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

Reducing statistical dependencies in natural signals using radial Gaussianization

We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.