Fix BoundedStandardDeviation test#153
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chinmayshah99 merged 1 commit intoOpenMined:devfrom May 24, 2020
replomancer:test_fix
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Fix BoundedStandardDeviation test#153chinmayshah99 merged 1 commit intoOpenMined:devfrom replomancer:test_fix
chinmayshah99 merged 1 commit intoOpenMined:devfrom
replomancer:test_fix
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| assert type(result) is float | ||
| assert lower_bound <= result <= upper_bound | ||
| assert type(result) is float and result >= 0 | ||
| assert result <= (upper_bound - lower_bound) / 2 |
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Is this again based on Popoviciu's inequality ?
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I don't know what's the usual proof, but here's how you can derive it from Popoviciu's inequality on variances (I probably made it too complicated):
σ2 ≤ 1/4 (M - m)2
0 ≤ (1/2 (M - m))2 - σ2 # a2 - b2 = (a + b)(a - b)
0 ≤ (1/2 (M - m) + σ) (1/2 (M - m) - σ) # divide by (1/2 (M - m) + σ) which is ≥ 0 because M ≥ m and σ ≥ 0
0 ≤ 1/2 (M - m) - σ
σ ≤ 1/2 (M - m)
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I suspected that; just wanted to verify
chinmayshah99
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Description
The test I've recently written for BoundedStandardDeviation made zero sense mathematically 🐛 There was an inequality satisfied only by accident.
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