Abstract
Capturing regularities in high-dimensional data is an important problem in machine learning and signal processing. Here we present a statistical model that learns a nonlinear representation from the data that reflects abstract, invariant properties of the signal without making requirements about the kind of signal that can be processed. The model has a hierarchy of two layers, with the first layer broadly corresponding to Independent Component Analysis (ICA) and a second layer to represent higher order structure. We estimate the model using the mathematical framework of Score Matching (SM), a novel method for the estimation of non-normalized statistical models. The model incorporates a squaring nonlinearity, which we propose to be suitable for forming a higher-order code of invariances. Additionally the squaring can be viewed as modelling subspaces to capture residual dependencies, which linear models cannot capture.
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Köster, U., Hyvärinen, A. (2007). A Two-Layer ICA-Like Model Estimated by Score Matching. In: de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D. (eds) Artificial Neural Networks – ICANN 2007. ICANN 2007. Lecture Notes in Computer Science, vol 4669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74695-9_82
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DOI: https://doi.org/10.1007/978-3-540-74695-9_82
Publisher Name: Springer, Berlin, Heidelberg
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