Hyperparameter optimization

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In the sections on feature engineering and predicting, we learned how to train both the feature learning algorithm and the machine learning algorithm used for prediction in the getML Engine. However, there are lots of parameters involved. Multirel, Relboost, RelMT, FastProp, LinearRegression, LogisticRegression, XGBoostClassifier, and XGBoostRegressor all have their own settings. That is why you might want to use hyperparameter optimization.

The most relevant parameters of these classes can be chosen to constitute individual dimensions of a parameter space. For each parameter, a lower and upper bound has to be provided and the hyperparameter optimization will search the space within these bounds. This will be done iteratively by drawing a specific parameter combination, overwriting the corresponding parameters in a base pipeline, and then fitting and scoring it. The algorithm used to draw from the parameter space is represented by the different classes of hyperopt.

While RandomSearch and LatinHypercubeSearch are purely statistical approaches, GaussianHyperparameterSearch uses prior knowledge obtained from evaluations of previous parameter combinations to select the next one.

Tuning routines

The easiest way to conduct a hyperparameter optimization in getML are the tuning routines tune_feature_learners() and tune_predictors(). They roughly work as follows:

They begin with a base pipeline, in which the default parameters for the feature learner or the predictor are used.
They then proceed by optimizing 2 or 3 parameters at a time using a GaussianHyperparameterSearch. If the best pipeline outperforms the base pipeline, the best pipeline becomes the new base pipeline.
Taking the base pipeline from the previous steps, the tuning routine then optimizes the next 2 or 3 hyperparameters. If the best pipeline from that hyperparameter optimization outperforms the current base pipeline, that pipeline becomes the new base pipeline.
These steps are then repeated for more hyperparameters.

The following tables list the tuning recipes and hyperparameter subspaces for each step:

Tuning recipes for predictors

Predictor	Stage	Hyperparameter	Subspace
`LinearRegression`; `LogisticRegression`	1 (base parameters)	reg_lambda	[1E-11, 100]
		learning_rate	[0.5, 0.99]
`XGBoostClassifier`; `XGBoostRegressor`	1 (base parameters)	learning_rate	[0.05, 0.3]
	2 (tree parameters)	max_depth	[1, 15]
		min_child_weights	[1, 6]
		gamma	[0, 5]
	3 (sampling parameters)	colsample_bytree	[0.75, 0.9]
		subsample	[0.75, 0.9]
	4 (regularization parameters)	reg_alpha	[0, 5]
		reg_lambda	[0, 10]

Tuning recipes for feature learners

Feature Learner	Stage	Hyperparameter	Subspace
`FastProp`	1 (base parameters)	num_features	[50, 500]
		n_most_frequent	[0, 20]
`Multirel`	1 (base parameters)	num_features	[10, 50]
		shrinkage	[0, 0.3]
	2 (tree parameters)	max_length	[0, 10]
		min_num_samples	[1, 500]
	3 (regularization parameters)	share_aggregations	[0.1, 0.5]
`Relboost`	1 (base parameters)	num_features	[10, 50]
		shrinkage	[0, 0.3]
	2 (tree parameters)	max_length	[0, 10]
		min_num_samples	[1, 500]
	3 (regularization parameters)	share_aggregations	[0.1, 0.5]
`RelMT`	1 (base parameters)	num_features	[10, 50]
		shrinkage	[0, 0.3]
	2 (tree parameters)	max_depth	[1, 8]
		min_num_samples	[1, 500]
	3 (regularization parameters)	reg_lambda	[0, 0.0001]

The advantage of the tuning routines is that they provide a convenient out-of-the-box experience for hyperparameter tuning. For most use cases, it is sufficient to tune the XGBoost predictor.

More advanced users can rely on the more low-level hyperparameter optimization routines.

Random search

A RandomSearch draws random hyperparameter sets from the hyperparameter space.

Latin hypercube search

A LatinHypercubeSearch draws almost random hyperparameter sets from the hyperparameter space, but ensures that they are sufficiently different from each other.

Gaussian hyperparameter search

A GaussianHyperparameterSearch works like this:

It begins with a burn-in phase, usually about 70% to 90% of all iterations. During that burn-in phase, the hyperparameter space is sampled more or less at random, using either a random search or a latin hypercube search. You can control this phase using ratio_iter and surrogate_burn_in_algorithm.
Once enough information has been collected, it fits a Gaussian process on the hyperparameters with the score we want to maximize or minimize as the predicted variable. Note that the Gaussian process has hyperparameters itself, which are also optimized. You can control this phase using gaussian_kernel, gaussian_optimization_algorithm, gaussian_optimization_burn_in_algorithm, and gaussian_optimization_burn_ins.
It then uses the Gaussian process to predict the expected information (EI). The EI is a measure of how much additional information it might get from evaluating a particular point in the hyperparameter space. The expected information is to be maximized. The point in the hyperparameter space with the maximum expected information is the next point that is actually evaluated (meaning a new pipeline with these hyperparameters is trained). You can control this phase using optimization_algorithm, optimization_burn_ins, and optimization_burn_in_algorithm.

Note

In a nutshell, the GaussianHyperparameterSearch behaves like human data scientists:

At first, it picks random hyperparameter combinations.
Once it has gained a better understanding of the hyperparameter space, it starts evaluating hyperparameter combinations that are particularly interesting.