Related papers: Sparse Convex Quantile Regression: A Generalized B…
Large-scale association analysis between multivariate responses and predictors is of great practical importance, as exemplified by modern business applications including social media marketing and crisis management. Despite the rapid…
We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…
The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…
This paper develops a new scalable sparse Cox regression tool for sparse high-dimensional massive sample size (sHDMSS) survival data. The method is a local $L_0$-penalized Cox regression via repeatedly performing reweighted $L_2$-penalized…
Stochastic Gradient Descent (SGD) is fundamental for training deep neural networks, especially in non-convex settings. Understanding SGD's generalization properties is crucial for ensuring robust model performance on unseen data. In this…
Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…
We present, QP-SBGD, a novel layer-wise stochastic optimiser tailored towards training neural networks with binary weights, known as binary neural networks (BNNs), on quantum hardware. BNNs reduce the computational requirements and energy…
Sparse regression methods have been proven effective in a wide range of signal processing problems such as image compression, speech coding, channel equalization, linear regression and classification. In this paper a new convex method of…
Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks…
In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
Sparse inversion of gravity data based on $L_1$-norm regularization is discussed. An iteratively reweighted least squares algorithm is used to solve the problem. At each iteration the solution of a linear system of equations and the…
Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
Distributed stochastic gradient descent (SGD) approach has been widely used in large-scale deep learning, and the gradient collective method is vital to ensure the training scalability of the distributed deep learning system. Collective…
Although a number of studies have developed fast geographically weighted regression (GWR) algorithms for large samples, none of them has achieved linear-time estimation, which is considered a requisite for big data analysis in machine…
We introduce a clipping strategy for Stochastic Gradient Descent (SGD) which uses quantiles of the gradient norm as clipping thresholds. We prove that this new strategy provides a robust and efficient optimization algorithm for smooth…
This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…
The use of low-bit quantization has emerged as an indispensable technique for enabling the efficient training of large-scale models. Despite its widespread empirical success, a rigorous theoretical understanding of its impact on learning…
We study linear quantile regression models when regressors and/or dependent variable are not directly observed but estimated in an initial first step and used in the second step quantile regression for estimating the quantile parameters.…