011). However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the wei…

Bayesian approach improves network lasso for multi-task learning.

We propose a method for finding alternate features missing in the Lasso optimal solution. In ordinary Lasso problem, one global optimum is obtained and the resulting features are interpreted as task-relevant features. However, this can overlook possibly relevant features not selected by the Lasso. With the proposed met…

This review summarizes five Lasso optimization algorithms.

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dim…

We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients ($r$), size of the parameter vector ($β$), …

Paper examines LASSO for high-dimensional predictive regression, improving its performance in forecasting unemployment.

Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.

Exclusive Group Lasso improves feature selection in correlated biological data.

A new method speeds up overlapping group lasso computations.

The "least absolute shrinkage and selection operator" (Lasso) method has been adapted recently for networkstructured datasets. In particular, this network Lasso method allows to learn graph signals from a small number of noisy signal samples by using the total variation of a graph signal for regularization. While effic…

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 alterna…

Paper improves Lasso for S&P500 index tracking with post-selection inference.

The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifi…

Proposes a new Lasso method with performance constraints.

This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.

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 property of the design matrix in the transformed Lasso problem, we find that the irrepresentable condition might not hold, …

Improves Lasso's stability in correlated predictor settings.

This paper is a survey of dictionary screening for the lasso problem. The lasso problem seeks a sparse linear combination of the columns of a dictionary to best match a given target vector. This sparse representation has proven useful in a variety of subsequent processing and decision tasks. For a given target vector, …

We apply network Lasso to semi-supervised regression problems involving network structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which represents the network structure of the data. By using a simple non-parametric regressi…

Proposes a method to improve Lasso stability via variable decorrelation.

Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.

Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.

A new estimator corrects bias in high-dimensional predictive regressions.

Robust Lasso-Zero handles missing covariates and sparse corruptions.

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is …