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In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…
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 $\mathrm{var}(X|\beta^\mathsf{T}X)$…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
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…
Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…
We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
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…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…
As deep learning methodologies have developed, it has been generally agreed that increasing neural network size improves model quality. However, this is at the expense of memory and compute requirements, which also need to be increased.…
In this paper, the existing Scheduling Dimension Reduction (SDR) methods for Linear Parameter-Varying (LPV) models are reviewed and a Deep Neural Network (DNN) approach is developed that achieves higher model accuracy under scheduling…
Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are…
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…
The multivariate adaptive regression spline (MARS) is one of the popular estimation methods for nonparametric multivariate regressions. However, as MARS is based on marginal splines, to incorporate interactions of covariates, products of…
Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for…
We in this paper consider Fr\'echet sufficient dimension reduction with responses being complex random objects in a metric space and high dimension Euclidean predictors. We propose a novel approach called weighted inverse regression…