Neural responses vary from cell to cell and from stimulus to stimulus. Even if the same cell is presented with the same stimulus many times, the responses will vary from presentation to presentation. Is this variability meaningful, or is it merely noise? And if only some portion of this variability is meaningful, how do we distinguish this from noise?
When a population of cells is presented with repeated presentations of the same stimulus, the variability in responses is correlated across cells. In one branch of work (see the population coding page), we are developing computational tools for isolating this correlated variability in small populations of retinal ganglion cells. We have found that the distribution and degree of correlations vary across different stimuli, suggesting that these correlations adapt to changes in input. We are currently working to understand whether, and how, these correlations shape the functional properties of the population code.
Is response variability correlated not only across repeated presentations of the same stimulus, but also across different stimuli? How do we infer this variability from limited experimental measurements?
Neural recordings are often performed on small populations of cells responding to a panel of stimuli, with measured cells representing a small fraction of the entire population of neurons and stimuli representing a small fraction of all possible inputs. If we are interested in probing the space of possible inputs, and possible neural responses, it would be useful to be able to extrapolate from these measured responses to a much larger set of "synthetic" responses. In the simplest model, we might imagine that the response of each neuron has two additive or multiplicative components -- one from the neurons itself, and one from the specific stimulus component to which it is responding -- plus additive/multiplicative noise. Such a model could, in principle, give rise the observed correlations in neural responses elicited by a given stimulus, and similarly the observed correlations in the response of a given neuron to different stimuli.
In practice, however, measured responses are much more complex, and these simple additive/multiplicative models do not adequately capture the observed variability in response patterns across different stimuli. We are developing computational and statistical techniques for disentangling noise from meaningful correlation. These techniques enable us to extrapolate neural responses to a much larger population responding to a much larger set of stimuli, while still preserving statistical features of the observed responses. We can then use these extrapolations in combination with other studies (see, e.g., our work on unstructured architectures) to test ideas about optimal representation of high-dimensional stimulus spaces.