from river.datasets import synth
import pandas as pd
import numpy as np
from spotriver.utils.data_conversion import convert_to_df
= 6_000
n_train = 4_000
n_test = n_train + n_test
n_samples = "y"
target_column
= synth.FriedmanDrift(
dataset ='gra',
drift_type=(n_train/4, n_train/2),
position=123
seed
)
= convert_to_df(dataset, n_total=n_train)
train = [f"x{i}" for i in range(1, 11)] + [target_column] train.columns
23 river
Hyperparameter Tuning: Hoeffding Tree Regressor with Friedman Drift Data
This chapter demonstrates hyperparameter tuning for river
’s Hoeffding Tree Regressor (HTR)
with the Friedman drift data set [SOURCE]. The Hoeffding Tree Regressor
is a regression tree that uses the Hoeffding bound to limit the number of splits evaluated at each node, i.e., it predicts a real value for each sample.
23.1 The Friedman Drift Data Set
We will use the Friedman synthetic dataset with concept drifts, which is described in detail in Section E.2. The following parameters are used to generate and handle the data set:
position
: The positions of the concept drifts.n_train
: The number of samples used for training.n_test
: The number of samples used for testing.seed
: The seed for the random number generator.target_column
: The name of the target column.drift_type
: The type of the concept drift.
We will use spotriver
’s convert_to_df
function [SOURCE] to convert the river
data set to a pandas
data frame. Then we add column names x1 until x10 to the first 10 columns of the dataframe and the column name y to the last column of the dataframe.
This data generation is independently repeated for the training and test data sets, because the data sets are generated with concept drifts and the usual train-test split would not work.
= synth.FriedmanDrift(
dataset ='gra',
drift_type=(n_test/4, n_test/2),
position=123
seed
)= convert_to_df(dataset, n_total=n_test)
test = [f"x{i}" for i in range(1, 11)] + [target_column] test.columns
Data sets that are available as pandas
dataframes can easily be passed to the spot
hyperparameter tuner. spotpython
requires a train
and a test
data set, where the column names must be identical.
We combine the train and test data sets and save them to a csv file.
= pd.concat([train, test])
df "./userData/friedman.csv", index=False) df.to_csv(
The Friedman Drift data set described in this section is avaialble as a csv
data file and can be downloaded from github: friedman.csv.
23.2 Setup
23.2.1 General Experiment Setup
To keep track of the different experiments, we use a PREFIX
for the experiment name. The PREFIX
is used to create a unique experiment name. The PREFIX
is also used to create a unique TensorBoard folder, which is used to store the TensorBoard log files.
spotpython
allows the specification of two different types of stopping criteria: first, the number of function evaluations (fun_evals
), and second, the maximum run time in seconds (max_time
). Here, we will set the number of function evaluations to infinity and the maximum run time to one minute.
Furthermore, we set the initial design size (init_size
) to 10. The initial design is used to train the surrogate model. The surrogate model is used to predict the performance of the hyperparameter configurations. The initial design is also used to train the first model. Since the init_size
belongs to the experimental design, it is set in the design_control
dictionary, see [SOURCE].
max_time
is set to one minute for demonstration purposes and init_size
is set to 10 for demonstration purposes. For real experiments, these values should be increased. Note, the total run time may exceed the specified max_time
, because the initial design is always evaluated, even if this takes longer than max_time
.
The following parameters are used to specify the general experiment setup:
= "024"
PREFIX = inf
fun_evals = 1
max_time = 10 init_size
23.2.2 Data Setup
We use the StandardScaler
[SOURCE] from river
as the data-preprocessing model. The StandardScaler
is used to standardize the data set, i.e., it has zero mean and unit variance.
The names of the training and test data sets are train
and test
, respectively. They are available as pandas
dataframes. Both must use the same column names. The column names were set to x1
to x10
for the features and y
for the target column during the data set generation in Section 23.1. Therefore, the target_column
is set to y
(as above).
