Matthias Bethge

Alumni

Empirical Inference

Publications

24 results (View BibTeX file of all listed publications)

2013

How Sensitive Is the Human Visual System to the Local Statistics of Natural Images?

Gerhard, H., Wichmann, F., Bethge, M.

PLoS Computational Biology, 9(1):e1002873, January 2013 (article)

Abstract

Several aspects of primate visual physiology have been identified as adaptations to local regularities of natural images. However, much less work has measured visual sensitivity to local natural image regularities. Most previous work focuses on global perception of large images and shows that observers are more sensitive to visual information when image properties resemble those of natural images. In this work we measure human sensitivity to local natural image regularities using stimuli generated by patch-based probabilistic natural image models that have been related to primate visual physiology. We find that human observers can learn to discriminate the statistical regularities of natural image patches from those represented by current natural image models after very few exposures and that discriminability depends on the degree of regularities captured by the model. The quick learning we observed suggests that the human visual system is biased for processing natural images, even at very fine spatial scales, and that it has a surprisingly large knowledge of the regularities in natural images, at least in comparison to the state-of-the-art statistical models of natural images.

DOI Project Page [BibTex]

2013

Gerhard, H., Wichmann, F., Bethge, M. How Sensitive Is the Human Visual System to the Local Statistics of Natural Images? PLoS Computational Biology, 9(1):e1002873, January 2013 (article)

DOI Project Page [BibTex]

2012

A New Perceptual Bias Reveals Suboptimal Population Decoding of Sensory Responses

Putzeys, T., Bethge, M., Wichmann, F., Wagemans, J., Goris, R.

PLoS Computational Biology, 8(4):1-13, April 2012 (article)

Abstract

Several studies have reported optimal population decoding of sensory responses in two-alternative visual discrimination tasks. Such decoding involves integrating noisy neural responses into a more reliable representation of the likelihood that the stimuli under consideration evoked the observed responses. Importantly, an ideal observer must be able to evaluate likelihood with high precision and only consider the likelihood of the two relevant stimuli involved in the discrimination task. We report a new perceptual bias suggesting that observers read out the likelihood representation with remarkably low precision when discriminating grating spatial frequencies. Using spectrally filtered noise, we induced an asymmetry in the likelihood function of spatial frequency. This manipulation mainly affects the likelihood of spatial frequencies that are irrelevant to the task at hand. Nevertheless, we find a significant shift in perceived grating frequency, indicating that observers evaluate likelihoods of a broad range of irrelevant frequencies and discard prior knowledge of stimulus alternatives when performing two-alternative discrimination.

Web DOI Project Page [BibTex]

2012

Putzeys, T., Bethge, M., Wichmann, F., Wagemans, J., Goris, R. A New Perceptual Bias Reveals Suboptimal Population Decoding of Sensory Responses PLoS Computational Biology, 8(4):1-13, April 2012 (article)

Web DOI Project Page [BibTex]

2011

The effect of noise correlations in populations of diversely tuned neurons

Ecker, A., Berens, P., Tolias, A., Bethge, M.

Journal of Neuroscience, 31(40):14272-14283, October 2011 (article)

Abstract

The amount of information encoded by networks of neurons critically depends on the correlation structure of their activity. Neurons with similar stimulus preferences tend to have higher noise correlations than others. In homogeneous populations of neurons, this limited range correlation structure is highly detrimental to the accuracy of a population code. Therefore, reduced spike count correlations under attention, after adaptation, or after learning have been interpreted as evidence for a more efficient population code. Here, we analyze the role of limited range correlations in more realistic, heterogeneous population models. We use Fisher information and maximum-likelihood decoding to show that reduced correlations do not necessarily improve encoding accuracy. In fact, in populations with more than a few hundred neurons, increasing the level of limited range correlations can substantially improve encoding accuracy. We found that this improvement results from a decrease in noise entropy that is associated with increasing correlations if the marginal distributions are unchanged. Surprisingly, for constant noise entropy and in the limit of large populations, the encoding accuracy is independent of both structure and magnitude of noise correlations.

