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"""This code implements benchmark for the black box optimization algorithms, applied to
a task of optimizing parameters of ML algorithms for the task of supervised learning.
The code implements benchmark on 4 datasets where parameters for 6
classes of supervised models are tuned to optimize performance on
datasets. Supervised learning models implementations are taken from
sklearn.
Regression learning task is solved on 2 datasets, and classification on
the rest of datasets. 3 model classes are regression models, and rest
are classification models.
"""
import json
import math
from collections import defaultdict
from datetime import datetime
from urllib import urlopen
from urllib.error import HTTPError
import numpy as np
from joblib import Parallel, delayed
from sklearn.base import ClassifierMixin, RegressorMixin
from sklearn.datasets import (
fetch_california_housing,
fetch_mldata,
load_boston,
load_digits,
)
from sklearn.metrics import log_loss, r2_score
from sklearn.model_selection import train_test_split
from sklearn.neural_network import MLPClassifier, MLPRegressor
from sklearn.preprocessing import StandardScaler
from sklearn.svm import SVC, SVR
from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor
from skopt import forest_minimize, gbrt_minimize, gp_minimize
from skopt.space import Categorical, Real
MODEL_PARAMETERS = "model parameters"
MODEL_BACKEND = "model backend"
# functions below are used to apply non - linear maps to parameter values, eg
# -3.0 -> 0.001
def pow10map(x):
return 10.0**x
def pow2intmap(x):
return int(2.0**x)
def nop(x):
return x
nnparams = {
# up to 1024 neurons
'hidden_layer_sizes': (Real(1.0, 10.0), pow2intmap),
'activation': (Categorical(['identity', 'logistic', 'tanh', 'relu']), nop),
'solver': (Categorical(['lbfgs', 'sgd', 'adam']), nop),
'alpha': (Real(-5.0, -1), pow10map),
'batch_size': (Real(5.0, 10.0), pow2intmap),
'learning_rate': (Categorical(['constant', 'invscaling', 'adaptive']), nop),
'max_iter': (Real(5.0, 8.0), pow2intmap),
'learning_rate_init': (Real(-5.0, -1), pow10map),
'power_t': (Real(0.01, 0.99), nop),
'momentum': (Real(0.1, 0.98), nop),
'nesterovs_momentum': (Categorical([True, False]), nop),
'beta_1': (Real(0.1, 0.98), nop),
'beta_2': (Real(0.1, 0.9999999), nop),
}
MODELS = {
MLPRegressor: nnparams,
SVR: {
'C': (Real(-4.0, 4.0), pow10map),
'epsilon': (Real(-4.0, 1.0), pow10map),
'gamma': (Real(-4.0, 1.0), pow10map),
},
DecisionTreeRegressor: {
'max_depth': (Real(1.0, 4.0), pow2intmap),
'min_samples_split': (Real(1.0, 8.0), pow2intmap),
},
MLPClassifier: nnparams,
SVC: {'C': (Real(-4.0, 4.0), pow10map), 'gamma': (Real(-4.0, 1.0), pow10map)},
DecisionTreeClassifier: {
'max_depth': (Real(1.0, 4.0), pow2intmap),
'min_samples_split': (Real(1.0, 8.0), pow2intmap),
},
}
# every dataset should have have a mapping to the mixin that can handle it.
DATASETS = {
"Boston": RegressorMixin,
"Housing": RegressorMixin,
"digits": ClassifierMixin,
"Climate Model Crashes": ClassifierMixin,
}
# bunch of dataset preprocessing functions below
def split_normalize(X, y, random_state):
"""Splits data into training and validation parts. Test data is assumed to be used
after optimization.
Parameters
----------
* `X` [array-like, shape = (n_samples, n_features)]:
Training data.
* `y`: [array-like, shape = (n_samples)]:
Target values.
Returns
-------
Split of data into training and validation sets.
70% of data is used for training, rest for validation.