The following parameters are used to specify the data setup:
= "StandardScaler"
prep_model_name = test
test = train
train = "y" target_column
23.2.3 Evaluation Setup
Here we use the mean_absolute_error
[SOURCE] as the evaluation metric. Internally, this metric is passed to the objective (or loss) function fun_oml_horizon
[SOURCE] and further to the evaluation function eval_oml_horizon
[SOURCE].
spotriver
also supports additional metrics. For example, the metric_river
is used for the river based evaluation via eval_oml_iter_progressive
[SOURCE]. The metric_river
is implemented to simulate the behaviour of the “original” river
metrics.
The following parameter are used to select the evaluation metric:
= "mean_absolute_error" metric_sklearn_name
23.2.4 River-Specific Setup
In the online-machine-learning (OML) setup, the model is trained on a fixed number of observations and then evaluated on a fixed number of observations. The horizon
defines the number of observations that are used for the evaluation. Here, a horizon of 7*24 is used, which corresponds to one week of data.
The oml_grace_period
defines the number of observations that are used for the initial training of the model. This value is relatively small, since the online-machine-learning is trained on the incoming data and the model is updated continuously. However, it needs a certain number of observations to start the training process. Therefore, this short training period aka oml_grace_period
is set to the horizon, i.e., the number of observations that are used for the evaluation. In this case, we use a horizon of 7*24.
The weights
provide a flexible way to define specific requirements, e.g., if the memory is more important than the time, the weight for the memory can be increased. spotriver
stores information about the model’ s score (metric), memory, and time. The hyperparamter tuner requires a single objective. Therefore, a weighted sum of the metric, memory, and time is computed. The weights are defined in the weights
array. The weights
provide a flexible way to define specific requirements, e.g., if the memory is more important than the time, the weight for the memory can be increased.
The weight_coeff
defines a multiplier for the results: results are multiplied by (step/n_steps)**weight_coeff, where n_steps is the total number of iterations. Results from the beginning have a lower weight than results from the end if weight_coeff > 1. If weight_coeff == 0, all results have equal weight. Note, that the weight_coeff
is only used internally for the tuner and does not affect the results that are used for the evaluation or comparisons.
The following parameters are used:
= 7*24
horizon = 7*24
oml_grace_period = np.array([1, 0.01, 0.01])
weights = 0.0 weight_coeff
23.2.5 Model Setup
By using core_model_name = "tree.HoeffdingTreeRegressor"
, the river
model class HoeffdingTreeRegressor
[SOURCE] from the tree
module is selected. For a given core_model_name
, the corresponding hyperparameters are automatically loaded from the associated dictionary, which is stored as a JSON file. The JSON file contains hyperparameter type information, names, and bounds. For river
models, the hyperparameters are stored in the RiverHyperDict
, see [SOURCE]
Alternatively, you can load a local hyper_dict. Simply set river_hyper_dict.json
as the filename. If filename
is set to None
, which is the default, the hyper_dict [SOURCE] is loaded from the spotriver
package.
How hyperparameter levels can be modified is described in Section D.15.1.
The following parameters are used for the model setup:
from spotriver.fun.hyperriver import HyperRiver
from spotriver.hyperdict.river_hyper_dict import RiverHyperDict
= "tree.HoeffdingTreeRegressor"
core_model_name = RiverHyperDict hyperdict
23.2.6 Objective Function Setup
The loss function (metric) values are passed to the objective function fun_oml_horizon
[SOURCE], which combines information about the loss, required memory and time as described in Section 23.2.4.
The following parameters are used:
= HyperRiver().fun_oml_horizon fun
23.2.7 Surrogate Model Setup
The default surrogate model is the Kriging
model, see [SOURCE]. We specify noise
as True
to include noise in the model. An anisotropic
kernel is used, which allows different length scales for each dimension, by setting n_theta = 2
. Furthermore, the interval for the Lambda
value is set to [1e-3, 1e2]
.
These parameters are set in the surrogate_control
dictionary and therefore passed to the surrogate_control_init
function [SOURCE].
= True
noise = 2
n_theta = 1e-3
min_Lambda = 10 max_Lambda
23.2.8 Summary: Setting up the Experiment
At this stage, all required information is available to set up the dictionaries for the hyperparameter tuning. Altogether, the fun_control
, design_control
, surrogate_control
, and optimize_control
dictionaries are initialized as follows:
from spotpython.utils.init import fun_control_init, design_control_init, surrogate_control_init, optimizer_control_init
= HyperRiver().fun_oml_horizon
fun
= fun_control_init(
fun_control ="024",
PREFIX=inf,
fun_evals=1,
max_time
="StandardScaler",
prep_model_name=test,
test=train,
train=target_column,
target_column
="mean_absolute_error",
metric_sklearn_name=7*24,
horizon=7*24,
oml_grace_period=0.0,
weight_coeff=np.array([1, 0.01, 0.01]),
weights
="tree.HoeffdingTreeRegressor",
core_model_name=RiverHyperDict,
hyperdict
)
= design_control_init(
design_control =10,
init_size
)
= surrogate_control_init(
surrogate_control =True,
noise=2,
n_theta=1e-3,
min_Lambda=10,
max_Lambda
)
= optimizer_control_init() optimizer_control
23.2.9 Run the Spot
Optimizer
The class Spot
[SOURCE] is the hyperparameter tuning workhorse. It is initialized with the following parameters, which were specified above.
fun
: the objective functionfun_control
: the dictionary with the control parameters for the objective functiondesign_control
: the dictionary with the control parameters for the experimental designsurrogate_control
: the dictionary with the control parameters for the surrogate modeloptimizer_control
: the dictionary with the control parameters for the optimizer
spotpython
allows maximum flexibility in the definition of the hyperparameter tuning setup. Alternative surrogate models, optimizers, and experimental designs can be used. Thus, interfaces for the surrogate
model, experimental design
, and optimizer
are provided. The default surrogate model is the kriging model, the default optimizer is the differential evolution, and default experimental design is the Latin hypercube design.
Spot
Setup
The following parameters are used for the Spot
setup. These were specified above:
= fun
fun = fun_control
fun_control = design_control
design_control = surrogate_control
surrogate_control = optimizer_control optimizer_control
from spotpython.spot import spot
= spot.Spot(
spot_tuner =fun,
fun=fun_control,
fun_control=design_control,
design_control=surrogate_control,
surrogate_control=optimizer_control,
optimizer_control
)= spot_tuner.run() res
spotpython tuning: 3.19765602089083 [----------] 1.52%
spotpython tuning: 2.237688629112152 [#---------] 8.43%
spotpython tuning: 2.237688629112152 [#---------] 11.83%
spotpython tuning: 2.237688629112152 [#---------] 13.29%
spotpython tuning: 2.237688629112152 [##--------] 17.60%
spotpython tuning: 2.237688629112152 [##--------] 19.21%
spotpython tuning: 2.237688629112152 [##--------] 20.88%
spotpython tuning: 2.237688629112152 [##--------] 23.42%
spotpython tuning: 2.237688629112152 [###-------] 29.15%
spotpython tuning: 2.2376253747495607 [#####-----] 45.23%
spotpython tuning: 2.1658743939851273 [######----] 63.84%
spotpython tuning: 2.1658743939851273 [##########] 95.40%
spotpython tuning: 2.1658743939851273 [##########] 100.00% Done...
23.3 Using the spotgui
The spotgui
[github] provides a convenient way to interact with the hyperparameter tuning process. To obtain the settings from Section 23.2.8, the spotgui
can be started as shown in Figure 26.1.
23.4 Results
After the hyperparameter tuning run is finished, the progress of the hyperparameter tuning can be visualized with spotpython
’s method plot_progress
. The black points represent the performace values (score or metric) of hyperparameter configurations from the initial design, whereas the red points represents the hyperparameter configurations found by the surrogate model based optimization.