Web DOI [BibTex]

2011

Ecker, A., Berens, P., Tolias, A., Bethge, M. The effect of noise correlations in populations of diversely tuned neurons Journal of Neuroscience, 31(40):14272-14283, October 2011 (article)

Web DOI [BibTex]

Gravitational Lensing Accuracy Testing 2010 (GREAT10) Challenge Handbook

Kitching, T., Amara, A., Gill, M., Harmeling, S., Heymans, C., Massey, R., Rowe, B., Schrabback, T., Voigt, L., Balan, S., Bernstein, G., Bethge, M., Bridle, S., Courbin, F., Gentile, M., Heavens, A., Hirsch, M., Hosseini, R., Kiessling, A., Kirk, D., Kuijken, K., Mandelbaum, R., Moghaddam, B., Nurbaeva, G., Paulin-Henriksson, S., Rassat, A., Rhodes, J., Schölkopf, B., Shawe-Taylor, J., Shmakova, M., Taylor, A., Velander, M., van Waerbeke, L., Witherick, D., Wittman, D.

Annals of Applied Statistics, 5(3):2231-2263, September 2011 (article)

Abstract

GRavitational lEnsing Accuracy Testing 2010 (GREAT10) is a public image analysis challenge aimed at the development of algorithms to analyze astronomical images. Specifically, the challenge is to measure varying image distortions in the presence of a variable convolution kernel, pixelization and noise. This is the second in a series of challenges set to the astronomy, computer science and statistics communities, providing a structured environment in which methods can be improved and tested in preparation for planned astronomical surveys. GREAT10 extends upon previous work by introducing variable fields into the challenge. The “Galaxy Challenge” involves the precise measurement of galaxy shape distortions, quantified locally by two parameters called shear, in the presence of a known convolution kernel. Crucially, the convolution kernel and the simulated gravitational lensing shape distortion both now vary as a function of position within the images, as is the case for real data. In addition, we introduce the “Star Challenge” that concerns the reconstruction of a variable convolution kernel, similar to that in a typical astronomical observation. This document details the GREAT10 Challenge for potential participants. Continually updated information is also available from www.greatchallenges.info.

PDF Web DOI [BibTex]

2010

Results of the GREAT08 Challenge: An image analysis competition for cosmological lensing

Bridle, S., Balan, S., Bethge, M., Gentile, M., Harmeling, S., Heymans, C., Hirsch, M., Hosseini, R., Jarvis, M., Kirk, D., Kitching, T., Kuijken, K., Lewis, A., Paulin-Henriksson, S., Schölkopf, B., Velander, M., Voigt, L., Witherick, D., Amara, A., Bernstein, G., Courbin, F., Gill, M., Heavens, A., Mandelbaum, R., Massey, R., Moghaddam, B., Rassat, A., Refregier, A., Rhodes, J., Schrabback, T., Shawe-Taylor, J., Shmakova, M., van Waerbeke, L., Wittman, D.

Monthly Notices of the Royal Astronomical Society, 405(3):2044-2061, July 2010 (article)

Abstract

We present the results of the GREAT08 Challenge, a blind analysis challenge to infer weak gravitational lensing shear distortions from images. The primary goal was to stimulate new ideas by presenting the problem to researchers outside the shear measurement community. Six GREAT08 Team methods were presented at the launch of the Challenge and five additional groups submitted results during the 6 month competition. Participants analyzed 30 million simulated galaxies with a range in signal to noise ratio, point-spread function ellipticity, galaxy size, and galaxy type. The large quantity of simulations allowed shear measurement methods to be assessed at a level of accuracy suitable for currently planned future cosmic shear observations for the first time. Different methods perform well in different parts of simulation parameter space and come close to the target level of accuracy in several of these. A number of fresh ideas have emerged as a result of the Challenge including a re-examination of the process of combining information from different galaxies, which reduces the dependence on realistic galaxy modelling. The image simulations will become increasingly sophis- ticated in future GREAT challenges, meanwhile the GREAT08 simulations remain as a benchmark for additional developments in shear measurement algorithms.

