Institut für Numerische Simulation (INS): Browsing Institut für Numerische Simulation (INS) by Author "Bohn, Bastian"
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A sparse grid based method for generative dimensionality reduction of high-dimensional data
Bohn, Bastian; Garcke, Jochen; Griebel, Michael (2015-11)Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a ... -
An adaptive sparse grid approach for time series predictions
Bohn, Bastian; Griebel, Michael (2012-01)A real valued, deterministic and stationary time series can be embedded in a — sometimes high-dimensional — real vector space. This leads to a one-to-one relationship between the embedded, time dependent vectors in ... -
Deep neural networks and PIDE discretizations
Bohn, Bastian; Griebel, Michael; Kannan, Dinesh (2021-08)In this paper, we propose neural networks that tackle the problems of stability and field-of-view of a Convolutional Neural Network (CNN). As an alternative to increasing the network’s depth or width to improve performance, ... -
Error estimates for multivariate regression on discretized function spaces
Bohn, Bastian; Griebel, Michael (2016-03)In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling ... -
On the convergence rate of sparse grid least squares regression
Bohn, Bastian (2017-08)While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, ... -
A representer theorem for deep kernel learning
Bohn, Bastian; Griebel, Michael; Rieger, Christian (2019-05)In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical ...