Related papers: Impacts of high dimensionality in finite samples
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We…
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…
We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…
In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows…
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…