GaussianHyperparameterSearch

class getml.hyperopt.GaussianHyperparameterSearch(param_space, pipeline, score='rmse', n_iter=100, seed=5483, ratio_iter=0.8, optimization_algorithm='nelderMead', optimization_burn_in_algorithm='latinHypercube', optimization_burn_ins=500, surrogate_burn_in_algorithm='latinHypercube', gaussian_kernel='matern52', gaussian_optimization_burn_in_algorithm='latinHypercube', gaussian_optimization_algorithm='nelderMead', gaussian_optimization_burn_ins=500, gaussian_nugget=50)

Bayesian hyperparameter optimization using a Gaussian process.

After a burn-in period, a Gaussian process is used to pick the most promising parameter combination to be evaluated next based on the knowledge gathered throughout previous evaluations. Accessing the quality of potential combinations will be done using the expected information (EI).

Args:

param_space (dict):

Dictionary containing numerical arrays of length two holding the lower and upper bounds of all parameters which will be altered in pipeline during the hyperparameter optimization.

If we have two feature learners and one predictor, the hyperparameter space might look like this:

param_space = {
    "feature_learners": [
        {
            "num_features": [10, 50],
        },
        {
            "max_depth": [1, 10],
            "min_num_samples": [100, 500],
            "num_features": [10, 50],
            "reg_lambda": [0.0, 0.1],
            "shrinkage": [0.01, 0.4]
        }],
    "predictors": [
        {
            "reg_lambda": [0.0, 10.0]
        }
    ]
}

If we only want to optimize the predictor, then we can leave out the feature learners.

pipeline (Pipeline):

Base pipeline used to derive all models fitted and scored during the hyperparameter optimization. Be careful when constructing it since only the parameters present in param_space will be overwritten. It defines the data schema and any hyperparameters that are not optimized.

score (str, optional):

The score to optimize. Must be from scores.

n_iter (int, optional):

Number of iterations in the hyperparameter optimization and thus the number of parameter combinations to draw and evaluate. Range: [1, \(\infty\)]

seed (int, optional):

Seed used for the random number generator that underlies the sampling procedure to make the calculation reproducable. Due to nature of the underlying algorithm, this is only the case if the fit is done without multithreading. To reflect this, a seed of None is only allowed to be set to an actual integer if both num_threads and n_jobs instance variables of the predictor and feature_selector in model - if they are instances of either XGBoostRegressor or XGBoostClassifier - are set to 1. Internally, a seed of None will be mapped to 5543. Range: [0, \(\infty\)]

ratio_iter (float, optional):

Ratio of the iterations used for the burn-in. For a ratio_iter of 1.0, all iterations will be spent in the burn-in period resulting in an equivalence of this class to LatinHypercubeSearch or RandomSearch - depending on surrogate_burn_in_algorithm. Range: [0, 1]

As a rule of thumb at least 70 percent of the evaluations should be spent in the burn-in phase. The more comprehensive the exploration of the param_space during the burn-in, the less likely it is that the Gaussian process gets stuck in local minima.

optimization_algorithm (string, optional):

Determines the optimization algorithm used for the local search in the optimization of the expected information (EI). Must be from optimization.

optimization_burn_in_algorithm (string, optional):

Specifies the algorithm used to draw initial points in the burn-in period of the optimization of the expected information (EI). Must be from burn_in.

optimization_burn_ins (int, optional):

Number of random evaluation points used during the burn-in of the minimization of the expected information (EI). After the surrogate model - the Gaussian process - was successfully fitted to the previous parameter combination, the algorithm is able to calculate the EI for a given point. In order to get to the next combination, the EI has to be maximized over the whole parameter space. Much like the GaussianProcess itself, this requires a burn-in phase. Range: [3, \(\infty\)]

surrogate_burn_in_algorithm (string, optional):

Specifies the algorithm used to draw new parameter combinations during the burn-in period. Must be from burn_in.

gaussian_kernel (string, optional):

Specifies the 1-dimensional kernel of the Gaussian process which will be used along each dimension of the parameter space. All of the choices below will result in continuous sample paths and their main difference is the degree of smoothness of the results with ‘exp’ yielding the least and ‘gauss’ yielding the most smooth paths. Must be from kernels.

gaussian_optimization_algorithm (string, optional):

Determines the optimization algorithm used for the local search in the fitting of the Gaussian process to the previous parameter combinations. Must be from optimization.

gaussian_optimization_burn_in_algorithm (string, optional):

Specifies the algorithm used to draw new parameter combinations during the burn-in period of the optimization of the Gaussian process. Must be from burn_in.

gaussian_optimization_burn_ins (int, optional):

Number of random evaluation points used during the burn-in of the fitting of the Gaussian process. Range: [3, \(\infty\)]

Raises:

KeyError: If an unsupported instance variable is

encountered (via validate()).

