probnode 0.1.2

Probability expression library

Probnode

Description

Probability expression library

Features

• Basic events and probability expressions modeling, similar to SymPy
• Calculation on a chain of probability expressions
• Contract and/or expand probability expressions chain, using probability mathematical characteristics

Installation

pip install probnode

Quick Usage

• Events and probability modeling:

  from probnode import Event, P

  e1 = Event("Sample event 1")
  p1 = P(e1)
  e2 = Event("Sample event 2")
  p2 = P(e2)

  p3 = P(p1 | p2) # Or Probability expression
  p4 = P(p1 & p2) # And Probability expression
  p5 = P(p1 // p2) # Conditional Probability expression

  # Display mathematical representation of the object(s)
  print(repr(p1))

• Mathematical treatment on probability expressions:

  # First convert probability expression to math node
  from probnode import N
  n1 = N(p1) # Each below is a (math) node
  n2 = N(p2)
  n3 = N(p3)
  n4 = N(p4)
  n5 = N(p5)

  # A sum of nodes
  snode = n1 + n2 - n4
  # A product of nodes
  pnode = n5 * n2

• Contract/ expand mathematical chain of probability nodes

  • Contract

    from probnode.computation import contract
  
    c1 = contract(snode) # P(A) + P(B) - P(A and B) -> P(A or B)
    print(repr(c1))
    c2 = contract(pnode)
    print(repr(c2)) # P(A when B) * P(B) -> P(A and B)
  

  • Expand

    from probnode.computation import expand
  
    x = expand(n3)
    print(repr(x[0])) # P(A or B) -> P(A) + P(B) - P(A and B)
  

• Value calculations

  node.value will return the value of node

  If node is a chain node (comprising multiple nodes in sum / product mathematic operation), and either children node.value is not defined, the result parent node.value will be None

  n1.value # None

  Node value can be calculated from probability expression value

  p1.value = 0.7
  n1.value # equals 0.7
  

  Or by assigning value to itself

  n1.value = 0.6
  n1.value # equals 0.6
  

  The value assigned to itself takes precedence over the calculated value from its probability expression, or calculated from children nodes (if it is a chain node)

Notes

• Event does not have value. Only probability of event P(Event("Raining")).value = 0.3 can be assigned value

• There are normal events, and SureEvent. Probability ofSureEvent is always 1, and assigning value to probability of SureEvent will raise error

• Nodes, probabilities, events comparisons:

  • Events will be compared based on its name only

  • Probability compared based on its representation (type, value)

  • Nodes compared based on its underlying structure (its probability expressions, children nodes (respecting order))

  • node.is_permutation_of(other) will check if 2 nodes are permutations. For example: N(P(event1)) + N(P(event2)) - N(P(event3)) is permutation of N(P(event2)) - N(P(event3)) + N(P(event1))

• Expansion returns a list of expanded nodes

• Contraction return a single contracted node

• Expansion and contraction will be done 1 time, not exhaustively until unexpandable / uncontractable

Details

Events

• Normal events

  from probnode import Event

• Sure events from probnode import SureEvent

Probability

• Simple probability expression: Probability of a single event P(Event("e1")

• And probability expression, Or probability expression: Probability expression of 2 probability expressions (Thus, there is only a And probability of 2 probability of events, not And probability of 2 events.

  ❌ P(Event("e1") & Event("e2")),

  ✅ use P(P(Event("e1")) & P(Event("e2"))) instead )

• Conditional probability expression: Probability of X when Y P(p1 // p2) (p1 and p2 are probability expressions)

  from probnode.probability import SimpleProbabilityExpression, AndProbabilityExpression, OrProbabilityExpression, ConditionalProbabilityExpression
  

Node

• Normal node (Pure node): Node of a single probability expression

  from probnode.core import Node
  

• Chain node: a sum or product of nodes

  ✅ use n1 + n2 - n3 to create SumNode instead of invoke directly SumNode() (n1, n2, n3 can be either normal nodes or chain nodes)

  ✅ use n1 * n2 / n3 to create ProductNode instead of invoke directly ProductNode() (n1, n2, n3 can be either normal nodes or chain nodes)