Related papers: Discriminant analysis in small and large dimension…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
This paper deals with the asymptotic statistical properties of a class of redescending M-estimators in linear models with increasing dimension. This class is wide enough to include popular high breakdown point estimators such as…
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…
Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient…
The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…
We study the problem of learning an unknown function using random feature models. Our main contribution is an exact asymptotic analysis of such learning problems with Gaussian data. Under mild regularity conditions for the feature matrix,…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and…
We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…
We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator…