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We present a new estimation principle for parameterized statistical models. The idea is to perform nonlinear logistic regression to discriminate between the observed data and some artificially generated noise, using the model log-density function in the regression nonlinearity. We show that this leads to a consistent (convergent) estimator of the parameters(More)
We consider the task of estimating, from observed data, a probabilistic model that is parameterized by a finite number of parameters. In particular, we are considering the situation where the model probability density function is unnormalized. That is, the model is only specified up to the partition function. The partition function normalizes a model so(More)
We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two sub-models, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image(More)
We present a nonlinear generalization of Canonical Correlation Analysis (CCA) to find related structure in multiple data sets. The new method allows to analyze an arbitrary number of data sets, and the extracted features capture higher-order statistical dependencies. The features are independent components that are coupled across the data sets. The coupling(More)
BACKGROUND It has been shown that the classical receptive fields of simple and complex cells in the primary visual cortex emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse or independent. We investigate how to learn features beyond the primary visual cortex from the statistical properties of(More)
We show that the Bregman divergence provides a rich framework to estimate unnor-malized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and score matching belong to the proposed(More)
A fundamental question in visual neuroscience is: Why are the receptive fields and response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input. In this paper, we will review work on modelling statistical regularities in ecologically valid visual input (" natural(More)
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