Model Selection#

Model selection is the data-driven approach to choosing the hyper-parameters of a model. It aims to find the best combination that maximizes a particular cross validation Metric. The Grid Search meta-estimator automates model selection by training and testing a unique model for each combination of user-defined hyper-parameters.

As an example, we could attempt to find the best setting for the hyper-parameter k in K Nearest Neighbors from a list of possible values 1, 3, 5, and 10. In addition, we could try each value of k with distance weighting turned on or off. We might also want to know if the data is sensitive to the underlying distance kernel so we'll try the standard Euclidean as well as the Manhattan distances. The order in which the sets of possible parameters are given to Grid Search is the same order they appear in the constructor of the learner.

use Rubix\ML\GridSearch;
use Rubix\ML\Classifiers\KNearestNeighbors;
use Rubix\ML\Kernels\Distance\Euclidean;
use Rubix\ML\Kernels\Distance\Manhattan;

$params = [
    [1, 3, 5, 10], [true, false], [new Euclidean(), new Manhattan()]
];

$estimator = new GridSearch(KNearestNeighbors::class, $params);

$estimator->train($dataset);

Once training is complete, Grid Search automatically trains the base learner with the best hyper-parameters on the full dataset. Once training is complete, Grid Search can either be used to perform inference like a normal estimator or you can dump the results for future reference using the results() method. In the example below, we'll return just the parameters that received the highest validation score using the best() method.

var_dump($estimator->best());
array(3) {
  [0]=> int(3)
  [1]=> bool(true)
  [2]=> object(Rubix\ML\Kernels\Distance\Manhattan) {}
}

When the possible values of the hyper-parameters are selected such that they are spaced out evenly, we call that grid search. You can use the static grid() method on the Params helper to generate an array of evenly-spaced values automatically. Instead of choosing the values of k manually, for this example we'll generate a grid of 4 values equally spaced between 1 and 10.

Example

use Rubix\ML\Other\Helpers\Params;

$params = [
    Params::grid(1, 10, 4), [true, false], // ...
];

When the list of possible hyper-parameters is randomly chosen from a distribution, we call that random search. In the absence of a good manual strategy, random search has the advantage of being able to search the hyper-parameter space more effectively by testing combinations of parameters that might not have been considered otherwise. To generate a list of random values from a uniform distribution you can use either the ints() or floats() method on the Params helper. In the example below, we'll generate 4 unique random integers between 1 and 10 as possible values for k.

Example

use Rubix\ML\Other\Helpers\Params;

$params = [
    Params::ints(1, 10, 4), [true, false], // ...
];