相关论文: Maximum Likelihood Ridge Regression
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…
The out-degree distribution of citation networks is investigated. Statistical data of the number of papers cited within a paper (out-degree) for different journals in the period 1991-1999 is reported. The out-degree distribution is…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
In a remarkable series of papers beginning in 1956, Charles Stein set the stage for the future development of minimax shrinkage estimators of a multivariate normal mean under quadratic loss. More recently, parallel developments have seen…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains…
We consider fully row/column-correlated linear regression models and study several classical estimators (including minimum norm interpolators (GLS), ordinary least squares (LS), and ridge regressors). We show that \emph{Random Duality…
A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
Features in predictive models are not exchangeable, yet common supervised models treat them as such. Here we study ridge regression when the analyst can partition the features into $K$ groups based on external side-information. For example,…
In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…
Random forests remain among the most popular off-the-shelf supervised machine learning tools with a well-established track record of predictive accuracy in both regression and classification settings. Despite their empirical success as well…
In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew t distribution,…
In "Li, L. and Yin, X. (2008). Sliced Inverse Regression with Regularizations. Biometrics, 64(1):124--131" a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least-squares…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
We propose to view non-rigid surface registration as a probabilistic inference problem. Given a target surface, we estimate the posterior distribution of surface registrations. We demonstrate how the posterior distribution can be used to…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even…