yonatanbitton
commited on
Commit
•
957fdb6
1
Parent(s):
2cea302
Update README.md
Browse files
README.md
CHANGED
@@ -87,7 +87,7 @@ There are different number of candidates, which creates different difficulty lev
|
|
87 |
It is a binomial distribution probability calculation.
|
88 |
|
89 |
Assuming N=5 candidates, and K=2 associations, there could be three events:
|
90 |
-
(1) The probability for a random guess is correct in 0 associations is 0.3 (elaborate below), and the Jaccard index is 0 (there is no intersection between the correct labels and the wrong guesses). Therefore the expected random score is 0.
|
91 |
(2) The probability for a random guess is correct in 1 associations is 0.6, and the Jaccard index is 0.33 (intersection=1, union=3, one of the correct guesses, and one of the wrong guesses). Therefore the expected random score is 0.6*0.33 = 0.198.
|
92 |
(3) The probability for a random guess is correct in 2 associations is 0.1, and the Jaccard index is 1 (intersection=2, union=2). Therefore the expected random score is 0.1*1 = 0.1.
|
93 |
* Together, when K=2, the expected score is 0+0.198+0.1 = 0.298.
|
@@ -97,7 +97,7 @@ There are different number of candidates, which creates different difficulty lev
|
|
97 |
|
98 |
Now we can perform the same calculation with K=3 associations.
|
99 |
Assuming N=5 candidates, and K=3 associations, there could be four events:
|
100 |
-
(4) The probability for a random guess is correct in 0 associations is 0, and the Jaccard index is 0. Therefore the expected random score is 0.
|
101 |
(5) The probability for a random guess is correct in 1 associations is 0.3, and the Jaccard index is 0.2 (intersection=1, union=4). Therefore the expected random score is 0.3*0.2 = 0.06.
|
102 |
(6) The probability for a random guess is correct in 2 associations is 0.6, and the Jaccard index is 0.5 (intersection=2, union=4). Therefore the expected random score is 0.6*5 = 0.3.
|
103 |
(7) The probability for a random guess is correct in 3 associations is 0.1, and the Jaccard index is 1 (intersection=3, union=3). Therefore the expected random score is 0.1*1 = 0.1.
|
|
|
87 |
It is a binomial distribution probability calculation.
|
88 |
|
89 |
Assuming N=5 candidates, and K=2 associations, there could be three events:
|
90 |
+
(1) The probability for a random guess is correct in 0 associations is 0.3 (elaborate below), and the Jaccard index is 0 (there is no intersection between the correct labels and the wrong guesses). Therefore the expected random score is 0.
|
91 |
(2) The probability for a random guess is correct in 1 associations is 0.6, and the Jaccard index is 0.33 (intersection=1, union=3, one of the correct guesses, and one of the wrong guesses). Therefore the expected random score is 0.6*0.33 = 0.198.
|
92 |
(3) The probability for a random guess is correct in 2 associations is 0.1, and the Jaccard index is 1 (intersection=2, union=2). Therefore the expected random score is 0.1*1 = 0.1.
|
93 |
* Together, when K=2, the expected score is 0+0.198+0.1 = 0.298.
|
|
|
97 |
|
98 |
Now we can perform the same calculation with K=3 associations.
|
99 |
Assuming N=5 candidates, and K=3 associations, there could be four events:
|
100 |
+
(4) The probability for a random guess is correct in 0 associations is 0, and the Jaccard index is 0. Therefore the expected random score is 0.
|
101 |
(5) The probability for a random guess is correct in 1 associations is 0.3, and the Jaccard index is 0.2 (intersection=1, union=4). Therefore the expected random score is 0.3*0.2 = 0.06.
|
102 |
(6) The probability for a random guess is correct in 2 associations is 0.6, and the Jaccard index is 0.5 (intersection=2, union=4). Therefore the expected random score is 0.6*5 = 0.3.
|
103 |
(7) The probability for a random guess is correct in 3 associations is 0.1, and the Jaccard index is 1 (intersection=3, union=3). Therefore the expected random score is 0.1*1 = 0.1.
|