In this example, the probability of hepatitis depends more on some symptoms than others; therefore, the Edges table includes edge weights (and the SQL call includes the EdgeWeight syntax element).
Input
- From LoopyBeliefPropagation Example: Equally Weighted Edges:
- Vertices: lbp_vertices
- ObservationTable: lbp_observation
- Edges: lbp_weighted_edges
| id | source | target | edgewt |
|---|---|---|---|
| 1 | Jaundice | Hepatitis | 0.2 |
| 2 | Internal bleeding | Hepatitis | 0.15 |
| 3 | Loss of appetite | Hepatitis | 0.05 |
| 4 | Fatigue | Hepatitis | 0.1 |
| 5 | Fever | Hepatitis | 0.1 |
| 6 | Dark urine | Hepatitis | 0.25 |
| 7 | Stupor | Hepatitis | 0.05 |
| 8 | Nausea/vomiting | Hepatitis | 0.1 |
SQL Call
SELECT * FROM LoopyBeliefPropagation (
ON lbp_weighted_edges AS Edges PARTITION BY source
ON lbp_vertices AS Vertices PARTITION BY vertex
ON lbp_observation AS ObservationTable PARTITION BY vertex
USING
TargetKey ('target')
ObservationColumn ('obs')
EdgeWeight ('edgewt')
Accumulate ('vertex')
MaxIterNum (20)
StopThreshold (1E-10)
) AS dt ORDER BY vertex;
Output
In the output table, 1 means that the symptom is present and 0 means that it is absent. The conditional probability of hepatitis is the sum of the weights of the symptoms that are present (0.25 + 0.1 + 0.05 + 0.15 + 0.2 = 0.75).
vertex prob_true ----------------- --------- dark urine 1.0 fatigue 1.0 fever 0.0 hepatitis 0.75 internal bleeding 1.0 jaundice 1.0 loss of appetite 1.0 nausea/vomiting 0.0 stupor 0.0
Download a zip file of all examples and a SQL script file that creates their input tables.