=True, filename=None) spot_tuner.plot_progress(log_y
Results can be printed in tabular form.
from spotpython.utils.eda import gen_design_table
print(gen_design_table(fun_control=fun_control, spot=spot_tuner))
| name | type | default | lower | upper | tuned | transform | importance | stars |
|------------------------|--------|------------------|---------|---------|-----------------------|------------------------|--------------|---------|
| grace_period | int | 200 | 10.0 | 1000.0 | 591.0 | None | 20.87 | * |
| max_depth | int | 20 | 2.0 | 20.0 | 2.0 | transform_power_2_int | 0.04 | |
| delta | float | 1e-07 | 1e-08 | 1e-06 | 4.994027045755513e-07 | None | 33.69 | * |
| tau | float | 0.05 | 0.01 | 0.1 | 0.04111324680641631 | None | 0.17 | . |
| leaf_prediction | factor | mean | 0.0 | 2.0 | model | None | 100.00 | *** |
| leaf_model | factor | LinearRegression | 0.0 | 2.0 | LinearRegression | None | 0.01 | |
| model_selector_decay | float | 0.95 | 0.9 | 0.99 | 0.9551828562792138 | None | 3.11 | * |
| splitter | factor | EBSTSplitter | 0.0 | 2.0 | QOSplitter | None | 1.91 | * |
| min_samples_split | int | 5 | 2.0 | 10.0 | 6.0 | None | 0.31 | . |
| binary_split | factor | 0 | 0.0 | 1.0 | 1 | None | 1.06 | * |
| max_size | float | 500.0 | 100.0 | 1000.0 | 685.1800577726956 | None | 3.16 | * |
| memory_estimate_period | int | 6 | 3.0 | 8.0 | 4.0 | transform_power_10_int | 0.00 | |
| stop_mem_management | factor | 0 | 0.0 | 1.0 | 1 | None | 0.04 | |
| remove_poor_attrs | factor | 0 | 0.0 | 1.0 | 0 | None | 0.09 | |
| merit_preprune | factor | 1 | 0.0 | 1.0 | 0 | None | 0.02 | |
A histogram can be used to visualize the most important hyperparameters.
=10.0) spot_tuner.plot_importance(threshold
23.5 Performance of the Model with Default Hyperparameters
23.5.1 Get Default Hyperparameters and Fit the Model
The default hyperparameters, which will be used for a comparion with the tuned hyperparameters, can be obtained with the following commands:
from spotpython.hyperparameters.values import get_default_hyperparameters_as_array
= get_default_hyperparameters_as_array(fun_control) X_start
spotpython
tunes numpy arrays, i.e., the hyperparameters are stored in a numpy array.
from spotpython.hyperparameters.values import get_one_core_model_from_X
= get_one_core_model_from_X(X_start, fun_control, default=True) model_default
23.5.2 Evaluate the Model with Default Hyperparameters
The model with the default hyperparameters can be trained and evaluated. The evaluation function eval_oml_horizon
[SOURCE] is the same function that was used for the hyperparameter tuning. During the hyperparameter tuning, the evaluation function was called from the objective (or loss) function fun_oml_horizon
[SOURCE].
from spotriver.evaluation.eval_bml import eval_oml_horizon
= eval_oml_horizon(
df_eval_default, df_true_default =model_default,
model=fun_control["train"],
train=fun_control["test"],
test=fun_control["target_column"],
target_column=fun_control["horizon"],
horizon=fun_control["oml_grace_period"],
oml_grace_period=fun_control["metric_sklearn"],
metric )
The three performance criteria, i.e., score (metric), runtime, and memory consumption, can be visualized with the following commands:
from spotriver.evaluation.eval_bml import plot_bml_oml_horizon_metrics, plot_bml_oml_horizon_predictions
=["default"]
df_labels= [df_eval_default], log_y=False, df_labels=df_labels, metric=fun_control["metric_sklearn"]) plot_bml_oml_horizon_metrics(df_eval
23.5.3 Show Predictions of the Model with Default Hyperparameters
- Select a subset of the data set for the visualization of the predictions:
- We use the mean, \(m\), of the data set as the center of the visualization.
- We use 100 data points, i.e., \(m \pm 50\) as the visualization window.
