implement NormalInverseWishart component model

[stephentu]

Here's our implementation of NIW, put in the distributions framework.

Several high level notes:

• Not optimized at all (emphasis is on readability)
• Introduces (compile-time) dependency on eigen3 library
• A few functions regarding wishart sampling (with credit in the comments) were taken from matt johnson's pyhsmm project
• C++ implementation is templated on the dimension size, with size=-1 indicated variable size (this is the same convention as eigen3). The library provides template instantiation for size \in (-1, 2, 3), the most common cases.

[fritzo]

To use external code under another license, we have adopted the convention of keeping the code in a separate vendor/ directory, e.g. distributions/include/dustributions/vendor/fmath. Could.you copy matt Johnsons to a new file in a distributions/distributions/vendor/ directory, add his MIT license header (as we are legally obligated) and import them in your code?

[stephentu]

Ugh, would there be any objection to bumping the compiler requirement from g++-4.6 to g++-4.8? the headers for std::chi_squared_distribution are sort of broken in 4.6 (see https://travis-ci.org/forcedotcom/distributions/jobs/32043162)

[fritzo]

@cap what's your estimate on when we might move from Ubuntu 12.04 to 14.04 internally? I develop distributions+loom on both already but those are only two components.

[stephentu]

I can also hack around this by copying the implementation into vendors for the time being

[fritzo]

Wait, we already get around this by using the <double> specialization: https://github.com/forcedotcom/distributions/blob/master/include/distributions/random.hpp#L73

[fritzo]

Hey Stephen , this is awesome and I'm excited to start using NIW2 for (long,lat) data. I'm happy to merge as soon as:

1. Matt's MIT license is added in vendor/
2. tests pass
3. advance vs add_group is resolved
4. style conforms (braces on if/else/for and whitespace between operators)

Post-merge I'd like to speed up Scorer (caching the inverted matrix) and implement Mixture.

[stephentu]

As for Matt's MIT license, I copied the license text into stats.py, is that sufficient or do we need a separate LICENSE file somewhere?

[stephentu]

I'm having a hard time reproducing the errors on OS X, so give me some time while I spin up an ubuntu VM to try to match the travis environment more closely

[stephentu]

Ah interesting, in setup.py-- is there any reason why -ffast-math -funsafe-math-optimizations is only enabled for linux builds and not OS X? this might be causing some of the discrepancy

[stephentu]

ok the bug was:

const VectorXf &x = ... // bad
const VectorXf x = ... // good

I moved some stuff around, so you may want to take another look at the diff

[fritzo]

OK, looks great. Just a little cleanup before we merge. Then Jonathan or I can take a look at the gof testing.

[fritzo]

I'm going to try to integrate cpplint with our tests to avoid manually checking style...

[fritzo]

OK I just pushed cpplint integration. Apologies for slightly changing style, but I thing this gets rid of some of my own idiosyncrasies.

pip install -r requirements.txt    # or just pip install cpplint
make lint_cc                       # or just make