nips nips2009 nips2009-43 nips2009-43-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Sebastian Gerwinn, Leonard White, Matthias Kaschube, Matthias Bethge, Jakob H. Macke
Abstract: Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial and temporal scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or pinwheel counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and quantitative model comparisons. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex. 1
[1] G G Blasdel and G Salama. Voltage-sensitive dyes reveal a modular organization in monkey striate cortex. Nature, 321(6070):579–85, Jan 1986.
[2] Kenichi Ohki, Sooyoung Chung, Yeang H Ch’ng, Prakash Kara, and R Clay Reid. Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature, 433(7026):597–603, 2005. 8
[3] F Wolf and T Geisel. Spontaneous pinwheel annihilation during visual development. Nature, 395(6697):73–8, 1998.
[4] M. Kaschube, M. Schnabel, and F. Wolf. Self-organization and the selection of pinwheel density in visual cortical development. New Journal of Physics, 10(1):015009, 2008.
[5] Naoum P Issa, Ari Rosenberg, and T Robert Husson. Models and measurements of functional maps in v1. J Neurophysiol, 99(6):2745–2754, 2008.
[6] Essa Yacoub, Noam Harel, and Kˆ mil Ugurbil. High-field fmri unveils orientation columns in humans. P a Natl Acad Sci Usa, 105(30):10607–12, Jul 2008.
[7] Ye Li, Stephen D Van Hooser, Mark Mazurek, Leonard E White, and David Fitzpatrick. Experience with moving visual stimuli drives the early development of cortical direction selectivity. Nature, 456(7224):952–6, Dec 2008.
[8] C.E. Rasmussen and C.K.I. Williams. Gaussian processes for machine learning. Springer, 2006.
[9] M Stetter, I Schiessl, T Otto, F Sengpiel, M H¨ bener, T Bonhoeffer, and K Obermayer. Principal compou nent analysis and blind separation of sources for optical imaging of intrinsic signals. Neuroimage, 11(5 Pt 1):482–90, May 2000.
[10] Jonathan R Polimeni, Domhnull Granquist-Fraser, Richard J Wood, and Eric L Schwartz. Physical limits to spatial resolution of optical recording: clarifying the spatial structure of cortical hypercolumns. Proc Natl Acad Sci U S A, 102(11):4158–4163, 2005 Mar 15.
[11] T. Yokoo, BW Knight, and L. Sirovich. An optimization approach to signal extraction from noisy multivariate data. Neuroimage, 14(6):1309–1326, 2001.
[12] R Everson, B W Knight, and L Sirovich. Separating spatially distributed response to stimulation from background. i. optical imaging. Biological cybernetics, 77(6):407–17, Dec 1997.
[13] Valery A Kalatsky and Michael P Stryker. New paradigm for optical imaging: temporally encoded maps of intrinsic signal. Neuron, 38(4):529–545, 2003 May 22.
[14] A Sornborger, C Sailstad, E Kaplan, and L Sirovich. Spatiotemporal analysis of optical imaging data. Neuroimage, 18(3):610–21, Mar 2003.
[15] D. Cornford, L. Csato, D.J. Evans, and M. Opper. Bayesian analysis of the scatterometer wind retrieval inverse problem: some new approaches. Journal of the Royal Statistical Society. Series B, Statistical Methodology, pages 609–652, 2004.
[16] N. Cressie. Statistics for spatial data. Terra Nova, 4(5):613–617, 1992.
[17] N. Cressie and G. Johannesson. Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(1):209–226, 2008.
[18] A S Rojer and E L Schwartz. Cat and monkey cortical columnar patterns modeled by bandpass-filtered 2d white noise. Biol Cybern, 62(5):381–391, 1990.
[19] D M Coppola, L E White, D Fitzpatrick, and D Purves. Unequal representation of cardinal and oblique contours in ferret visual cortex. P Natl Acad Sci Usa, 95(5):2621–3, Mar 1998.
[20] Francis R Bach and Michael I Jordan. Kernel independent component analysis. Journal of Machine Learning Research, 3:1:48, 2002.
[21] C. Williams and M. Seeger. Using the Nystrom method to speed up kernel machines. In International Conference on Machine Learning, volume 17, 2000.
[22] Donald Robertson and James Symons. Maximum likelihood factor analysis with rank-deficient sample covariance matrices. J. Multivar. Anal., 98(4):813–828, 2007.
[23] Byron M Yu, John P Cunningham, Gopal Santhanam, Stephen I Ryu, Krishna V Shenoy, and Maneesh Sahani. Gaussian-process factor analysis for low-dimensional single-trial analysis of neural population activity. J Neurophysiol, 102(1):614–635, 2009 Jul.
[24] K. Kersting, C. Plagemann, P. Pfaff, and W. Burgard. Most likely heteroscedastic Gaussian process regression. In Proceedings of the 24th international conference on Machine learning, pages 393–400. ACM New York, NY, USA, 2007.
[25] Ian Nauhaus, Andrea Benucci, Matteo Carandini, and Dario L Ringach. Neuronal selectivity and local map structure in visual cortex. Neuron, 57(5):673–679, 2008 Mar 13.
[26] H. Nickisch and M. Seeger. Convex variational bayesian inference for large scale generalized linear models. In International Conference on Machine Learning, 2009.
[27] F. Wolf, K. Pawelzik, T. Geisel, DS Kim, and T. Bonhoeffer. Optimal smoothness of orientation preference maps. Network: Computation in Neural SystemsComputation in neurons and neural systems, pages 97– 101, 1994.
[28] K. Rahnama Rad and L. Paninski. Efficient estimation of two-dimensional firing rate surfaces via gaussian process methods. Network: Computation in Neural Systems, under review, 2009. 9