Related papers: A robust variable screening procedure for ultra-hi…
Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…
Feature screening for ultrahigh-dimension, in general, proceeds with two essential steps. The first step is measuring and ranking the marginal dependence between response and covariates, and the second is determining the threshold. We…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…
Distributed optimization has been widely used as one of the most efficient approaches for model training with massive samples. However, large-scale learning problems with both massive samples and high-dimensional features widely exist in…
In recent years we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a…
In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…
Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting. Most existing screening methods are designed to rank the predictors according to their individual contributions to…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…
Variable screening has been a useful research area that deals with ultrahigh-dimensional data. When there exist both marginally and jointly dependent predictors to the response, existing methods such as conditional screening or iterative…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
We address the problem of dynamic variable selection in time series regression with unknown residual variances, where the set of active predictors is allowed to evolve over time. To capture time-varying variable selection uncertainty, we…
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…
Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…
Feature screening for ultra high dimensional feature spaces plays a critical role in the analysis of data sets whose predictors exponentially exceed the number of observations. Such data sets are becoming increasingly prevalent in areas…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
We propose a new model-free feature screening method based on energy distances for ultrahigh-dimensional binary classification problems. With a high probability, the proposed method retains only relevant features after discarding all the…
A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…
Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an…