Probabilistic Population Markov Chain
I am performing my research under the supervision of Professor Aldo Faisal trying to develope a model of cortical computation and learning. The human brain is a noisy non-linear dynamical system which operates in a far-from-equilibrium low-entropy regime and exibits a large variety of complex global behaviours. We have known for several years that human brain is Bayes optimal, meaning that we are able to optimally learn and to get in correspondence with the statistical properties of the environment.
In our research, we are interested in understanding how the human brain can optimally encode, sample and infer about complex probability distributions starting from its neural constituents. We also try to explain these behaviours as the result of a highly generative process that exploits microscopic noise.
We developed a neural model of cortical computation which, by exploiting local plasticity rules such as Hebbian learning, provides three features: a) It supports the development of a population of neurons that optimally represents sensing information with regard of the input statistics. b) In absence of information inflow, the system autonomously samples from the learned prior distribution and can integrate it with the information received via a feedback system in order to implement a Metropolis-like Markov Chain Monte Carlo that samples from the inferred posterior distribution. c) The system’s behaviour can autonomously interpolate between high and low information inflow regimes, and it can optimally integrate cues coming from different information sources.
In order to test this model in silico, we simulated in Matlab the activity and the synaptic plasticity of a population of stochastic integrate-and-fire neurons encoding an external real variable according ly to a Probabilistic Population Code. The system prooved to be able to encode information, sample and infer over complex probability distributions optimally. The dynamics of the system revealed to be stable within a wide range of values for the parameters controlling neural activity and plasticity, meaning that no fine tuning of the system is required in order to achieve the desired behaviour.