Web DOI [BibTex]

2010

Web DOI [BibTex]

2009

Generating Spike Trains with Specified Correlation Coefficients

Macke, J., Berens, P., Ecker, A., Tolias, A., Bethge, M.

Neural Computation, 21(2):397-423, February 2009 (article)

Abstract

Spike trains recorded from populations of neurons can exhibit substantial pairwise correlations between neurons and rich temporal structure. Thus, for the realistic simulation and analysis of neural systems, it is essential to have efficient methods for generating artificial spike trains with specified correlation structure. Here we show how correlated binary spike trains can be simulated by means of a latent multivariate gaussian model. Sampling from the model is computationally very efficient and, in particular, feasible even for large populations of neurons. The entropy of the model is close to the theoretical maximum for a wide range of parameters. In addition, this framework naturally extends to correlations over time and offers an elegant way to model correlated neural spike counts with arbitrary marginal distributions.

PDF Web DOI [BibTex]

2009

Macke, J., Berens, P., Ecker, A., Tolias, A., Bethge, M. Generating Spike Trains with Specified Correlation Coefficients Neural Computation, 21(2):397-423, February 2009 (article)

PDF Web DOI [BibTex]

2008

Near-Maximum Entropy Models for Binary Neural Representations of Natural Images

Bethge, M., Berens, P.

In Advances in neural information processing systems 20, pages: 97-104, (Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis), Curran, Red Hook, NY, USA, Twenty-First Annual Conference on Neural Information Processing Systems (NIPS), September 2008 (inproceedings)

Abstract

Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data - the model parameters can be derived in closed form and sampling is easy. We demonstrate its usefulness by studying a simple neural representation model of natural images. For the first time, we are able to directly compare predictions from a pairwise maximum entropy model not only in small groups of neurons, but also in larger populations of more than thousand units. Our results indicate that in such larger networks interactions exist that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics extrem ely well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

PDF Web [BibTex]

2008

Bethge, M., Berens, P. Near-Maximum Entropy Models for Binary Neural Representations of Natural Images In Advances in neural information processing systems 20, pages: 97-104, (Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis), Curran, Red Hook, NY, USA, Twenty-First Annual Conference on Neural Information Processing Systems (NIPS), September 2008 (inproceedings)

PDF Web [BibTex]

Receptive Fields without Spike-Triggering

Macke, J., Zeck, G., Bethge, M.

In Advances in neural information processing systems 20, pages: 969-976, (Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis), Curran, Red Hook, NY, USA, Twenty-First Annual Conference on Neural Information Processing Systems (NIPS), September 2008 (inproceedings)

Abstract

Stimulus selectivity of sensory neurons is often characterized by estimating their receptive field properties such as orientation selectivity. Receptive fields are usually derived from the mean (or covariance) of the spike-triggered stimulus ensemble. This approach treats each spike as an independent message but does not take into account that information might be conveyed through patterns of neural activity that are distributed across space or time. Can we find a concise description for the processing of a whole population of neurons analogous to the receptive field for single neurons? Here, we present a generalization of the linear receptive field which is not bound to be triggered on individual spikes but can be meaningfully linked to distributed response patterns. More precisely, we seek to identify those stimulus features and the corresponding patterns of neural activity that are most reliably coupled. We use an extension of reverse-correlation methods based on canonical correlation analysis. The resulting population receptive fields span the subspace of stimuli that is most informative about the population response. We evaluate our approach using both neuronal models and multi-electrode recordings from rabbit retinal ganglion cells. We show how the model can be extended to capture nonlinear stimulus-response relationships using kernel canonical correlation analysis, which makes it possible to test different coding mechanisms. Our technique can also be used to calculate receptive fields from multi-dimensional neural measurements such as those obtained from dynamic imaging methods.

