conexp-clj provides methods to discover causal rules within a context as described in “Mining Causal Association Rules” (https://www.researchgate.net/publication/262240022_Mining_Causal_Association_Rules).
We will consider the following data set:
(def smoking-ctx (make-context [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40]
["smoking" "male" "female" "education-level-high" "education-level-low" "cancer"]
#{[0 "smoking"] [0 "male"] [0 "education-level-high"] [0 "cancer"]
[1 "smoking"] [1 "male"] [1 "education-level-high"] [1 "cancer"]
[2 "smoking"] [2 "male"] [2 "education-level-high"] [2 "cancer"]
[3 "smoking"] [3 "male"] [3 "education-level-high"] [3 "cancer"]
[4 "smoking"] [4 "male"] [4 "education-level-high"] [4 "cancer"]
[5 "smoking"] [5 "male"] [5 "education-level-high"] [5 "cancer"]
[6 "smoking"] [6 "male"] [6 "education-level-high"]
[7 "smoking"] [7 "male"] [7 "education-level-high"]
[8 "smoking"] [8 "male"] [8 "education-level-low"] [8 "cancer"]
[9 "smoking"] [9 "male"] [9 "education-level-low"] [9 "cancer"]
[10 "smoking"] [10 "male"] [10 "education-level-low"] [10 "cancer"]
[11 "smoking"] [11 "male"] [11 "education-level-low"] [11 "cancer"]
[12 "smoking"] [12 "male"] [12 "education-level-low"]
[13 "smoking"] [13 "female"] [13 "education-level-high"] [13 "cancer"]
[14 "smoking"] [14 "female"] [14 "education-level-high"] [14 "cancer"]
[15 "smoking"] [15 "female"] [15 "education-level-high"] [15 "cancer"]
[16 "smoking"] [16 "female"] [16 "education-level-high"] [16 "cancer"]
[17 "smoking"] [17 "female"] [17 "education-level-high"] [17 "cancer"]
[18 "smoking"] [18 "female"] [18 "education-level-high"]
[19 "smoking"] [19 "female"] [19 "education-level-high"]
[20 "smoking"] [20 "female"] [20 "education-level-low"] [20 "cancer"]
[21 "smoking"] [21 "female"] [21 "education-level-low"] [21 "cancer"]
[22 "smoking"] [22 "female"] [22 "education-level-low"] [22 "cancer"]
[23 "smoking"] [23 "female"] [23 "education-level-low"] [23 "cancer"]
[24 "smoking"] [24 "female"] [24 "education-level-low"]
[25 "male"] [25 "education-level-high"] [25 "cancer"]
[26 "male"] [26 "education-level-high"] [26 "cancer"]
[27 "male"] [27 "education-level-high"]
[28 "male"] [28 "education-level-high"]
[29 "male"] [29 "education-level-high"]
[30 "male"] [30 "education-level-low"] [30 "cancer"]
[31 "male"] [31 "education-level-low"]
[32 "male"] [32 "education-level-low"]
[33 "male"] [33 "education-level-low"]
[34 "female"] [34 "education-level-high"] [34 "cancer"]
[35 "female"] [35 "education-level-high"]
[36 "female"] [36 "education-level-high"]
[37 "female"] [37 "education-level-low"] [37 "cancer"]
[38 "female"] [38 "education-level-low"]
[39 "female"] [39 "education-level-low"]
[40 "female"] [40 "education-level-low"]})
)We would like to ascertain, if smoking is causally related to cancer:
(def smoking-rule (make-implication #{"smoking"} #{"cancer"}))The algorith determines causality by emulating a controlled study, in which one group is exposed to the premise attribute, in this case “smoking” and the control group is not. Additionally, we choose a set of controlled variables. These are supposed to have the same values across pairs of objects in the exposure group and control group, to make sure neither of these is the true cause for the conclusion attribute, in this case “cancer”.
If two objects in the context satisfy these conditions, they are considerd a matched record pair. For example, if we control for variables “male” “female” “education-level-high” and “education-level-low” (0, 25), (9, 31) and (13 34)
each form a matched record pair. This can be verified using the method matched-record-pair?:
(matched-record-pair? smoking-ctx
smoking-rule
#{"male" "female" "education-level-high" "education-level-low"}
0
25)
(matched-record-pair? smoking-ctx
smoking-rule
#{"male" "female" "education-level-high" "education-level-low"}
9
31)
(matched-record-pair? smoking-ctx
smoking-rule
#{"male" "female" "education-level-high" "education-level-low"}
13
34)The method fair-data-set computes a set of matched record pairs, by trying to match each object to exactly one different object.
(= (fair-data-set smoking-ctx
smoking-rule
#{"male" "female" "education-level-high" "education-level-low"})
smoking-fair-data-set)([#{7 29}
#{13 34}
#{15 36}
#{6 26}
#{1 28}
#{0 27}
#{17 35}
#{33 9}
#{31 12}
#{30 10}
#{22 37}
#{4 25}
#{21 38}
#{32 11}
#{24 40}
#{20 39}])This set is used to verify whether an association rule is causal in nature.
The method causal? tests causality for a specific implication:
(causal? smoking-ctx smoking-rule #{} 1.7 1)The final three parameters are: -the irrelevant variables, variables that will not be controlled for -the confidence in the causality of the implication; a value of 1.7 corresponds to a 70% confidence -a threshold for computing exclusive variables. Two variables a and b are mutually exclusive, if the absolute support for (a and b) or (b and not a) is no larger than the threshold
To discover all causes of a certain attribute in the context the method causal-association-rule-discovery can be used:
(causal-association-rule-discovery smoking-ctx 0.7 3 "cancer" 1.7)(#{"smoking"})0.7 represents the minimum local support that a generated variable must exceet to be considered. 1.7 again represents the confidence of the rule, and 3 represents the maximum number of attributes of the premise.