"""
X_train, X_test, y_train, y_test = train_test_split(
X, y, train_size=0.7, random_state=random_state
)
sc = StandardScaler()
sc.fit(X_train, y_train)
X_train, X_test = sc.transform(X_train), sc.transform(X_test)
return X_train, y_train, X_test, y_test
# this is used to process the output of fetch_mldata
def load_data_target(name):
"""Loads data and target given the name of the dataset."""
if name == "Boston":
data = load_boston()
elif name == "Housing":
data = fetch_california_housing()
dataset_size = 1000 # this is necessary so that SVR does not slow down too much
data["data"] = data["data"][:dataset_size]
data["target"] = data["target"][:dataset_size]
elif name == "digits":
data = load_digits()
elif name == "Climate Model Crashes":
try:
data = fetch_mldata("climate-model-simulation-crashes")
except HTTPError as e:
print(e)
url = "https://archive.ics.uci.edu/ml/machine-learning-databases/00252/pop_failures.dat"
data = urlopen(url).read().split('\n')[1:]
data = [[float(v) for v in d.split()] for d in data]
samples = np.array(data)
data = dict()
data["data"] = samples[:, :-1]
data["target"] = np.array(samples[:, -1], dtype=np.int)
else:
raise ValueError("dataset not supported.")
return data["data"], data["target"]
class MLBench:
"""A class which is used to perform benchmarking of black box optimization
algorithms on various machine learning problems. On instantiation, the dataset is
loaded that is used for experimentation and is kept in memory in order to avoid
delays due to reloading of data.
Parameters
----------
* `model`: scikit-learn estimator
An instance of a sklearn estimator.
* `dataset`: str
Name of the dataset.
* `random_state`: seed
Initialization for the random number generator in numpy.
"""
def __init__(self, model, dataset, random_state):
X, Y = load_data_target(dataset)
self.X_train, self.y_train, self.X_test, self.y_test = split_normalize(
X, Y, random_state
)
self.random_state = random_state
self.model = model
self.space = MODELS[model]
def evaluate(self, point):
"""Fits model using the particular setting of hyperparameters and evaluates the
model validation data.
Parameters
----------
* `point`: dict
A mapping of parameter names to the corresponding values
Returns
-------
* `score`: float
Score (more is better!) for some specific point
"""
X_train, y_train, X_test, y_test = (
self.X_train,
self.y_train,
self.X_test,
self.y_test,
)
# apply transformation to model parameters, for example exp transformation
point_mapped = {}
for param, val in point.items():
point_mapped[param] = self.space[param][1](val)
model_instance = self.model(**point_mapped)
if 'random_state' in model_instance.get_params():
model_instance.set_params(random_state=self.random_state)
min_obj_val = -5.0
# Infeasible parameters are expected to raise an exception, thus the try
# catch below, infeasible parameters yield assumed smallest objective.
try:
model_instance.fit(X_train, y_train)
if isinstance(model_instance, RegressorMixin): # r^2 metric
y_predicted = model_instance.predict(X_test)
score = r2_score(y_test, y_predicted)
elif isinstance(model_instance, ClassifierMixin): # log loss
y_predicted = model_instance.predict_proba(X_test)
score = -log_loss(
y_test, y_predicted
) # in the context of this function, the higher score is better
# avoid any kind of singularitites, eg probability being zero, and thus breaking the log_loss
if math.isnan(score):
score = min_obj_val
score = max(score, min_obj_val) # this is necessary to avoid -inf or NaN
except BaseException:
score = min_obj_val # on error: return assumed smallest value of objective function
return score
# this is necessary to generate table for README in the end
table_template = """|Blackbox Function| Minimum | Best minimum | Mean f_calls to min | Std f_calls to min | Fastest f_calls to min
------------------|------------|-----------|---------------------|--------------------|-----------------------
| """
def calculate_performance(all_data):
"""Calculates the performance metrics as found in "benchmarks" folder of scikit-
optimize and prints them in console.
Parameters
----------
* `all_data`: dict
Traces data collected during run of algorithms. For more details, see
'evaluate_optimizer' function.
"""
sorted_traces = defaultdict(list)
for model in all_data:
for dataset in all_data[model]:
for algorithm in all_data[model][dataset]:
data = all_data[model][dataset][algorithm]
# leave only best objective values at particular iteration
best = [[v[-1] for v in d] for d in data]
supervised_learning_type = (
"Regression" if ("Regressor" in model) else "Classification"
)
# for every item in sorted_traces it is 2d array, where first dimension corresponds to
# particular repeat of experiment, and second dimension corresponds to index
# of optimization step during optimization
key = (algorithm, supervised_learning_type)
sorted_traces[key].append(best)
# calculate averages
for key in sorted_traces:
# the meta objective: average over multiple tasks
mean_obj_vals = np.mean(sorted_traces[key], axis=0)
minimums = np.min(mean_obj_vals, axis=1)
f_calls = np.argmin(mean_obj_vals, axis=1)
min_mean = np.mean(minimums)
min_stdd = np.std(minimums)
min_best = np.min(minimums)
f_mean = np.mean(f_calls)
f_stdd = np.std(f_calls)
f_best = np.min(f_calls)
def fmt(float_value):
return "%.3f" % float_value
output = (
str(key[0])
+ " | "
+ " | ".join(
[fmt(min_mean) + " +/- " + fmt(min_stdd)]
+ [fmt(v) for v in [min_best, f_mean, f_stdd, f_best]]
)
)
result = table_template + output
print("")
print(key[1])
print(result)
def evaluate_optimizer(surrogate_minimize, model, dataset, n_calls, random_state):
"""Evaluates some estimator for the task of optimization of parameters of some
model, given limited number of model evaluations.
