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We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first…
Sufficient dimension reduction (SDR) provides a framework for reducing the predictor space dimension in regression problems. We consider SDR in the context of deterministic functions of several variables such as those arising in computer…
Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While…
For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…
Sliced inverse regression (SIR) is a popular sufficient dimension reduction method that identifies a few linear transformations of the covariates without losing regression information with the response. In high-dimensional settings, SIR can…
Sliced inverse regression (SIR) is the most widely-used sufficient dimension reduction method due to its simplicity, generality and computational efficiency. However, when the distribution of the covariates deviates from the multivariate…
Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for additive error regressions with continuous predictors and link function. It operates under the assumption that the predictors can be replaced…
Sufficient dimension reduction (SDR) methods aim to identify a dimension reduction subspace (DRS) that preserves all the information about the conditional distribution of a response given its predictor. Traditional SDR methods determine the…
Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is…
With the rapid development of data collection techniques, complex data objects that are not in the Euclidean space are frequently encountered in new statistical applications. Fr\'echet regression model (Peterson & M\"uller 2019) provides a…
Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and…
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…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…
Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
We employ distribution regression (DR) to estimate the joint distribution of two outcome variables conditional on chosen covariates. While Bivariate Distribution Regression (BDR) is useful in a variety of settings, it is particularly…
We present a forward sufficient dimension reduction method for categorical or ordinal responses by extending the outer product of gradients and minimum average variance estimator to multinomial generalized linear model. Previous work in…
We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the…