seth-swiftnav/albatross

A framework for statistical modelling in C++.

albatross

A framework for statistical modelling in C++, with a focus on Gaussian processes.

Features

• Gaussian process regression which is accomplished using composable covariance functions and templated predictor types.
• Evaluation utilities, with a focus on cross validation.
• Written using generics in an attempt to make these core routines applicable to a number of fields.
• Parameter handling which makes it easy to get and set parameters in a standardized way as well as compose and (de)serialize models to string.

Install

albatross is a header only library so incorporating it in your C++ project should be as simple as adding ./albatross as an include directory.

Make sure you've run git submodule update --recursive --init to be sure all the third party libraries required by albatross are up to date.

If you want to run the tests you can do so using cmake,

mkdir build;
cd build;
cmake ../
make run_albatross_unit_tests

Similarly you can make/run the examples,

make sinc_example
./examples/sinc_example -input ./examples/sinc_input.csv -output ./examples/sinc_predictions.csv

and plot the results (though this'll require a numerical python environment),

python ../examples/plot_example_predictions.py ./examples/sinc_input.csv ./examples/sinc_predictions.csv
./examples/sinc_example -input ../examples/sinc_input.csv -output ./examples/sinc_predictions.csv -n 10

Examples

As an example we can build a model which estimates a function f(x),

f(x) = a x + b + c sin(x) / x

by using noisy observations of the function y = f(x) + N(0, s^2). To do so we can build up our model,

  using Noise = IndependentNoise<double>;
  using SqrExp = SquaredExponential<ScalarDistance>;

  CovarianceFunction<Constant> mean = {Constant(100.)};
  CovarianceFunction<SlopeTerm> slope = {SlopeTerm(100.)};
  CovarianceFunction<Noise> noise = {Noise(meas_noise)};
  CovarianceFunction<SqrExp> sqrexp = {SqrExp(2., 5.)};

  auto linear_model = mean + slope + noise + sqrexp;

which incorporates prior knowledge that the function consists of a mean offset, a linear term, measurement noise and an unknown smooth compontent (which we captures using a squared exponential covariance function).

We can inspect the model and its parameters,

>> std::cout << linear_model.to_string() << std::endl;
model_name: (((constant+slope_term)+independent_noise)+squared_exponential[scalar_distance])
model_params:
  length_scale: 2
  sigma_constant: 100
  sigma_independent_noise: 1
  sigma_slope: 100
  sigma_squared_exponential: 5

then condition the model on random observations, which we stored in data,

  auto model = gp_from_covariance(linear_model);
  model.fit(data);

and make some gridded predictions,

  const int k = 161;
  const auto grid_xs = uniform_points_on_line(k, low - 2., high + 2.);
  const auto predictions = model.predict(grid_xs);

Here are the resulting predictions when we have only two noisy observations,

2 Observations

not great, but at least it knows it isn't great. As we start to add more observations we can watch the model slowly get more confident,

5 Observations

10 Observations

30 Observations

Credit

The fit, predict, get_params functionality was inspired by scikit-learn and the covariance function composition by george.

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