Related papers: Cross validation in sparse linear regression with …
Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…
In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to…
In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…
Recovering sparse signals from observed data is an important topic in signal/imaging processing, statistics and machine learning. Nonconvex penalized least squares have been attracted a lot of attentions since they enjoy nice statistical…
Cross validation is commonly used for selecting tuning parameters in penalized regression, but its use in penalized Cox regression models has received relatively little attention in the literature. Due to its partial likelihood…
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…
This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…
By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
In the rapidly evolving internet-of-things (IoT) ecosystem, effective data analysis techniques are crucial for handling distributed data generated by sensors. Addressing the limitations of existing methods, such as the sub-gradient…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse…
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been…
Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…
One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…
One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing.…
We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…