Assessment of categorical causal assertions.
From the perspective of logic a statement x => y is equivalent to its contrapositive ~y => ~x.
Acca assesses a simple assertion (a statement and its contrapositive) for identifying potentially causal relationships. A statement of the form x => y is scored as S(x => y) := prob(y | x) prob(~x | ~y) with the conditional probabilities estimated from a set of data. A value of S near unity is viewed as an indicator of a good candidate for a causally-related assertion.
Suppose we have four weeks of observations of the weather first thing in the morning as well as the condition of the front lawn:
| Observe | Lawn dry | Lawn wet |
|---|---|---|
| Cloudy | 6 | 5 |
| Raining | 0 | 9 |
| Sunny | 5 | 3 |
The file rainy.txt provides the data summarized in the table and demonstrates Acca input. Lines beginning with # are treated as comments.
The lawn will be wet if it's raining, but it could be wet for other reasons such as sprinklers, nighttime rain, dew. Acca will attempt to discover the relationship Raining => Lawn wet.
For this input data Acca will report
Tokenset x count 3, tokenset y count 2
1.000000 1.000000 [9.000000 17.000000] x:is_raining => y:lawn_is_wet
there were three categorical values of x (is_cloudy, is_raining, is_sunny) in the data set and two of y (lawn_is_dry, lawn_is_wet), and that it finds the plausible relationship is_raining => lawn_is_wet.