Related papers: Robust Global Fr'echet Regression via Weight Regul…
Forward regression is a classical and effective tool for variable screening in ultra-high dimensional linear models, but its standard projection-based implementation can be computationally costly and numerically unstable when predictors are…
This paper revisits an adaptation of the random forest algorithm for Fr\'echet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we…
We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
Ensemble models are powerful model building tools that are developed with a focus to improve the accuracy of model predictions. They find applications in time series forecasting in varied scenarios including but not limited to process…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
The tracking method based on the extreme learning machine (ELM) is efficient and effective. ELM randomly generates input weights and biases in the hidden layer, and then calculates and computes the output weights by reducing the iterative…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…
In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…
We propose and analyze a variant of the classic Polyak-Ruppert averaging scheme, broadly used in stochastic gradient methods. Rather than a uniform average of the iterates, we consider a weighted average, with weights decaying in a…
In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components…
A central part of geometric statistics is to compute the Fr\'echet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian distances from the mean point to all other data points. The…
Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from…