HyBit

HyBit is a bit blasting based probabilistic programming system for discrete-continuous probabilistic programs. It is built on top of another probabilistic programming language Dice See https://github.com/SHoltzen/dice.

Installation

Install Julia 1.8.5 or higher using these instructions.

Then, install SymPy and IRTools using the following command:

pip3 install sympy

Next, clone the repository and start julia in project mode for current folder:

cd Dice.jl
julia --project

In Julia REPL, then use the following command to install all the needed dependencies

using Pkg; Pkg.instantiate()

Once the Dice Julia package is instantiated, its inference algorithm and HyBit is ready to use.

Quick Start

Example: Discrete

Let's first start with a discrete probabilistic program. Imagine you have two coins a and b with probability of landing on heads as 0.4 and 0.6 respectively. You flip both the coins and see that one of them has landed heads. What is the probability that a lands heads?

using Dice
code = @dice begin
    a = flip(0.4)
    b = flip(0.6)
    observe(a | b)
    return a
end
@show pr(code)

We have this example written up in the file examples/example1.jl. It can be run as follows:

julia --project examples/example1.jl

And it should print the result as following showing that a is true with probability 0.526316:

DataStructures.DefaultOrderedDict{Any, Any, Float64} with 2 entries:
  true  => 0.526316
  false => 0.473684

Example: Discrete-Continuous

To see the use of HyBit to write discrete-continuous probabilistic programs, consider the following example. Here, we compute the probability of a random variable a being less than 0.

using Dice, Distributions
DFiP = DistFix{6, 2}
code = @dice begin
            a = bitblast(DFiP, Normal(0, 1), 4, -8.0, 8.0)
            b = a < DFiP(0.0)
            b
end
pr(code)

We have this example written up in the file examples/example2.jl. It can be run as follows:

julia --project examples/example2.jl

And it should print the result as following:

DataStructures.DefaultOrderedDict{Any, Any, Float64} with 2 entries:
  true  => 0.5
  false => 0.5

The Julia package Dice makes available the following constructs

• @dice macro that encapsulates the probabilistic program
• observe() to condition on a Boolean random variable being true.
• DistFix{W, F} as types to represent fixed point numbers with W bits, F bits being after the binary point. If the floating point numbers passed as an argument to DistFix{W, F} are outside the range $[-2^{W-F-1},2^{W-F-1}-2^{-F}]$, one would encounter an error.
• bitblast to bitblast continuous density functions using linear pieces with the following signature.

function bitblast(::Type{DistFix{W,F}}, dist::ContinuousUnivariateDistribution, 
                  numpieces::Int, start::Float64, stop::Float64) where {W,F}

• 'general_gamma' to bitblast general gamma densities $x^{\alpha }{e}^{\beta x}$ soundly with the following signature

function general_gamma(::Type{DistFix{W, F}}, alpha::Int, beta::Float64, ll::Float64, ul::Float64) where {W, F}

It also offers different probabilistic inference queries such as the following:

• pr(code) that computes the probability distribution of the returned types of code.
• expectation(code) computes the mean of the value returned by code
• variance(code) computes the variance of the value returned by code.

More Examples

More examples can be found at the following directories:

• test/ directory contains unit test cases for all the functions and data types implemented.
• examples/ contains simple examples to get started with using Dice Julia package to write probabilistic programs.
• benchmarks/ contains discrete-continuous probabilistic programs to get started with using bit blasting.