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The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. However, application of QR can become very challenging when dealing with high-dimensional data, making it necessary to use…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
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…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
We review sufficient dimension reduction (SDR) estimators with multivariate response in this paper. A wide range of SDR methods are characterized as inverse regression SDR estimators or forward regression SDR estimators. The inverse…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…
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…
Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually…
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…
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…
Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…
Bird's eye view (BEV) is widely adopted by most of the current point cloud detectors due to the applicability of well-explored 2D detection techniques. However, existing methods obtain BEV features by simply collapsing voxel or point…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a…
Due to the demand for tackling the problem of streaming data with high dimensional covariates, we propose an online sparse sliced inverse regression (OSSIR) method for online sufficient dimension reduction. The existing online sufficient…