@article{MeineckeHarmelingMueller2005,
  author    = {Meinecke, Frank C. and Harmeling, Stefan and M{\"u}ller, Klaus-Robert},
  title     = {Inlier-based ICA with an application to superimposed images},
  issn      = {0899-9457},
  year      = {2005},
  abstract  = {This paper proposes a new independent component analysis (ICA) method which is able to unmix overcomplete mixtures of sparce or structured signals like speech, music or images. Furthermore, the method is designed to be robust against outliers, which is a favorable feature for ICA algorithms since most of them are extremely sensitive to outliers. Our approach is based on a simple outlier index. However, instead of robustifying an existing algorithm by some outlier rejection technique we show how this index can be used directly to solve the ICA problem for super-Gaussian sources. The resulting inlier-based ICA (IBICA) is outlier-robust by construction and can be used for standard ICA as well as for overcomplete ICA (i.e. more source signals than observed signals). (c) 2005 Wiley Periodicals, Inc},
  language  = {en}
}
@article{HarmelingMeineckeMueller2004,
  author    = {Harmeling, Stefan and Meinecke, Frank C. and M{\"u}ller, Klaus-Robert},
  title     = {Injecting noise for analysing the stability of ICA components},
  issn      = {0165-1684},
  year      = {2004},
  abstract  = {Usually, noise is considered to be destructive. We present a new method that constructively injects noise to assess the reliability and the grouping structure of empirical ICA component estimates. Our method can be viewed as a Monte-Carlo-style approximation of the curvature of some performance measure at the solution. Simulations show that the true root-mean-squared angle distances between the real sources and the source estimates can be approximated well by our method. In a toy experiment, we see that we are also able to reveal the underlying grouping structure of the extracted ICA components. Furthermore, an experiment with fetal ECG data demonstrates that our approach is useful for exploratory data analysis of real-world data. (C) 2003 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{ZieheKawanabeHarmeling2004,
  author    = {Ziehe, Andreas and Kawanabe, Motoaki and Harmeling, Stefan},
  title     = {Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation},
  issn      = {1532-4435},
  year      = {2004},
  abstract  = {We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply the alternating conditional expectation (ACE) algorithm-a powerful technique from nonparametric statistics-to approximately invert the componentwise nonlinear functions. The second method is a Gaussianizing transformation, which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately Gaussian distributed. This heuristic, but simple and efficient procedure works as good as the ACE method. Using the framework provided by ACE, convergence can be proven. The optimal transformations obtained by ACE coincide with the sought-after inverse functions of the nonlinearitics. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations testing "ACE-TD" and "Gauss-TD" on realistic examples are performed with excellent results},
  language  = {en}
}
@phdthesis{Harmeling2004,
  author    = {Harmeling, Stefan},
  title     = {Independent component analysis and beyond},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0001540},
  school      = {Universit{\"a}t Potsdam},
  year      = {2004},
  abstract  = {'Independent component analysis' (ICA) ist ein Werkzeug der statistischen Datenanalyse und Signalverarbeitung, welches multivariate Signale in ihre Quellkomponenten zerlegen kann. Obwohl das klassische ICA Modell sehr n{\"u}tzlich ist, gibt es viele Anwendungen, die Erweiterungen von ICA erfordern. In dieser Dissertation pr{\"a}sentieren wir neue Verfahren, die die Funktionalit{\"a}t von ICA erweitern: (1) Zuverl{\"a}ssigkeitsanalyse und Gruppierung von unabh{\"a}ngigen Komponenten durch Hinzuf{\"u}gen von Rauschen, (2) robuste und {\"u}berbestimmte ('over-complete') ICA durch Ausreissererkennung, und (3) nichtlineare ICA mit Kernmethoden.},
  language  = {en}
}
@article{HarmelingDornhegeTaxetal.2006,
  author    = {Harmeling, Stefan and Dornhege, Guido and Tax, David and Meinecke, Frank C. and M{\"u}ller, Klaus-Robert},
  title     = {From outliers to prototypes : Ordering data},
  issn      = {0925-2312},
  doi       = {10.1016/j.neucom.2005.05.015},
  year      = {2006},
  abstract  = {We propose simple and fast methods based on nearest neighbors that order objects from high-dimensional data sets from typical points to untypical points. On the one hand, we show that these easy-to-compute orderings allow us to detect outliers (i.e. very untypical points) with a performance comparable to or better than other often much more sophisticated methods. On the other hand, we show how to use these orderings to detect prototypes (very typical points) which facilitate exploratory data analysis algorithms such as noisy nonlinear dimensionality reduction and clustering. Comprehensive experiments demonstrate the validity of our approach.},
  language  = {en}
}
@article{SchuettHarmelingMackeetal.2016,
  author    = {Sch{\"u}tt, Heiko Herbert and Harmeling, Stefan and Macke, Jakob H. and Wichmann, Felix A.},
  title     = {Painfree and accurate Bayesian estimation of psychometric functions for (potentially) overdispersed data},
  series = {Vision research : an international journal for functional aspects of vision.},
  volume    = {122},
  journal   = {Vision research : an international journal for functional aspects of vision.},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0042-6989},
  doi       = {10.1016/j.visres.2016.02.002},
  pages     = {105 -- 123},
  year      = {2016},
  abstract  = {The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion goodness-of-fit which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4 performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available. (C) 2016 The Authors. Published by Elsevier Ltd.},
  language  = {en}
}