Parameters
----------
* `surrogate_minimize`:
Minimization function from skopt (eg gp_minimize) that is used
to minimize the objective.
* `model`: scikit-learn estimator.
sklearn estimator used for parameter tuning.
* `dataset`: str
Name of dataset to train ML model on.
* `n_calls`: int
Budget of evaluations
* `random_state`: seed
Set the random number generator in numpy.
Returns
-------
* `trace`: list of tuples
(p, f(p), best), where p is a dictionary of the form "param name":value,
and f(p) is performance achieved by the model for configuration p
and best is the best value till that index.
Such a list contains history of execution of optimization.
"""
# below seed is necessary for processes which fork at the same time
# so that random numbers generated in processes are different
np.random.seed(random_state)
problem = MLBench(model, dataset, random_state)
space = problem.space
dimensions_names = sorted(space)
dimensions = [space[d][0] for d in dimensions_names]
def objective(x):
# convert list of dimension values to dictionary
x = dict(zip(dimensions_names, x))
# the result of "evaluate" is accuracy / r^2, which is the more the better
y = -problem.evaluate(x)
return y
# optimization loop
result = surrogate_minimize(
objective, dimensions, n_calls=n_calls, random_state=random_state
)
trace = []
min_y = np.inf
for x, y in zip(result.x_iters, result.func_vals):
min_y = min(y, min_y)
x_dct = dict(zip(dimensions_names, x))
trace.append((x_dct, y, min_y))
print(random_state)
return trace
def run(n_calls=32, n_runs=1, save_traces=True, n_jobs=1):
"""Main function used to run the experiments.
Parameters
----------
* `n_calls`: int
Evaluation budget.
* `n_runs`: int
Number of times to repeat the optimization in order to average out noise.
* `save_traces`: bool
Whether or not to save data collected during optimization
* `n_jobs`: int
Number of different repeats of optimization to run in parallel.
"""
surrogate_minimizers = [gbrt_minimize, forest_minimize, gp_minimize]
selected_models = sorted(MODELS, key=lambda x: x.__name__)
selected_datasets = DATASETS.keys()
# all the parameter values and objectives collected during execution are stored in list below
all_data = {}
for model in selected_models:
all_data[model] = {}
for dataset in selected_datasets:
if not issubclass(model, DATASETS[dataset]):
continue
all_data[model][dataset] = {}
for surrogate_minimizer in surrogate_minimizers:
print(surrogate_minimizer.__name__, model.__name__, dataset)
seeds = np.random.randint(0, 2**30, n_runs)
raw_trace = Parallel(n_jobs=n_jobs)(
delayed(evaluate_optimizer)(
surrogate_minimizer, model, dataset, n_calls, seed
)
for seed in seeds
)
all_data[model][dataset][surrogate_minimizer.__name__] = raw_trace
# convert the model keys to strings so that results can be saved as json
all_data = {k.__name__: v for k, v in all_data.items()}
# dump the recorded objective values as json
if save_traces:
with open(datetime.now().strftime("%m_%Y_%d_%H_%m_%s") + '.json', 'w') as f:
json.dump(all_data, f)
calculate_performance(all_data)
if __name__ == "__main__":
import argparse
parser = argparse.ArgumentParser()
parser.add_argument(
'--n_calls', nargs="?", default=50, type=int, help="Number of function calls."
)
parser.add_argument(
'--n_runs',
nargs="?",
default=10,
type=int,
help="Number of re-runs of single algorithm on single instance of a "
"problem, in order to average out the noise.",
)
parser.add_argument(
'--save_traces',
nargs="?",
default=False,
type=bool,
help="Whether to save pairs (point, objective, best_objective) obtained"
" during experiments in a json file.",
)
parser.add_argument(
'--n_jobs',
nargs="?",
default=1,
type=int,
help="Number of worker processes used for the benchmark.",
)
args = parser.parse_args()
run(args.n_calls, args.n_runs, args.save_traces, args.n_jobs)
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