PDF Web [BibTex]

Macke, J., Zeck, G., Bethge, M. Receptive Fields without Spike-Triggering In Advances in neural information processing systems 20, pages: 969-976, (Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis), Curran, Red Hook, NY, USA, Twenty-First Annual Conference on Neural Information Processing Systems (NIPS), September 2008 (inproceedings)

PDF Web [BibTex]

Towards the neural basis of the flash-lag effect

Ecker, A., Berens, P., Hoenselaar, A., Subramaniyan, M., Tolias, A., Bethge, M.

International Workshop on Aspects of Adaptive Cortex Dynamics, 2008, pages: 1, September 2008 (poster)

PDF [BibTex]

Ecker, A., Berens, P., Hoenselaar, A., Subramaniyan, M., Tolias, A., Bethge, M. Towards the neural basis of the flash-lag effect International Workshop on Aspects of Adaptive Cortex Dynamics, 2008, pages: 1, September 2008 (poster)

PDF [BibTex]

Bayesian Inference for Spiking Neuron Models with a Sparsity Prior

Gerwinn, S., Macke, J., Seeger, M., Bethge, M.

In Advances in neural information processing systems 20, pages: 529-536, (Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis), Curran, Red Hook, NY, USA, Twenty-First Annual Conference on Neural Information Processing Systems (NIPS), September 2008 (inproceedings)

Abstract

Generalized linear models are the most commonly used tools to describe the stimulus selectivity of sensory neurons. Here we present a Bayesian treatment of such models. Using the expectation propagation algorithm, we are able to approximate the full posterior distribution over all weights. In addition, we use a Laplacian prior to favor sparse solutions. Therefore, stimulus features that do not critically influence neural activity will be assigned zero weights and thus be effectively excluded by the model. This feature selection mechanism facilitates both the interpretation of the neuron model as well as its predictive abilities. The posterior distribution can be used to obtain confidence intervals which makes it possible to assess the statistical significance of the solution. In neural data analysis, the available amount of experimental measurements is often limited whereas the parameter space is large. In such a situation, both regularization by a sparsity prior and uncertainty estimates for the model parameters are essential. We apply our method to multi-electrode recordings of retinal ganglion cells and use our uncertainty estimate to test the statistical significance of functional couplings between neurons. Furthermore we used the sparsity of the Laplace prior to select those filters from a spike-triggered covariance analysis that are most informative about the neural response.

PDF Web [BibTex]

Gerwinn, S., Macke, J., Seeger, M., Bethge, M. Bayesian Inference for Spiking Neuron Models with a Sparsity Prior In Advances in neural information processing systems 20, pages: 529-536, (Editors: Platt, J. C., D. Koller, Y. Singer, S. Roweis), Curran, Red Hook, NY, USA, Twenty-First Annual Conference on Neural Information Processing Systems (NIPS), September 2008 (inproceedings)

PDF Web [BibTex]

Flexible Models for Population Spike Trains

Bethge, M., Macke, J., Berens, P., Ecker, A., Tolias, A.

AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles, 2, pages: 52, June 2008 (poster)

PDF [BibTex]

Bethge, M., Macke, J., Berens, P., Ecker, A., Tolias, A. Flexible Models for Population Spike Trains AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles, 2, pages: 52, June 2008 (poster)

PDF [BibTex]

Pairwise Correlations and Multineuronal Firing Patterns in the Primary Visual Cortex of the Awake, Behaving Macaque

Berens, P., Ecker, A., Subramaniyan, M., Macke, J., Hauck, P., Bethge, M., Tolias, A.

AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles, 2, pages: 48, June 2008 (poster)

PDF [BibTex]

Berens, P., Ecker, A., Subramaniyan, M., Macke, J., Hauck, P., Bethge, M., Tolias, A. Pairwise Correlations and Multineuronal Firing Patterns in the Primary Visual Cortex of the Awake, Behaving Macaque AREADNE 2008: Research in Encoding and Decoding of Neural Ensembles, 2, pages: 48, June 2008 (poster)

PDF [BibTex]

2007

Estimating receptive fields without spike-triggering

Macke, J., Zeck, G., Bethge, M.

37th annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37(768.1):1, November 2007 (poster)

Web [BibTex]

2007

Macke, J., Zeck, G., Bethge, M. Estimating receptive fields without spike-triggering 37th annual Meeting of the Society for Neuroscience (Neuroscience 2007), 37(768.1):1, November 2007 (poster)

Web [BibTex]

Studying the effects of noise correlations on population coding using a sampling method

Ecker, A., Berens, P., Bethge, M., Logothetis, N., Tolias, A.

Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 21, September 2007 (poster)

PDF [BibTex]

Ecker, A., Berens, P., Bethge, M., Logothetis, N., Tolias, A. Studying the effects of noise correlations on population coding using a sampling method Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 21, September 2007 (poster)

PDF [BibTex]

Bayesian Inference for Sparse Generalized Linear Models

Seeger, M., Gerwinn, S., Bethge, M.

In ECML 2007, pages: 298-309, Lecture Notes in Computer Science ; 4701, (Editors: Kok, J. N., J. Koronacki, R. Lopez de Mantaras, S. Matwin, D. Mladenic, A. Skowron), Springer, Berlin, Germany, 18th European Conference on Machine Learning, September 2007 (inproceedings)

Abstract

We present a framework for efficient, accurate approximate Bayesian inference in generalized linear models (GLMs), based on the expectation propagation (EP) technique. The parameters can be endowed with a factorizing prior distribution, encoding properties such as sparsity or non-negativity. The central role of posterior log-concavity in Bayesian GLMs is emphasized and related to stability issues in EP. In particular, we use our technique to infer the parameters of a point process model for neuronal spiking data from multiple electrodes, demonstrating significantly superior predictive performance when a sparsity assumption is enforced via a Laplace prior distribution.

PDF DOI [BibTex]

Seeger, M., Gerwinn, S., Bethge, M. Bayesian Inference for Sparse Generalized Linear Models In ECML 2007, pages: 298-309, Lecture Notes in Computer Science ; 4701, (Editors: Kok, J. N., J. Koronacki, R. Lopez de Mantaras, S. Matwin, D. Mladenic, A. Skowron), Springer, Berlin, Germany, 18th European Conference on Machine Learning, September 2007 (inproceedings)

PDF DOI [BibTex]

Near-Maximum Entropy Models for Binary Neural Representations of Natural Images

Berens, P., Bethge, M.

Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 19, September 2007 (poster)

Abstract

Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data---the model parameters can be derived in closed form and sampling is easy. We demonstrate its usefulness by studying a simple neural representation model of natural images. For the first time, we are able to directly compare predictions from a pairwise maximum entropy model not only in small groups of neurons, but also in larger populations of more than thousand units. Our results indicate that in such larger networks interactions exist that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics extrem ely well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

PDF [BibTex]

Berens, P., Bethge, M. Near-Maximum Entropy Models for Binary Neural Representations of Natural Images Neural Coding, Computation and Dynamics (NCCD 07), 1, pages: 19, September 2007 (poster)

PDF [BibTex]

Do We Know What the Early Visual System Computes?

