Probabilistic models for neural populations that naturally capture global coupling and criticality

Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality

Estimating mutual information and multi--information in large networks

We address the practical problems of estimating the information relations that characterize large networks. Building on methods developed for analysis of the neural code, we show that reliable estimates of mutual information can be obtained with manageable computational effort. The same methods allow estimation of higher order, multi--information terms. These ideas are illustrated by analyses of gene expression, financial markets, and consumer preferences. In each case, information theoretic measures correlate with independent, intuitive measures of the underlying structures in the system

The statistics of contour fragments in natural scenes

Summary: Recent electrophysiology recordings in macaque V4/IT suggest that single neuron response to synthetic closed contours can be largely captured by models which only consider a small number of contour fragments (Brincat and Connor 2004). Motivated by this experimental work, we sought firstly to characterize the statistics of contour fragments in natural scenes, and secondly to generate synthetic images which reflect the measured contour-fragment statistics.

To detect contour fragments, we defined a set of feature detectors which respond only in the presence of two edges co-occurring at a fixed relative angle – implemented as a logical ‘AND’ of two Gabor-like, laplacian-of-gaussian linear filters. We then determined the pairwise correlations of these contour fragments in a natural image ensemble. If efficient coding extends to higher cortical centers and processing in the ventral visual stream can be modeled as a sequence of logical operations on linear shape features, then the pairwise statistics we measure should be informative about neural shape coding. 

Using these statistics directly, it is possible to produce a generative model of simple images which contain the measured statistics. We implemented a modified Ising model and solved the inverse problem of determining the optimal model parameters which satisfy the measured correlations. The resulting Ising-like model of the pairwise statistics can generate the probability of any arrangement of contour fragments as measured in the natural image ensemble. 

As a complementary approach to producing images with naturalistic contour fragment statistics, it is possible to start with a natural scene and isolate the target features. This is achieved by applying our contour fragment detection processing to the single scene and then separately visualizing the fragments detected. This second procedure lends itself to parametric randomization of the generated image.

Narrative Elaboration: The central question guiding our study is how shapes are represented in inferotemporal cortex. To that end, we have investigated natural images in order to motivate experiments capable of targeting the extent to which neural processing of shapes involves representing shapes as combinations of key contour features. To simplify, we are focusing on black-and-white images and prioritizing contour features. This project suggests it is possible to generate synthetic images containing only a select set of contour statistics. Our subsequent goals include conducting collaborative macaque electrophysiology experiments with our generated images as visual stimuli

Probabilistic models of individual and collective animal behavior

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie's Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.Comment: 26 pages, 11 figure