Dr. Philipp Metzner (currently working on inverse problems in fluid mechanics and their HPC-implementation, funded from the German DFG research initiative MetStroem),
Dr. Susanne Gerber (working on problems from computational systems biology and bioinformatics, funded from HP2C USI Lugano corp. funds),
Dr. Olga Kaiser (working on mathematical methods for non-stationary analysis and data-based prediction of extreme events),
Dipl.-Math. Lars Putzig (working on inverse problems from computational finance and risk theory, funded from the corporate funds of the USI faculty of informatics),
Dipl.-Inf. Dimitri Igdalov (working on data-based identification of temporal changes in very large graphs and HPC implementation of time series analysis methods library developed in the group, funded from the SNF-project AnaGraph),
Dipl.-Math. Jana de Wiljes (working on data-based parameter identification for non-stationary and non-homogenous percolation models and Ising models with application to Arctic ice shield modeling based on satellite data, funded by the interdisciplinary research centre GeoSim of the German Helmholtz-foundation in Berlin),
M.Sc. Anna Marchenko (working on mathematical modeling of credit and equity risk beyond homogeneity and stationarity assumptions: statistical factor models and high-performance data mining).
Time series and high-dimensional data analysis beyond stationarity and homogeneity assumptions, inverse stochastic modelling of dynamical systems.
Methods for analysis of discrete jump processes and categorical model inference.
Developement of high-performance stochastic computing methods for applications in fluid mechanics, meteorology, climate research, biophysics, sociology and finance.
One of the major limitations of the currently existing standard methods of time series analysis is their narrowness with respect to the data types (e.g., univariate vector-valued data, multivariate data, categorical data, etc.), i.e. every specific time series type can be analyzed only applying a distinct appropriate standard time series analysis methodology that is in general not applicable to other data types. There exist almost no standard and universal time series analysis methods applicable to all of the data classes that can be found in the applications. Besides of this limited generality of the standard methods, another major limitation is that standard methods implicitly deploy the assumptions of stationarity (i.e., assuming that the statistical model parameters are constant in time) and /or homogeneity (i.e., assuming that the statistical model parameters are constant for a certain, a priori defined group of realizations or spatial dimensions). E.g., Fourier analysis assumes the constancy (i.e., stationarity) of the amplitudes and frequencies; building of the expectations and the variances over groups of data relies on the weak stationarity assumptions for these groups. In context of time series analysis with standard methods, these implicit assumptions may induce a biased and over-simplified interpretation of the analyzed data, and, therefore, result in the wrong predictions.
Research of I. Horenko and his USI/ICS group ”Computational Time Series Analysis” was concentrated on the development of a new family of adaptive variational methods called Finite Element Methods of time series analysis with Bounded Variation of model parameters (FEM-BV). Distinctive property of these methods is that they allow an analysis of a very general class of data types (including real-valued, categorical and functional data). For all these data types, time series analysis within the FEM-BV-methodology can be performed beyond the stationarity and homogeneity assumptions and in context of the same mathematical and computational framework. In combination with information theory, FEM-BV-framework allows an adaptive data-based inference of the most appropriate dynamical model in a pre-defined set of possible models that, from the viewpoint of the information, describes the time series data in an optimal way. In context of the FEM-BV, not only the dynamical model for the desired quantities is parameterized, but also the optimal discrete dynamical models for the parameters are identified. This issue represents a major distinction of the FEM-BV-methods to the other methods of data mining (e.g., support vector machines, Bayesian learning methods and artificial neuronal networks), implicitly relying on the constancy (and, therefore, on the stationarity and homogeneity) of the underlying model parameters.
High-performance computing implementation of the developed computational methods in a massively-parallel setting allowed analysis of very large data sets from different application areas. Current applications include: (1) historical climate data analysis and analysis of climate impact factors; (2) analysis and prediction of cloud cover dynamics in meteorology; (3) data-based analysis of job market dynamics in sociology; (4) DNA sequence analysis and microarray data analysis in genomics; (5) computational portfolio theory and risk minimization in finance; (6) identification of metastable molecular conformations in biophysics.