Related papers: A Unified Framework for High-Dimensional Analysis …
This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression,…
Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…
1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine…
Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
Reverse Unrestricted MIxed DAta Sampling (RU-MIDAS) regressions are used to model high-frequency responses by means of low-frequency variables. However, due to the periodic structure of RU-MIDAS regressions, the dimensionality grows quickly…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…
Medical imaging involves high-dimensional data, yet their acquisition is obtained for limited samples. Multivariate predictive models have become popular in the last decades to fit some external variables from imaging data, and standard…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…