Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.
problem Sparse-penalized quantile regression with non-convex penalties.
method Single-loop smoothing ADMM (SIAD) algorithm for faster convergence.
result SIAD method outperforms existing approaches in solving sparse-penalized quantile regression.
The paper develops adaptive deep learning methods for nonlinear time series models.
problem Estimating mean functions of non-stationary and nonlinear time series models.
method Develops non-penalized and sparse-penalized DNN estimators for general non-stationary time series, derives minimax lower bounds, and shows the sparse-penalized DNN estimator is adaptive and optimal.
result Sparse-penalized DNN estimator achieves minimax optimal rates for many nonlinear AR models.
The paper develops a deep neural network estimator for weakly dependent processes with various loss functions.
problem Learning weakly dependent processes with a broad class of loss functions.
method Sparse-penalized deep neural networks with ψ-weak dependence structure and θ∞-coefficients. result Oracle inequalities for the excess risk of the sparse-penalized deep neural networks estimators.
Distance weighted discrimination (DWD) was originally proposed to handle the data piling issue in the support vector machine. In this paper, we consider the sparse penalized DWD for high-dimensional classification. The state-of-the-art algorithm for solving the standard DWD is based on second-order cone programming, ho…
The paper tackles deep learning from dependent data, achieving optimal performance.
problem Deep learning from strongly mixing observations, especially with regularization and optimality.
method Sparse-penalized regularization for deep neural networks, oracle inequality for expected excess risk.
result Deep neural network estimator achieves minimax optimal rate for nonparametric autoregression.
Paper proposes a new method to optimize deep neural networks with sparse regularization.
problem Difficulty in achieving optimal convergence rates for deep neural networks due to sparsity constraints.
method Introduces a novel penalized estimation method for sparse DNNs, resolving computational and theoretical issues.
result Establishes an oracle inequality for the excess risk of the proposed sparse-penalized DNN estimator and derives convergence rates.
Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.
problem Challenges of classical Lasso in handling heavy-tailed noise and outliers.
method Data-augmented soft-thresholding with Student's t-distribution loss.
result Heavy Lasso achieves comparable rates to Huber loss under theoretical bounds.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result generalizes from orthonormal designs to full rank designs (Theorem 1). Theorem …
Develops a deep learning framework for various data types.
problem Handling nonparametric regression and classification across different data types.
method Introduces a general framework with two estimators: NPDNN and SPDNN, based on data satisfying generalized Bernstein-type inequalities.
result Both NPDNN and SPDNN estimators are minimax optimal in many classical settings.
Paper tackles distributed linear regression with compositional covariates.
problem Solving distributed statistical methodology and computing for massive compositional data.
method Proposes two distributed optimization techniques based on ADMM and CDMM for solving constrained convex optimization problems.
result Established convergence theories for the proposed algorithms under regularity conditions.
Paper proposes sparse classification method for high-dimensional data.
problem Sparse classification in high-dimensional data with positive-confidence samples.
method Developed a novel sparse-penalization framework using L1, SCAD, and MCP penalties for convex and non-convex shrinkage.
result Proved near minimax-optimal sparse recovery rates under Restricted Strong Convexity condition.
New method robustly discovers causal relationships from imperfect data.
problem Challenges in causal discovery from imperfect structural constraints.
method Prior alignment and conflict resolution through surrogate model and multi-task learning.
result Proposes a robust method for causal discovery under imperfect constraints.
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
problem Lasso's sensitivity to outliers and heavy-tailed noise in high-dimensional statistics.
method Integrates an exponential-type loss function into the Lasso framework.
result Achieves strong statistical convergence rates robust to heavy-tailed contamination.
New method controls FDR for sparse GLMs, identifying positive and negative relationships.
problem Sparse GLMs with high-dimensional data and varying sample size.
method Debiased-Lasso estimator and CLIME method for precision matrix estimation.
result Asymptotically controls directional FDR and FDV for sparse GLMs.