= fun_control["test"].shape[0]
m = int(m/2)-50
a = int(m/2)+50
b = [df_true_default[a:b]], target_column=target_column, df_labels=df_labels) plot_bml_oml_horizon_predictions(df_true
23.6 Get SPOT Results
In a similar way, we can obtain the hyperparameters found by spotpython
.
from spotpython.hyperparameters.values import get_one_core_model_from_X
= spot_tuner.to_all_dim(spot_tuner.min_X.reshape(1,-1))
X = get_one_core_model_from_X(X, fun_control) model_spot
= eval_oml_horizon(
df_eval_spot, df_true_spot =model_spot,
model=fun_control["train"],
train=fun_control["test"],
test=fun_control["target_column"],
target_column=fun_control["horizon"],
horizon=fun_control["oml_grace_period"],
oml_grace_period=fun_control["metric_sklearn"],
metric )
=["default", "spot"]
df_labels= [df_eval_default, df_eval_spot], log_y=False, df_labels=df_labels, metric=fun_control["metric_sklearn"]) plot_bml_oml_horizon_metrics(df_eval
= [df_true_default[a:b], df_true_spot[a:b]], target_column=target_column, df_labels=df_labels) plot_bml_oml_horizon_predictions(df_true
from spotpython.plot.validation import plot_actual_vs_predicted
=df_true_default[target_column], y_pred=df_true_default["Prediction"], title="Default")
plot_actual_vs_predicted(y_test=df_true_spot[target_column], y_pred=df_true_spot["Prediction"], title="SPOT") plot_actual_vs_predicted(y_test
23.7 Visualize Regression Trees
= dataset.take(n_samples)
dataset_f print(f"n_samples: {n_samples}")
for x, y in dataset_f:
model_default.learn_one(x, y)
n_samples: 10000
- Since the trees are large, the visualization is suppressed by default.
- To visualize the trees, uncomment the following line.
# model_default.draw()
model_default.summary
{'n_nodes': 23,
'n_branches': 11,
'n_leaves': 12,
'n_active_leaves': 12,
'n_inactive_leaves': 0,
'height': 7,
'total_observed_weight': 14168.0}
23.7.1 Spot Model
print(f"n_samples: {n_samples}")
= dataset.take(n_samples)
dataset_f for x, y in dataset_f:
model_spot.learn_one(x, y)
n_samples: 10000
- Since the trees are large, the visualization is suppressed by default.
- To visualize the trees, uncomment the following line.
# model_spot.draw()
model_spot.summary
{'n_nodes': 11,
'n_branches': 5,
'n_leaves': 6,
'n_active_leaves': 4,
'n_inactive_leaves': 2,
'height': 5,
'total_observed_weight': 14168.0}
from spotpython.utils.eda import compare_two_tree_models
print(compare_two_tree_models(model_default, model_spot))
| Parameter | Default | Spot |
|-----------------------|-----------|--------|
| n_nodes | 23 | 11 |
| n_branches | 11 | 5 |
| n_leaves | 12 | 6 |
| n_active_leaves | 12 | 4 |
| n_inactive_leaves | 0 | 2 |
| height | 7 | 5 |
| total_observed_weight | 14168 | 14168 |
23.8 Detailed Hyperparameter Plots
=3) spot_tuner.plot_important_hyperparameter_contour(max_imp
grace_period: 20.873139039731644
max_depth: 0.03511587880120552
delta: 33.69309470902903
tau: 0.1679770885200379
leaf_prediction: 100.0
leaf_model: 0.006846012567192482
model_selector_decay: 3.1056711928301426
splitter: 1.9103105617533682
min_samples_split: 0.31151861155710786
binary_split: 1.0635492633913082
max_size: 3.1639735224217698
memory_estimate_period: 0.003630545866184321
stop_mem_management: 0.03606141484237544
remove_poor_attrs: 0.09174212775479652
merit_preprune: 0.018082433169196704
23.9 Parallel Coordinates Plots
spot_tuner.parallel_plot()