Gaussian-Bernoulli RBM

Quote from the Paper of *To be Bernoulli or to be Gaussian, for a Restricted
Boltzmann Machine* 1

The Guassian-Bernoulli RGM(GBRBM) has visible units with real value vm and binary hidden units hn. Based on the same idea as GBRGM, the energy function of GBRGM is defined as:

E(v,h)=−∑i=1m∑j=1nwijhjviσi−∑i=1m(vi−bi)22σ2i−∑j=1mcjhj

Where bi and ci are biases corresponding respectively to visible and hidden units, wij are the connecting weights between the visible and hidden units and σi is the standard deviation associated with Guassian visible units vi. Conditional probablities for visible and hidden units are:

p(vi=v|h)=N(v|bi+∑jhjwij,σ2)

p(hj=1|v)=sigmoid(cj+∑wijviσ2

Where N(μ,σ2) demotes the Gaussian probability destiny function with mean μ and standard deviation σ.

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1. To be Bernoulli or to be Gaussian, for a Restricted
   Boltzmann Machine ↩