Related papers: Derivative Principal Component Analysis for Repres…
Recent literature has shown how linear time-invariant (LTI) systems can be represented by trajectories features, that is relying on a single input-output (IO) data dictionary to span all possible system trajectories, as long as the input is…
Getting tools that allow simple representations and comparisons of a set of categorical trajectories is of major interest for statisticians. Without loosing any information, we associate to each state a binary random indicator function,…
Shannon in his 1949 paper suggested the use of derivatives to increase the W*T product of the sampled signal. Use of derivatives enables improved reconstruction particularly in the case of non-uniformly sampled signals. An FM-AM…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
In clinical practice and biomedical research, measurements are often collected sparsely and irregularly in time while the data acquisition is expensive and inconvenient. Examples include measurements of spine bone mineral density, cancer…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…
We study non-equilibrium quantum dynamics by performing principal component analysis on the data sets of wavefunction snapshots. We show that a specific transformation of the data sets maximizes the information content in the largest…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the…
When measurements fall below or above a detection threshold, the resulting data are missing not at random (MNAR), posing challenges for statistical analysis. For example, in longitudinal biomarker studies, observations may be subject to…
We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
Learning the governing equations from time-series data has gained increasing attention due to its potential to extract useful dynamics from real-world data. Despite significant progress, it becomes challenging in the presence of noise,…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all…
Linear quantile regression models aim at providing a detailed and robust picture of the (conditional) response distribution as function of a set of observed covariates. Longitudinal data represent an interesting field of application of such…
Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice.…
This paper addresses differential inference in time-varying parametric probabilistic models, like graphical models with changing structures. Instead of estimating a high-dimensional model at each time point and estimating changes later, we…