Related papers: Lecture Notes on High Dimensional Linear Regressio…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
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…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…
The past decade has witnessed two important new developments in the study of linear series on algebraic varieties. First, vector bundles have emerged as powerful tools for analyzing linear series on curves and surfaces. More recently, the…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We…
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…
The lasso has become an important practical tool for high dimensional regression as well as the object of intense theoretical investigation. But despite the availability of efficient algorithms, the lasso remains computationally demanding…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…
These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
We derive expressions for the finite-sample distribution of the Lasso estimator in the context of a linear regression model in low as well as in high dimensions by exploiting the structure of the optimization problem defining the estimator.…
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…
Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…