Bethge, M., Kayser, C.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 352, March 2007 (poster)

Abstract

Decades of research provided much data and insights into the mechanisms of the early visual system. Currently, however, there is great controversy on whether these findings can provide us with a thorough functional understanding of what the early visual system does, or formulated differently, of what it computes. At the Society for Neuroscience meeting 2005 in Washington, a symposium was held on the question "Do we know that the early visual system does", which was accompanied by a widely regarded publication in the Journal of Neuroscience. Yet, that discussion was rather specialized as it predominantly addressed the question of how well neural responses in retina, LGN, and cortex can be predicted from noise stimuli, but did not emphasize the question of whether we understand what the function of these early visual areas is. Here we will concentrate on this neuro-computational aspect of vision. Experts from neurobiology, psychophysics and computational neuroscience will present studies which approach this question from different viewpoints and promote a critical discussion of whether we actually understand what early areas contribute to the processing and perception of visual information.

PDF [BibTex]

Bethge, M., Kayser, C. Do We Know What the Early Visual System Computes? 31st G{\"o}ttingen Neurobiology Conference, 31, pages: 352, March 2007 (poster)

PDF [BibTex]

Identifying temporal population codes in the retina using canonical correlation analysis

Bethge, M., Macke, J., Gerwinn, S., Zeck, G.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 359, March 2007 (poster)

PDF PDF [BibTex]

Bethge, M., Macke, J., Gerwinn, S., Zeck, G. Identifying temporal population codes in the retina using canonical correlation analysis 31st G{\"o}ttingen Neurobiology Conference, 31, pages: 359, March 2007 (poster)

PDF PDF [BibTex]

Bayesian Neural System identification: error bars, receptive fields and neural couplings

Gerwinn, S., Seeger, M., Zeck, G., Bethge, M.

31st G{\"o}ttingen Neurobiology Conference, 31, pages: 360, March 2007 (poster)

PDF PDF [BibTex]

Gerwinn, S., Seeger, M., Zeck, G., Bethge, M. Bayesian Neural System identification: error bars, receptive fields and neural couplings 31st G{\"o}ttingen Neurobiology Conference, 31, pages: 360, March 2007 (poster)

PDF PDF [BibTex]

The Independent Components of Natural Images are Perceptually Dependent

Bethge, M., Wiecki, T., Wichmann, F.

In Human Vision and Electronic Imaging XII, pages: 1-12, (Editors: Rogowitz, B. E.), SPIE, Bellingham, WA, USA, SPIE Human Vision and Electronic Imaging Conference, February 2007 (inproceedings)

Abstract

The independent components of natural images are a set of linear filters which are optimized for statistical independence. With such a set of filters images can be represented without loss of information. Intriguingly, the filter shapes are localized, oriented, and bandpass, resembling important properties of V1 simple cell receptive fields. Here we address the question of whether the independent components of natural images are also perceptually less dependent than other image components. We compared the pixel basis, the ICA basis and the discrete cosine basis by asking subjects to interactively predict missing pixels (for the pixel basis) or to predict the coefficients of ICA and DCT basis functions in patches of natural images. Like Kersten (1987) we find the pixel basis to be perceptually highly redundant but perhaps surprisingly, the ICA basis showed significantly higher perceptual dependencies than the DCT basis. This shows a dissociation between statistical and perceptual dependence measures.

PDF Web DOI [BibTex]

Bethge, M., Wiecki, T., Wichmann, F. The Independent Components of Natural Images are Perceptually Dependent In Human Vision and Electronic Imaging XII, pages: 1-12, (Editors: Rogowitz, B. E.), SPIE, Bellingham, WA, USA, SPIE Human Vision and Electronic Imaging Conference, February 2007 (inproceedings)

PDF Web DOI [BibTex]

Unsupervised learning of a steerable basis for invariant image representations

Bethge, M., Gerwinn, S., Macke, J.

