A firing rate map, also known as a tuning curve, describes the nonlinear relationship between a neuron's spike rate and a low-dimensional stimulus (e.g., orientation, head direction, contrast, color). Here we investigate Bayesian active learning methods for estimating firing rate maps in closed-loop neurophysiology experiments. These methods can accelerate the characterization of such maps through the intelligent, adaptive selection of stimuli. Specifically, we explore the manner in which the prior and utility function used in Bayesian active learning affect stimulus selection and performance. Our approach relies on a flexible model that involves a nonlinearly transformed gaussian process (GP) prior over maps and conditionally Poisson spiking. We show that infomax learning, which selects stimuli to maximize the information gain about the firing rate map, exhibits strong dependence on the seemingly innocuous choice of nonlinear transformation function. We derive an alternate utility function that selects stimuli to minimize the average posterior variance of the firing rate map and analyze the surprising relationship between prior parameterization, stimulus selection, and active learning performance in GP-Poisson models. We apply these methods to color tuning measurements of neurons in macaque primary visual cortex.

Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are overdispersed relative to a Poisson distribution. Recent work (Goris, Movshon, & Simoncelli, 2014 ) has proposed to explain this variability in terms of a multiplicative interaction between a stochastic gain variable and a stimulus-dependent Poisson firing rate, which produces quadratic relationships between spike count mean and variance. Here we examine this quadratic assumption and propose a more flexible family of models that can account for a more diverse set of mean-variance relationships. Our model contains additive gaussian noise that is transformed nonlinearly to produce a Poisson spike rate. Different choices of the nonlinear function can give rise to qualitatively different mean-variance relationships, ranging from sublinear to linear to quadratic. Intriguingly, a rectified squaring nonlinearity produces a linear mean-variance function, corresponding to responses with a constant Fano factor. We describe a computationally efficient method for fitting this model to data and demonstrate that a majority of neurons in a V1 population are better described by a model with a nonquadratic relationship between mean and variance. Finally, we demonstrate a practical use of our model via an application to Bayesian adaptive stimulus selection in closed-loop neurophysiology experiments, which shows that accounting for overdispersion can lead to dramatic improvements in adaptive tuning curve estimation.

Neurons in many brain areas exhibit high trial-to-trial variability, with spike counts that are over-dispersed relative to a Poisson distribution. Recent work (Goris et al., 2014) has proposed to explain this variability in terms of a multiplicative interaction between a stochastic gain variable and a stimulus-dependent Poisson firing rate, which produces quadratic relationships between spike count mean and variance. Here we examine this quadratic assumption and propose a more flexible family of models that can account for a more diverse set of mean-variance relationships. Our model contains additive Gaussian noise that is transformed nonlinearly to produce a Poisson spike rate. Different choices of the nonlinear function can give rise to qualitatively different mean-variance relationships, ranging from sub-linear to linear to multiplicative. Intriguingly, a rectified squaring nonlinearity produces a linear mean-variance function, corresponding to responses with constant Fano factor. We describe a computationally efficient method for fitting this model to data, and demonstrate that a majority of neurons in a V1 population are better described by a model with non-quadratic relationship between mean and variance. Lastly, we develop an application to Bayesian adaptive stimulus selection in closed-loop neurophysiology experiments, which shows that accounting for overdispersion can lead to dramatic improvements in adaptive tuning curve estimation.

Measuring the color tuning of visual neurons is important for understanding the neural basis of vision, but it is challenging because of the inherently three-dimensional nature of color. Color tuning cannot be represented by a one-dimensional curve, and measuring three-dimensional tuning curves is difficult. One approach to addressing this challenge is to analyze neuronal color tuning data through the lens of mathematical models that make assumptions about the shapes of tuning curves. In this paper, we discuss the linear-nonlinear cascade model as a platform for measuring neuronal color tuning. We compare fitting this model by three techniques: two using response-weighted averaging and one using numerical optimization of likelihood. We highlight the advantages and disadvantages of each technique and emphasize the effects of the stimulus distribution on color tuning measurements.

Spatial selectivity, as measured by functional magnetic resonance imaging (fMRI) activity patterns that vary consistently with the location of visual stimuli, has been documented in many human brain regions, notably the occipital visual cortex and the frontal and parietal regions that are active during endogenous, goal-directed attention. We hypothesized that spatial selectivity also exists in regions that are active during exogenous, stimulus-driven attention. To test this hypothesis, we acquired fMRI data while subjects maintained passive fixation. At jittered time intervals, a briefly presented wedge-shaped array of rapidly expanding circles appeared at one of three contralateral or one of three ipsilateral locations. Positive fMRI activations were identified in multiple brain regions commonly associated with exogenous attention, including the temporoparietal junction, the inferior parietal lobule, and the inferior frontal sulcus. These activations were not organized as a map across the cortical surface. However, multivoxel pattern analysis of the fMRI activity correctly classified every pair of stimulus locations, demonstrating that patterns of fMRI activity were correlated with spatial location. These observations held for both contralateral and ipsilateral stimulus pairs as well as for stimuli of different textures (radial checkerboard) and shapes (squares and rings). Permutation testing verified that the obtained accuracies were not due to systematic biases and demonstrated that the findings were statistically significant.