Related papers: Generalized ridge estimator and model selection cr…
Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention for modeling extreme events in signal and image processing applications. Considering the…
We observe a random measure $N$ and aim at estimating its intensity $s$. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with…
We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius…
We consider learning with possibilistic supervision for multi-class classification. For each training instance, the supervision is a normalized possibility distribution that expresses graded plausibility over the classes. From this…
The purpose of this paper is to pursue our study of rho-estimators built from i.i.d. observations that we defined in Baraud et al. (2014). For a \rho-estimator based on some model S (which means that the estimator belongs to S) and a true…
High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of…
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…
We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…
In order to overcome multicollinearity, we propose a stochastic restricted Liu-type max- imum likelihood estimator by incorporating Liu-type maximum likelihood estimator (Inan and Erdo- gan, 2013) to the logistic regression model when the…
In supervised batch learning, the predictive normalized maximum likelihood (pNML) has been proposed as the min-max regret solution for the distribution-free setting, where no distributional assumptions are made on the data. However, the…
In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based…
Recent work on algorithmic fairness has largely focused on the fairness of discrete decisions, or classifications. While such decisions are often based on risk score models, the fairness of the risk models themselves has received…
Generalization is a central problem in Machine Learning. Indeed most prediction methods require careful calibration of hyperparameters usually carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of…
Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…