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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…
In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support…
Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…
This paper presents a unified framework for sufficient dimension reduction (SDR) that generalizes several existing SDR techniques and offers new insights into the connection between inverse conditional moment independence and dimension…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
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…
Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of negligible variation for the response surface. These directions span the orthogonal complement of the minimal space…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of…