Related papers: Transformed sufficient dimension reduction
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…
Variable selection is a procedure to attain the truly important predictors from inputs. Complex nonlinear dependencies and strong coupling pose great challenges for variable selection in high-dimensional data. In addition, real-world…
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of…
Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks…
We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…
We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…
We study a dimensionality reduction technique for finite mixtures of high-dimensional multivariate response regression models. Both the dimension of the response and the number of predictors are allowed to exceed the sample size. We…
The current landscape in time-series forecasting is dominated by Transformer-based models. Their high parameter count and corresponding demand in computational resources pose a challenge to real-world deployment, especially for commercial…
Negative binomial regression is essential for analyzing over-dispersed count data in in comparative studies, but parameter estimation becomes computationally challenging in large screens requiring millions of comparisons. We investigate…
The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism…
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
Many learning algorithms require categorical data to be transformed into real vectors before it can be used as input. Often, categorical variables are encoded as one-hot (or dummy) vectors. However, this mode of representation can be…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
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…