Related papers: Adaptive scaling for soft-thresholding estimator

In this paper, we study the problem of estimation and learning under temporal distribution shift. Consider an observation sequence of length $n$, which is a noisy realization of a time-varying groundtruth sequence. Our focus is to develop…

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite…

In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity." Classical sparse regression…

Sparsity in Deep Neural Networks (DNNs) is studied extensively with the focus of maximizing prediction accuracy given an overall parameter budget. Existing methods rely on uniform or heuristic non-uniform sparsity budgets which have…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…

Self-supervised learning (SSL) has emerged as a powerful strategy for representation learning under limited annotation regimes, yet its effectiveness remains highly sensitive to many factors, especially the nature of the target task. In…

Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection operator), the use of which requires…

We consider a class of Cox models with time-dependent effects that may be zero over certain unknown time regions or, in short, sparse time-varying effects. The model is particularly useful for biomedical studies as it conveniently depicts…

Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

Adapting large pre-trained language models to downstream tasks often entails fine-tuning millions of parameters or deploying costly dense weight updates, which hinders their use in resource-constrained environments. Low-rank Adaptation…

Tomographic SAR technique has attracted remarkable interest for its ability of three-dimensional resolving along the elevation direction via a stack of SAR images collected from different cross-track angles. The emerged compressed sensing…

We introduce a smooth variant of the SCAD thresholding rule for wavelet denoising by replacing its piecewise linear transition with a raised cosine. The resulting shrinkage function is odd, continuous on R, and continuously differentiable…

The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…

Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…

In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…

Stability selection has gained popularity as a method for enhancing the performance of variable selection algorithms while controlling false discovery rates. However, achieving these desirable properties depends on correctly specifying the…

We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…