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Probability Tables

Overview

Probability Tables (PTables) provide a compact way to specify probabilistic relationships between entities in a Knowledge Base (KB). They are particularly useful for working with ontology alignment problems where multiple sources need to be integrated.

File Format

A Probability Table is a Tab-Separated Values (TSV) file with 6 columns:

  1. Subject ID: The identifier for the subject entity
  2. Object ID: The identifier for the object entity
  3. P(SubClassOf): Probability that Subject is a subclass of Object (range: 0.0-1.0)
  4. P(SuperClassOf): Probability that Object is a subclass of Subject (range: 0.0-1.0)
  5. P(EquivalentTo): Probability that Subject and Object are equivalent (range: 0.0-1.0)
  6. P(DisjointWith): Probability that Subject and Object are not in a subsumption relationship (range: 0.0-1.0)

Example row: 

ORDO:464724 MONDO:0000023   0.033333333333333326    0.033333333333333326    0.9 0.033333333333333326

This specifies: - Subject: ORDO:464724 - Object: MONDO:0000023 - P(ORDO:464724 SubClassOf MONDO:0000023) = 0.033... - P(MONDO:0000023 SubClassOf ORDO:464724) = 0.033... - P(ORDO:464724 EquivalentTo MONDO:0000023) = 0.9 - P(ORDO:464724 DisjointWith MONDO:0000023) = 0.033...

Interpretation

Each row in a PTable generates four probabilistic facts, one for each possible relationship between the subject and object:

  1. ProperSubClassOf(Subject, Object)
  2. ProperSubClassOf(Object, Subject)
  3. EquivalentTo(Subject, Object)
  4. NotInSubsumptionWith(Subject, Object)

Additionally, each unique entity ID is assigned to a disjoint group based on its prefix (e.g., "MONDO", "ORDO", "ICD10CM"). This helps model the constraint that terms from different ontologies should not be confused.

Usage in BOOMER

To use a Probability Table with BOOMER:

from boomer.io import ptable_to_kb
from boomer.search import solve

# Create a KB directly from a PTable file
kb = ptable_to_kb(
    "path/to/file.ptable.tsv",
    name="My KB",  # Optional, defaults to filename
    description="Description of the KB"
)

# Solve the KB
solution = solve(kb)

# Analyze the results
for spf in solution.solved_pfacts:
    if spf.truth_value and spf.posterior_prob > 0.8:
        print(f"High confidence: {spf.pfact.fact} (posterior: {spf.posterior_prob})")

Common Use Cases

PTables are particularly useful for:

  1. Ontology Alignment: Mapping terms between different ontologies (e.g., MONDO to ICD10)
  2. Disease Classification: Relating disease terms across different medical coding systems
  3. Entity Resolution: Determining when entities from different sources refer to the same concept

Generating PTables

PTables can be created:

  1. Manually, for small test cases
  2. Using machine learning to generate relationship probabilities
  3. From existing ontology mappings with confidence values
  4. By converting other probabilistic relationship formats

Limitations

  • Each row only models the direct relationship between two entities
  • More complex relationships involving more than two entities require multiple rows
  • The sum of probabilities in a row does not need to equal 1.0, as the relationships are not mutually exclusive