Search results for "Robust statistics"
showing 5 items of 15 documents
Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence
2016
The geometric median, also called L 1 -median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et?al. (2013). This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The L p rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rates of convergence in quadratic mean of the averaged algorithm are also given.
Stochastic algorithms for robust statistics in high dimension
2016
This thesis focus on stochastic algorithms in high dimension as well as their application in robust statistics. In what follows, the expression high dimension may be used when the the size of the studied sample is large or when the variables we consider take values in high dimensional spaces (not necessarily finite). In order to analyze these kind of data, it can be interesting to consider algorithms which are fast, which do not need to store all the data, and which allow to update easily the estimates. In large sample of high dimensional data, outliers detection is often complicated. Nevertheless, these outliers, even if they are not many, can strongly disturb simple indicators like the me…
Application of a Knowledge Discovery Process to Study Instances of Capacitated Vehicle Routing Problems
2020
Vehicle Routing Problems (VRP) are computationally challenging, constrained optimization problems, which have central role in logistics management. Usually different solvers are being developed and applied for different kind of problems. However, if descriptive and general features could be extracted to describe such problems and their solution attempts, then one could apply data mining and machine learning methods in order to discover general knowledge on such problems. The aim then would be to improve understanding of the most important characteristics of VRPs from both efficient solution and utilization points of view. The purpose of this article is to address these challenges by proposi…
CLUSTERING INCOMPLETE SPECTRAL DATA WITH ROBUST METHODS
2018
Abstract. Missing value imputation is a common approach for preprocessing incomplete data sets. In case of data clustering, imputation methods may cause unexpected bias because they may change the underlying structure of the data. In order to avoid prior imputation of missing values the computational operations must be projected on the available data values. In this paper, we apply a robust nan-K-spatmed algorithm to the clustering problem on hyperspectral image data. Robust statistics, such as multivariate medians, are more insensitive to outliers than classical statistics relying on the Gaussian assumptions. They are, however, computationally more intractable due to the lack of closed-for…
Student agency analytics: learning analytics as a tool for analysing student agency in higher education
2020
This paper presents a novel approach and a method of learning analytics to study student agency in higher education. Agency is a concept that holistically depicts important constituents of intentional, purposeful, and meaningful learning. Within workplace learning research, agency is seen at the core of expertise. However, in the higher education field, agency is an empirically less studied phenomenon with also lacking coherent conceptual base. Furthermore, tools for students and teachers need to be developed to support learners in their agency construction. We study student agency as a multidimensional phenomenon centring on student-experienced resources of their agency. We call the analyt…