TypeError: If any instance variable is of wrong type (via

validate()).

ValueError: If any instance variable does not match its

possible choices (string) or is out of the expected bounds (numerical) (via validate()).

Note:

A Gaussian hyperparameter search 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. 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), which is 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.

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.

References:

• Carl Edward Rasmussen and Christopher K. I. Williams, MIT Press, 2006

• Julien Villemonteix, Emmanuel Vazquez, and Eric Walter, 2009

Example:

from getml import data
from getml import datasets
from getml import engine
from getml import feature_learning
from getml.feature_learning import aggregations
from getml.feature_learning import loss_functions
from getml import hyperopt
from getml import pipeline
from getml import predictors

# ----------------

engine.set_project("examples")

# ----------------

population_table, peripheral_table = datasets.make_numerical()

# ----------------
# Construct placeholders

population_placeholder = data.Placeholder("POPULATION")
peripheral_placeholder = data.Placeholder("PERIPHERAL")
population_placeholder.join(peripheral_placeholder, "join_key", "time_stamp")

# ----------------
# Base model - any parameters not included
# in param_space will be taken from this.

fe1 = feature_learning.MultirelModel(
    aggregation=[
        aggregations.Count,
        aggregations.Sum
    ],
    loss_function=loss_functions.SquareLoss,
    num_features=10,
    share_aggregations=1.0,
    max_length=1,
    num_threads=0
)

# ----------------
# Base model - any parameters not included
# in param_space will be taken from this.

fe2 = feature_learning.RelboostModel(
    loss_function=loss_functions.SquareLoss,
    num_features=10
)

# ----------------
# Base model - any parameters not included
# in param_space will be taken from this.

predictor = predictors.LinearRegression()

# ----------------

pipe = pipeline.Pipeline(
    population=population_placeholder,
    peripheral=[peripheral_placeholder],
    feature_learners=[fe1, fe2],
    predictors=[predictor]
)

# ----------------
# Build a hyperparameter space.
# We have two feature learners and one
# predictor, so this is how we must
# construct our hyperparameter space.
# If we only wanted to optimize the predictor,
# we could just leave out the feature_learners.

param_space = {
    "feature_learners": [
        {
            "num_features": [10, 50],
        },
        {
            "max_depth": [1, 10],
            "min_num_samples": [100, 500],
            "num_features": [10, 50],
            "reg_lambda": [0.0, 0.1],
            "shrinkage": [0.01, 0.4]
        }],
    "predictors": [
        {
            "reg_lambda": [0.0, 10.0]
        }
    ]
}

# ----------------
# Wrap a GaussianHyperparameterSearch around the reference model

gaussian_search = hyperopt.GaussianHyperparameterSearch(
    pipeline=pipe,
    param_space=param_space,
    n_iter=30,
    score=pipeline.scores.rsquared
)

gaussian_search.fit(
    population_table_training=population_table,
    population_table_validation=population_table,
    peripheral_tables=[peripheral_table]
)

# ----------------

# We want 5 additional iterations.
gaussian_search.n_iter = 5

# We do not want another burn-in-phase,
# so we set ratio_iter to 0.
gaussian_search.ratio_iter = 0.0

# This widens the hyperparameter space.
gaussian_search.param_space["feature_learners"][1]["num_features"] = [10, 100]

# This narrows the hyperparameter space.
gaussian_search.param_space["predictors"][0]["reg_lambda"] = [0.0, 0.0]

# This continues the hyperparameter search using the previous iterations as
# prior knowledge.
gaussian_search.fit(
    population_table_training=population_table,
    population_table_validation=population_table,
    peripheral_tables=[peripheral_table]
)

# ----------------

all_hyp = hyperopt.list_hyperopts()

best_pipeline = gaussian_search.best_pipeline

Methods

fit(population_table_training, …[, …])	Launches the hyperparameter optimization.
refresh()	Reloads the hyperparameter optimization from the engine.
validate()	Validate the parameters of the hyperparameter optimization.

Attributes

best_pipeline	The best pipeline that is part of the hyperparameter optimization.
id	Name of the hyperparameter optimization.
name	Returns the ID of the hyperparameter optimization.
score	The score to be optimized.
type	The algorithm used for the hyperparameter optimization.