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Reduce spurious test failures by increasing threshold to 4 sigma #44

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Sep 26, 2023
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Reduce spurious test failures by increasing threshold to 4 sigma #44

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64 changes: 32 additions & 32 deletions tests/Tests.dfy
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Original file line number Diff line number Diff line change
Expand Up @@ -19,18 +19,18 @@
if x < 0.0 then -x else x
}

method testBernoulliIsWithin3SigmaOfTrueMean(
method testBernoulliIsWithin4SigmaOfTrueMean(
n: nat,
empiricalSum: real,
successProb: real,
description: string
)
requires n > 0
{
testEmpiricalIsWithin3SigmaOfTrueMean(n, empiricalSum, successProb, successProb * (1.0 - successProb), description);
testEmpiricalIsWithin4SigmaOfTrueMean(n, empiricalSum, successProb, successProb * (1.0 - successProb), description);
}

method testEmpiricalIsWithin3SigmaOfTrueMean(
method testEmpiricalIsWithin4SigmaOfTrueMean(
n: nat,
empiricalSum: real,
trueMean: real,
Expand All @@ -41,14 +41,14 @@
{
var empiricalMean := empiricalSum / n as real;
var diff := Abs(empiricalMean - trueMean);
var threshold := 3.0 * 3.0 * trueVariance / n as real;
var threshold := 4.0 * 4.0 * trueVariance / n as real;
if diff * diff > threshold {
print "Test failed: ", description, "\n";
print "Difference between empirical and true mean: ", diff, "\n";
print "squared difference: ", diff * diff, "\n";
print "sigma squared: ", trueVariance / n as real, "\n";
}
expect diff * diff < threshold, "Empirical mean should be within 3 sigma of true mean. This individual test may fail with probability of about 0.27%.";
expect diff * diff < threshold, "Empirical mean should be within 3 sigma of true mean. This individual test may fail with probability of about 6.3e-5.";
}


Expand All @@ -63,7 +63,7 @@
t := t + 1;
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, t as real, 0.5, "p(true)");
testBernoulliIsWithin4SigmaOfTrueMean(n, t as real, 0.5, "p(true)");
}

method TestUniform(n: nat, r: UniformInterface.IUniform)
Expand All @@ -82,9 +82,9 @@
case 2 => c := c + 1;
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, a as real, 1.0 / 3.0, "p(0)");
testBernoulliIsWithin3SigmaOfTrueMean(n, b as real, 1.0 / 3.0, "p(1)");
testBernoulliIsWithin3SigmaOfTrueMean(n, c as real, 1.0 / 3.0, "p(2)");
testBernoulliIsWithin4SigmaOfTrueMean(n, a as real, 1.0 / 3.0, "p(0)");
testBernoulliIsWithin4SigmaOfTrueMean(n, b as real, 1.0 / 3.0, "p(1)");
testBernoulliIsWithin4SigmaOfTrueMean(n, c as real, 1.0 / 3.0, "p(2)");
}

method TestUniformInterval(n: nat, r: UniformInterface.IUniform)
Expand All @@ -103,9 +103,9 @@
case 9 => c := c + 1;
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, a as real, 1.0 / 3.0, "p(7)");
testBernoulliIsWithin3SigmaOfTrueMean(n, b as real, 1.0 / 3.0, "p(8)");
testBernoulliIsWithin3SigmaOfTrueMean(n, c as real, 1.0 / 3.0, "p(9)");
testBernoulliIsWithin4SigmaOfTrueMean(n, a as real, 1.0 / 3.0, "p(7)");
testBernoulliIsWithin4SigmaOfTrueMean(n, b as real, 1.0 / 3.0, "p(8)");
testBernoulliIsWithin4SigmaOfTrueMean(n, c as real, 1.0 / 3.0, "p(9)");
}

method TestGeometric(n: nat, r: GeometricInterface.IGeometric)
Expand All @@ -126,9 +126,9 @@
case _ =>
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, a as real, 0.015625, "p(5)");
testBernoulliIsWithin3SigmaOfTrueMean(n, b as real, 0.00048828125, "p(10)");
testEmpiricalIsWithin3SigmaOfTrueMean(n, sum as real, (1.0 - 0.5) / 0.5, (1.0 - 0.5) / (0.5 * 0.5), "mean");
testBernoulliIsWithin4SigmaOfTrueMean(n, a as real, 0.015625, "p(5)");
testBernoulliIsWithin4SigmaOfTrueMean(n, b as real, 0.00048828125, "p(10)");
testEmpiricalIsWithin4SigmaOfTrueMean(n, sum as real, (1.0 - 0.5) / 0.5, (1.0 - 0.5) / (0.5 * 0.5), "mean");
}

method TestBernoulliRational(n: nat, r: BernoulliRationalInterface.IBernoulliRational)
Expand All @@ -143,7 +143,7 @@
t := t + 1;
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, t as real, 0.2, "p(true)");
testBernoulliIsWithin4SigmaOfTrueMean(n, t as real, 0.2, "p(true)");
}

method TestBernoulliRational2(n: nat, r: BernoulliRationalInterface.IBernoulliRational)
Expand All @@ -159,7 +159,7 @@
}

expect t == 0;
}
}

method TestBernoulliRational3(n: nat, r: BernoulliRationalInterface.IBernoulliRational)
decreases *
Expand All @@ -174,7 +174,7 @@
}

