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We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
The sparse precision matrix plays an essential role in the Gaussian graphical model since a zero off-diagonal element indicates conditional independence of the corresponding two variables given others. In the Gaussian graphical model, many…
When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…
We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state\textendash of\textendash art asset allocation rules. First, we use a post\textendash…
Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their…
The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed…
The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a…
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…
Quantile regression is a very important tool to explore the relationship between the response variable and its covariates. Motivated by mean regression with LASSO for compositional covariates proposed by Lin et al. (2014), we consider…
We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…
Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
We propose Nodewise Loreg, a nodewise $L_0$-penalized regression method for estimating high-dimensional sparse precision matrices. We establish its asymptotic properties, including convergence rates, support recovery, and asymptotic…
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…