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Motivated by an increasing demand for models that can effectively describe features of complex multivariate time series, e.g. from sensor data in biomechanics, motion analysis, and sports science, we introduce a novel state-space modeling…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes…
The least-mean-squares (LMS) algorithm is the most popular algorithm in adaptive filtering. Several variable step-size strategies have been suggested to improve the performance of the LMS algorithm. These strategies enhance the performance…
Edge bundling methods can effectively alleviate visual clutter and reveal high-level graph structures in large graph visualization. Researchers have devoted significant efforts to improve edge bundling according to different metrics. As the…
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…
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…
In real data analysis with structural equation modeling, data are unlikely to be exactly normally distributed. If we ignore the non-normality reality, the parameter estimates, standard error estimates, and model fit statistics from normal…
In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…
The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…
Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…
We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of…
Inspired by recent developments in subdivision schemes founded on the Weighted Least Squares technique, we construct linear approximants for noisy data in which the weighting strategy minimizes the output variance, thereby establishing a…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…
An accurate predictor is crucial for histogram-shifting (HS) based reversible data hiding methods. The embedding capacity is increased and the embedding distortion is decreased simultaneously if the predictor can generate accurate…
The Material Point Method (MPM) is a hybrid Eulerian Lagrangian simulation technique for solid mechanics with significant deformation. Structured background grids are commonly employed in the standard MPM, but they may give rise to several…