[mlpack] [mlpack/mlpack] adds GammaDistribution::Train(observations, probabilities) (#834)

Tue Dec 27 11:45:43 EST 2016

Thanks!  I made some style changes in c739839 and ec65745 and changed the random number generators to use the mlpack random number generator object in 1ef2a02 (some of the tests I changed there were not yours, but still this is an improvement because you can now set the random number seed with `mlpack::math::RandomSeed()`).

Then, for each test, I added a line at the top: `math::RandomSeed(std::time(NULL))` and recompiled.  I ran a bash script like this:

```
while(true); do bin/mlpack_test -t GammaDistributionTrainWithProbabilitiesTest; sleep 1; done
```

This will give output like this:

```
Running 1 test case...

*** No errors detected
Running 1 test case...

*** No errors detected
Running 1 test case...
/home/ryan/src/mlpack/src/mlpack/tests/distribution_test.cpp(483): fatal error in "GammaDistributionTrainWithProbabilitiesTest": difference{2.03727%} between betaReal{6.7000000000000002} and gDist.Beta(0){6.5662282671947327} exceeds 2%

*** 1 failure detected in test suite "mlpackTest"
Running 1 test case...

*** No errors detected
Running 1 test case...

*** No errors detected
```

Using this strategy I found that some of the tolerances needed to be modified to prevent failures, in the test `GammaDistributionTrainWithProbabilitiesTest`: the comparison between `gDist` and `gDist2` parameters occasionally failed, so I loosened the tolerance to 1.5% from 1%.  The comparisons between `alphaReal` and `betaReal` and the trained distributions often failed, so I loosened the tolerance from 1% to 2.5%.  I think this is an ok change to make and I think these are reasonable bounds for the expected noise.

This strategy is important to test with, because each compilation will (effectively) have a different random seed associated with it, so to ensure that tests pass on users' systems, we have to check with many different random seeds.

Anyway, about the Perceptron code, definitely, if you would like to add tests, it would be much appreciated!  You can create an issue if you like or just open a PR, whatever you prefer is fine.

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