Related papers: Dimensionality Reduction for Tukey Regression
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for…
Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…
Is there a natural way to order data in dimension greater than one? The approach based on the notion of data depth, often associated with John Tukey, is among the most popular. Tukey's depth has found applications in robust statistics,…
Dimensionality reduction has always been one of the most significant and challenging problems in the analysis of high-dimensional data. In the context of time series analysis, our focus is on the estimation and inference of conditional mean…
Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one is interested in analyzing the stochastic response of the…
We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…
Fully convolutional deep neural networks carry out excellent potential for fast and accurate image segmentation. One of the main challenges in training these networks is data imbalance, which is particularly problematic in medical imaging…
Determining the representativeness of a point within a data cloud has recently become a desirable task in multivariate analysis. The concept of statistical depth function, which reflects centrality of an arbitrary point, appears to be…
We study the temporal-spatial regularity properties of tamed Euler approximations for L\'evy-driven SDEs with superlinearly growing drift and diffusion coefficients. We first introduce a novel tamed Euler-type scheme and establish its…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
The $k$-dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative $k$-dimensional vectors, and include non-negative matrix factorization, dictionary learning, sparse coding,…
We investigate an application of the Tukey's methodology in Theil's regression to obtain a confidence interval for the true slope in the straight line regression model with not necessarily normal errors. This specific approach is…
Given data in $\mathbb{R}^{p}$, a Tukey $\kappa$-trimmed region is the set of all points that have at least Tukey depth $\kappa$ w.r.t. the data. As they are visual, affine equivariant and robust, Tukey regions are useful tools in…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…