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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Köster, U., & Hyvärinen, A. (2007). A two-layer ICA-Like model estimated by score matching. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4669 LNCS, pp. 798–807). Springer Verlag. https://doi.org/10.1007/978-3-540-74695-9_82
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