expect t == n;
}
}

method TestBernoulli(n: nat, r: BernoulliInterface.IBernoulli)
decreases *
Expand All @@ -188,7 +188,7 @@
t := t + 1;
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, t as real, 0.2, "p(true)");
testBernoulliIsWithin4SigmaOfTrueMean(n, t as real, 0.2, "p(true)");
}

method TestBernoulliExpNeg(n: nat, r: BernoulliExpNegInterface.IBernoulliExpNeg)
Expand All @@ -203,7 +203,7 @@
t := t + 1;
}
}
testBernoulliIsWithin3SigmaOfTrueMean(n, t as real, 0.1, "p(true)");
testBernoulliIsWithin4SigmaOfTrueMean(n, t as real, 0.1, "p(true)");
}

method TestDiscreteLaplace(n: nat, r: DiscreteLaplaceInterface.IDiscreteLaplace)
Expand All @@ -228,13 +228,13 @@
// https://www.wolframalpha.com/input?i=ReplaceAll%5B%28E%5E%5B1%2Ft%5D+-+1%29+%2F+%28E%5E%5B1%2Ft%5D+%2B+1%29+*+E%5E%28-Abs%5Bx%5D%2Ft%29%2C+%7Bt+-%3E+7%2F5%2C+x+-%3E+0%7D%5D
// https://www.wolframalpha.com/input?i=ReplaceAll%5B%28E%5E%5B1%2Ft%5D+-+1%29+%2F+%28E%5E%5B1%2Ft%5D+%2B+1%29+*+E%5E%28-Abs%5Bx%5D%2Ft%29%2C+%7Bt+-%3E+7%2F5%2C+x+-%3E+1%7D%5D
// https://www.wolframalpha.com/input?i=ReplaceAll%5B%28E%5E%5B1%2Ft%5D+-+1%29+%2F+%28E%5E%5B1%2Ft%5D+%2B+1%29+*+E%5E%28-Abs%5Bx%5D%2Ft%29%2C+%7Bt+-%3E+7%2F5%2C+x+-%3E+2%7D%5D
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[0] as real, 0.3426949, "p(0)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[1] as real, 0.1677634, "p(1)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[-1] as real, 0.1677634, "p(-1)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[2] as real, 0.0821272, "p(2)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[-2] as real, 0.0821272, "p(-2)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[0] as real, 0.3426949, "p(0)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[1] as real, 0.1677634, "p(1)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[-1] as real, 0.1677634, "p(-1)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[2] as real, 0.0821272, "p(2)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[-2] as real, 0.0821272, "p(-2)");
var variance := 3.7575005; // variance of DiscreteLaplace(7/5) is (2*exp(5/7))/(exp(5/7)-1)^2
testEmpiricalIsWithin3SigmaOfTrueMean(n, sum as real, 0.0, variance, "mean");
testEmpiricalIsWithin4SigmaOfTrueMean(n, sum as real, 0.0, variance, "mean");
}

method TestDiscreteGaussian(n: nat, r: DiscreteGaussianInterface.IDiscreteGaussian)
Expand All @@ -259,12 +259,12 @@
// https://www.wolframalpha.com/input?i=ReplaceAll%5BE%5E%28-x%5E2+%2F+%282+*%CF%83%5E2%29%29+%2F+Sum%5BE%5E%28-y%5E2%2F%282+%CF%83%5E2%29%29%2C+%7By%2C+-Infinity%2C+Infinity%7D%5D%2C+%7Bx+-%3E+0%2C+%CF%83+-%3E+1.4%7D%5D
// https://www.wolframalpha.com/input?i=ReplaceAll%5BE%5E%28-x%5E2+%2F+%282+*%CF%83%5E2%29%29+%2F+Sum%5BE%5E%28-y%5E2%2F%282+%CF%83%5E2%29%29%2C+%7By%2C+-Infinity%2C+Infinity%7D%5D%2C+%7Bx+-%3E+1%2C+%CF%83+-%3E+1.4%7D%5D
// https://www.wolframalpha.com/input?i=ReplaceAll%5BE%5E%28-x%5E2+%2F+%282+*%CF%83%5E2%29%29+%2F+Sum%5BE%5E%28-y%5E2%2F%282+%CF%83%5E2%29%29%2C+%7By%2C+-Infinity%2C+Infinity%7D%5D%2C+%7Bx+-%3E+2%2C+%CF%83+-%3E+1.4%7D%5D
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[0] as real, 0.284959, "p(0)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[1] as real, 0.220797, "p(1)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[-1] as real, 0.220797, "p(-1)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[2] as real, 0.102713, "p(2)");
testBernoulliIsWithin3SigmaOfTrueMean(n, counts[-2] as real, 0.102713, "p(-2)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[0] as real, 0.284959, "p(0)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[1] as real, 0.220797, "p(1)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[-1] as real, 0.220797, "p(-1)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[2] as real, 0.102713, "p(2)");
testBernoulliIsWithin4SigmaOfTrueMean(n, counts[-2] as real, 0.102713, "p(-2)");
var varianceBound := 1.4 * 1.4; // variance of DiscreteGaussian(1.4) is < 1.4^2
testEmpiricalIsWithin3SigmaOfTrueMean(n, sum as real, 0.0, varianceBound, "mean");
testEmpiricalIsWithin4SigmaOfTrueMean(n, sum as real, 0.0, varianceBound, "mean");
}
}