Modeling stereopsis via Markov random field

Probabilistic inference of binary Markov random fields in spiking neural networks through mean-field approximation

Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in the brain. Previous studies have tried to relate the inference equation of binary Markov random fields to the dynamic equation of spiking neural networks through belief propagation algorithm and reparameterization, but they are valid only for Markov random fields with limited network structure. In this paper, we propose a spiking neural network model that can implement inference of arbitrary binary Markov random fields. Specifically, we design a spiking recurrent neural network and prove that its neuronal dynamics are mathematically equivalent to the inference process of Markov random fields by adopting mean-field theory. Furthermore, our mean-field approach unifies previous works. Theoretical analysis and experimental results, together with the application to image denoising, demonstrate that our proposed spiking neural network can get comparable results to that of mean-field inference.

Unification of MAP Estimation and Marginal Inference in Recurrent Neural Networks

Numerous experimental data show that human brain can represent probability distributions and perform Bayesian inference. However, it remains unclear how the brain implements probabilistic inference in the form of neural circuits. Several models have been proposed that aim at explaining how the network of neurons carry out maximum a posterior inference (MAP) estimation and marginal inference, but they are all task specific in that they treat MAP estimation and marginal inference separately. In this brief, we propose that human brain could implement MAP estimation and marginal inference in the same network of neurons. We illustrate our result in hidden Markov models and prove that a recurrent neural network (RNN) implementation of belief propagation can be tuned to perform approximate Bayesian inference (to provide posterior or conditional distribution over the latent causes of observations) or identify the MAP or peak of the joint distribution. The key tuning parameter is a temperature parameter that controls the precision of probability distributions that are optimized. Theoretical analyses and experimental results demonstrate that RNNs can carry out near-optimal MAP estimation and marginal inference.