In Human Vision and Electronic Imaging XII, pages: 1-12, (Editors: Rogowitz, B. E.), SPIE, Bellingham, WA, USA, SPIE Human Vision and Electronic Imaging Conference, February 2007 (inproceedings)

Abstract

There are two aspects to unsupervised learning of invariant representations of images: First, we can reduce the dimensionality of the representation by finding an optimal trade-off between temporal stability and informativeness. We show that the answer to this optimization problem is generally not unique so that there is still considerable freedom in choosing a suitable basis. Which of the many optimal representations should be selected? Here, we focus on this second aspect, and seek to find representations that are invariant under geometrical transformations occuring in sequences of natural images. We utilize ideas of steerability and Lie groups, which have been developed in the context of filter design. In particular, we show how an anti-symmetric version of canonical correlation analysis can be used to learn a full-rank image basis which is steerable with respect to rotations. We provide a geometric interpretation of this algorithm by showing that it finds the two-dimensional eigensubspaces of the avera ge bivector. For data which exhibits a variety of transformations, we develop a bivector clustering algorithm, which we use to learn a basis of generalized quadrature pairs (i.e. complex cells) from sequences of natural images.

PDF Web DOI [BibTex]

Bethge, M., Gerwinn, S., Macke, J. Unsupervised learning of a steerable basis for invariant image representations In Human Vision and Electronic Imaging XII, pages: 1-12, (Editors: Rogowitz, B. E.), SPIE, Bellingham, WA, USA, SPIE Human Vision and Electronic Imaging Conference, February 2007 (inproceedings)

PDF Web DOI [BibTex]

Estimating Population Receptive Fields in Space and Time

Macke, J., Zeck, G., Bethge, M.

Computational and Systems Neuroscience Meeting 2007 (COSYNE 2007), 4, pages: 44, February 2007 (poster)

PDF Web [BibTex]

Macke, J., Zeck, G., Bethge, M. Estimating Population Receptive Fields in Space and Time Computational and Systems Neuroscience Meeting 2007 (COSYNE 2007), 4, pages: 44, February 2007 (poster)

PDF Web [BibTex]

2006

Factorial coding of natural images: how effective are linear models in removing higher-order dependencies?

Bethge, M.

Journal of the Optical Society of America A, 23(6):1253-1268, June 2006 (article)

Abstract

The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multi-information reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), zero-phase whitening, and predictive coding. Predictive coding is translated into the transform coding framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the Haar wavelet are included into the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multi-information between all decorrelation transforms (5% or less) for all patch sizes. Among the second-order methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the `edge filters&amp;amp;amp;lsquo; found with ICA lead only to a surprisingly small improvement in terms of its actual objective.

PDF Web [BibTex]

2006

Bethge, M. Factorial coding of natural images: how effective are linear models in removing higher-order dependencies? Journal of the Optical Society of America A, 23(6):1253-1268, June 2006 (article)

PDF Web [BibTex]

Factorial Coding of Natural Images: How Effective are Linear Models in Removing Higher-Order Dependencies?

Bethge, M.

9, pages: 90, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Abstract

The performance of unsupervised learning models for natural images is evaluated quantitatively by means of information theory. We estimate the gain in statistical independence (the multi-information reduction) achieved with independent component analysis (ICA), principal component analysis (PCA), zero-phase whitening, and predictive coding. Predictive coding is translated into the transform coding framework, where it can be characterized by the constraint of a triangular filter matrix. A randomly sampled whitening basis and the Haar wavelet are included into the comparison as well. The comparison of all these methods is carried out for different patch sizes, ranging from 2x2 to 16x16 pixels. In spite of large differences in the shape of the basis functions, we find only small differences in the multi-information between all decorrelation transforms (5% or less) for all patch sizes. Among the second-order methods, PCA is optimal for small patch sizes and predictive coding performs best for large patch sizes. The extra gain achieved with ICA is always less than 2%. In conclusion, the `edge filters‘ found with ICA lead only to a surprisingly small improvement in terms of its actual objective.

Web [BibTex]

Bethge, M. Factorial Coding of Natural Images: How Effective are Linear Models in Removing Higher-Order Dependencies? 9, pages: 90, 9th T{\"u}bingen Perception Conference (TWK), March 2006 (poster)

Web [BibTex]

Matthias Bethge

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