Probability Distribution Calculations with Stochastic Circuits

Stochastic circuits are an alternative computation model where real numbers are represented by probabilistic bit-streams. This paper takes tools and lessons from stochastic circuits and uses them to analyze more general inputs to any logic circuit, where the joint input distribution may be complex and unknown. Even if the inputs are not designed to be stochastic numbers, circuits from stochastic computing can be applied to them in order to perform various calculations regarding the input distribution. Methods for the calculation of joint probabilities, marginalizations, conditional probabilities, and other quantities are presented. These methods can be applied anywhere a circuit has logical inputs. The inputs could represent readings from a sensor, intermediate values during a computation, or any other set of bit-streams. In any of these cases, it may be useful to know certain properties of their distribution, and this paper discusses how these can be calculated with low cost. A number of ideas are also presented for future work that could further analyze and create complex distributions.