text: divergence between the approximate posterior q(s) and the exact posterior, which is also 
  sometimes called the perceptual divergence: 
  
  q(s) 
  p(s|o) 
  DKL[q(s)∥p(s|o)] = ∑ 
  q(s) ln  (2) 
  s 
  
  It is a property of the KL divergence that the two distributions are identical when 
  DKL[q(s)∥p(s|o)] = 0. Minimising this divergence then corresponds to approximating 
  the exact posterior p(s|o) with q(s). We cannot evaluate this divergence directly since the 
  exact posterior is still unknown. We therefore replace the expression of the exact posterior 
  with the right-hand side of Equation (1). Note that here we use the joint likelihood p(o, s) 
  notation, fraction rule a  = a 
  b ∗ c and logarithmic rule ln(a ∗ b) = ln a + ln b: 
  b 
  c 
  
  q(s) 
  p(o,s) 
  p(o) 
  q(s) 
  p(o, s) 
  ∑ 
  s  = ∑ 
  s 
  q(s) ln  q(s) ln  + ln p(o)  (3) 