Related papers: Sparse Tensor Additive Regression
We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…
This paper introduces a Factor Augmented Sparse Throughput (FAST) model that utilizes both latent factors and sparse idiosyncratic components for nonparametric regression. The FAST model bridges factor models on one end and sparse…
Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…
Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…
High-dimensional vector autoregressive (VAR) models have numerous applications in fields such as econometrics, biology, climatology, among others. While prior research has mainly focused on linear VAR models, these approaches can be…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
In recent years, promising statistical modeling approaches to tensor data analysis have been rapidly developed. Traditional multivariate analysis tools, such as multivariate regression and discriminant analysis, are generalized from…
Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
Large language models (LLMs) rely on self-attention for contextual understanding, demanding high-throughput inference and large-scale token parallelism (LTPP). Existing dynamic sparsity accelerators falter under LTPP scenarios due to…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the $\ell_0$-penalized least squares solutions. It generates…
We consider estimation in a sparse additive regression model with the design points on a regular lattice. We establish the minimax convergence rates over Sobolev classes and propose a Fourier-based rate-optimal estimator which is adaptive…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic…