Related papers: Sparse Convex Quantile Regression: A Generalized B…
In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularization has received considerable attention due to its superiorities on sparsity-inducing and bias reduction over the $l_1$ regularization.In this paper, we propose a cyclic…
In this paper, we propose a new regularization technique called "functional SCAD". We then combine this technique with the smoothing spline method to develop a smooth and locally sparse (i.e., zero on some sub-regions) estimator for the…
The scalability of Distributed Stochastic Gradient Descent (SGD) is today limited by communication bottlenecks. We propose a novel SGD variant: Communication-efficient SGD with Error Reset, or CSER. The key idea in CSER is first a new…
Variable selection and dimension reduction are two commonly adopted approaches for high-dimensional data analysis, but have traditionally been treated separately. Here we propose an integrated approach, called sparse gradient learning…
Single-source domain generalization (SDG) for object detection is a challenging yet essential task as the distribution bias of the unseen domain degrades the algorithm performance significantly. However, existing methods attempt to extract…
Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…
We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…
Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
The generalization capacity of various machine learning models exhibits different phenomena in the under- and over-parameterized regimes. In this paper, we focus on regression models such as feature regression and kernel regression and…
Vector Quantization (VQ) is a well-known technique in deep learning for extracting informative discrete latent representations. VQ-embedded models have shown impressive results in a range of applications including image and speech…
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…
Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising…
Multivariate regression techniques are commonly applied to explore the associations between large numbers of outcomes and predictors. In real-world applications, the outcomes are often of mixed types, including continuous measurements,…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In…
We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…