Sampling-based causal inference in cue combination and its neural implementation

Abstract

Causal inference in cue combination is to decide whether the cues have a single cause or multiple causes. Although the Bayesian causal inference model explains the problem of causal inference in cue combination successfully, how causal inference in cue combination could be implemented by neural circuits, is unclear. The existing method based on calculating log posterior ratio with variable elimination has the problem of being unrealistic and task-specific. In this paper, we take advantages of the special structure of the Bayesian causal inference model and propose a hierarchical inference algorithm based on importance sampling. A simple neural circuit is designed to implement the proposed inference algorithm. Theoretical analyses and experimental results demonstrate that our algorithm converges to the accurate value as the sample size goes to infinite. Moreover, the neural circuit we design can be easily generalized to implement inference for other problems, such as the multi-stimuli cause inference and the same-different judgment.

Bayesian Causal Inference: A Unifying Neuroscience Theory

“…In contrast, Cuppini, Ursino and collaborators created a neural network based on two parallel layers representing two unisensory modalities as well as a crossmodal layer receiving inputs from the uni-sensory layers 91,100,101 . Although not explicitly encoding probabilities, the connectivity within, and across layers, produced behavior very similar to the non-linear cue combination of causal inference, with cues being pulled together when close together, but unaffected when further apart.…”

Emergent Inference of Hidden Markov Models in Spiking Neural Networks Through Winner-Take-All

“…This means the values for the hidden variables will be the same no matter what time they are observed. This model is important to many inference and decision making problems [23], [24], [25] since in many cases we have the prior knowledge where the state of the environment doesn't change or changes very slowly with respect to time [15].…”

“…When the new observation y t of the HMM comes, an external current of I k = 1 ε0τ ln p(y t |x t = x k ) is added to the input current of neuron z k in WTA circuit at time T t . The membrane potential of each spiking neuron in WTA circuit encodes the logarithm of posterior probability of the hidden variable being in each state (see equation (22)), and the firing rate of each neuron is proportional to the posterior probability of hidden variable in each state (see equation (23)). Moreover, the time course of neural firing rate can implement posterior inference of HMMs.…”

“…It is worthwhile to note that for arbitrary t, equation 22and (23) hold only on the condition that T t+1 − T t is large enough, which has nothing to do with T 1 , T 2 , .., T t . Thus, if we want to conduct inference of HMM at time t, i.e.…”

“…This Bayesian network can also be seen as a HMM with time-invariant hidden variable S, to which the evidences S V and S H are given in sequence. Similar to [15], [23], the prior distribution p(S) is supposed to be a uniform distribution, p(S V |S) and p(S H |S) are Gaussian distributions with means being S and variances being σ 2 S V and σ 2 S H respectively. The network receives visual cue and haptic cue in sequence and the problem is to infer the posterior distribution p(S|S H , S V ).…”