TY - GEN
T1 - Active learning of neural response functions with Gaussian processes
AU - Park, Mijung
AU - Horwitz, Greg
AU - Pillow, Jonathan W.
PY - 2011
Y1 - 2011
N2 - A sizeable literature has focused on the problem of estimating a low-dimensional feature space for a neuron's stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to spike rate. Here, we use a Gaussian process (GP) prior over the infinitedimensional space of nonlinear functions to obtain Bayesian estimates of the "nonlinearity" in the linear-nonlinear- Poisson (LNP) encoding model. This approach offers increased flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). We then develop a framework for optimal experimental design under the GP-Poisson model using uncertainty sampling. This involves adaptively selecting stimuli according to an information-theoretic criterion, with the goal of characterizing the nonlinearity with as little experimental data as possible. Our framework relies on a method for rapidly updating hyperparameters under a Gaussian approximation to the posterior. We apply these methods to neural data from a color-tuned simple cell in macaque V1, characterizing its nonlinear response function in the 3D space of cone contrasts. We find that it combines cone inputs in a highly nonlinear manner. With simulated experiments, we show that optimal design substantially reduces the amount of data required to estimate these nonlinear combination rules.
AB - A sizeable literature has focused on the problem of estimating a low-dimensional feature space for a neuron's stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to spike rate. Here, we use a Gaussian process (GP) prior over the infinitedimensional space of nonlinear functions to obtain Bayesian estimates of the "nonlinearity" in the linear-nonlinear- Poisson (LNP) encoding model. This approach offers increased flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). We then develop a framework for optimal experimental design under the GP-Poisson model using uncertainty sampling. This involves adaptively selecting stimuli according to an information-theoretic criterion, with the goal of characterizing the nonlinearity with as little experimental data as possible. Our framework relies on a method for rapidly updating hyperparameters under a Gaussian approximation to the posterior. We apply these methods to neural data from a color-tuned simple cell in macaque V1, characterizing its nonlinear response function in the 3D space of cone contrasts. We find that it combines cone inputs in a highly nonlinear manner. With simulated experiments, we show that optimal design substantially reduces the amount of data required to estimate these nonlinear combination rules.
UR - http://www.scopus.com/inward/record.url?scp=85162477467&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85162477467&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85162477467
SN - 9781618395993
T3 - Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
BT - Advances in Neural Information Processing Systems 24
PB - Neural Information Processing Systems
T2 - 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
Y2 - 12 December 2011 through 14 December 2011
ER -