Related papers: A least distance estimator for a multivariate regr…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
Convolutional Neural Network (CNN) have been widely used in image classification. Over the years, they have also benefited from various enhancements and they are now considered as state of the art techniques for image like data. However,…
Data-driven approaches to automated machine condition monitoring are gaining popularity due to advancements made in sensing technologies and computing algorithms. This paper proposes the use of a deep learning model, based on Long…
Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…
Least Absolute Deviations (LAD) regression provides a robust alternative to ordinary least squares by minimizing the sum of absolute residuals. However, its widespread use has been limited by the computational cost of existing solvers,…
The Lasso (Least Absolute Shrinkage and Selection Operator) has been a popular technique for simultaneous linear regression estimation and variable selection. In this paper, we propose a new novel approach for robust Lasso that follows the…
A deep neural network (DNN) consists of a nonlinear transformation from an input to a feature representation, followed by a common softmax linear classifier. Though many efforts have been devoted to designing a proper architecture for…
We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…
Remaining useful life (RUL) estimation is a crucial component in the implementation of intelligent predictive maintenance and health management. Deep neural network (DNN) approaches have been proven effective in RUL estimation due to their…
During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the…
In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended…
Integrating probability and nonprobability survey samples is an important problem in modern survey sampling. Nonprobability samples often contain rich outcome information but may lack population representativeness, whereas probability…
In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral…
This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates…
To investigate the theoretical foundations of deep learning from the viewpoint of the minimum description length (MDL) principle, we analyse risk bounds of MDL estimators based on two-stage codes for simple two-layers neural networks (NNs)…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
Deep neural networks (DNNs) are often prone to learn the spurious correlations between target classes and bias attributes, like gender and race, inherent in a major portion of training data (bias-aligned samples), thus showing unfair…
In recent years Deep Neural Networks (DNNs) have been rapidly developed in various applications, together with increasingly complex architectures. The performance gain of these DNNs generally comes with high computational costs and large…
We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations,…
This paper discusses minimum distance estimation method in the linear regression model with dependent errors which are strongly mixing. The regression parameters are estimated through the minimum distance estimation method, and asymptotic…