View Jupyter notebook on the GitHub.
Ensembles#
This notebook contains the simple examples of using the ensemble models with ETNA library.
Table of contents
Loading dataset
Building pipelines
Ensembles
VotingEnsemble
StackingEnsamble
Results
[1]:
import warnings
warnings.filterwarnings("ignore")
[2]:
import pandas as pd
from etna.datasets import TSDataset
from etna.metrics import MAE
from etna.metrics import MAPE
from etna.metrics import MSE
from etna.metrics import SMAPE
from etna.models import CatBoostMultiSegmentModel
from etna.models import NaiveModel
from etna.models import SeasonalMovingAverageModel
from etna.pipeline import Pipeline
from etna.transforms import LagTransform
1. Loading dataset#
In this notebook we will work with the dataset contains only one segment with monthly wine sales. Working process with the dataset containing more segments will be absolutely the same.
[3]:
df = pd.read_csv("data/monthly-australian-wine-sales.csv")
df["timestamp"] = pd.to_datetime(df["month"])
df["target"] = df["sales"]
df.drop(columns=["month", "sales"], inplace=True)
df["segment"] = "main"
ts = TSDataset(df=df, freq="MS")
ts.plot()
2. Building pipelines#
Given the sales’ history, we want to select the best model(pipeline) to forecast future sales.
[4]:
HORIZON = 3
N_FOLDS = 5
Let’s build four pipelines using the different models
[5]:
naive_pipeline = Pipeline(model=NaiveModel(lag=12), transforms=[], horizon=HORIZON)
seasonalma_pipeline = Pipeline(
model=SeasonalMovingAverageModel(window=5, seasonality=12),
transforms=[],
horizon=HORIZON,
)
catboost_pipeline = Pipeline(
model=CatBoostMultiSegmentModel(),
transforms=[LagTransform(lags=[6, 7, 8, 9, 10, 11, 12], in_column="target")],
horizon=HORIZON,
)
pipeline_names = ["naive", "moving average", "catboost"]
pipelines = [naive_pipeline, seasonalma_pipeline, catboost_pipeline]
And evaluate their performance on the backtest
[6]:
metrics = []
for pipeline in pipelines:
metrics.append(
pipeline.backtest(
ts=ts,
metrics=[MAE(), MSE(), SMAPE(), MAPE()],
n_folds=N_FOLDS,
aggregate_metrics=True,
n_jobs=5,
)[0].iloc[:, 1:]
)
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[7]:
metrics = pd.concat(metrics)
metrics.index = pipeline_names
metrics
[7]:
| MAE | MSE | SMAPE | MAPE | |
|---|---|---|---|---|
| naive | 2437.466667 | 1.089199e+07 | 9.949886 | 10.222106 |
| moving average | 1913.826667 | 6.113701e+06 | 7.897570 | 7.824056 |
| catboost | 2271.766726 | 8.923741e+06 | 9.376638 | 10.013138 |
3. Ensembles#
To improve the performance of the individual models, we can try to make ensembles out of them. Our library contains two ensembling methods, which we will try on now.
3.1 VotingEnsemble#
VotingEnsemble forecasts future values with weighted averaging of it’s pipelines forecasts.
[8]:
from etna.ensembles import VotingEnsemble
By default, VotingEnsemble uses uniform weights for the pipelines’ forecasts. However, you can specify the weights manually using the weights parameter. The higher weight the more you trust the base model. In addition, you can set weights with the literal auto. In this case, the weights of pipelines are assigned with the importances got from feature_importance_ property of regressor.
Note: The weights are automatically normalized.
[9]:
voting_ensemble = VotingEnsemble(pipelines=pipelines, weights=[1, 9, 4], n_jobs=4)
[10]:
voting_ensamble_metrics = voting_ensemble.backtest(
ts=ts,
metrics=[MAE(), MSE(), SMAPE(), MAPE()],
n_folds=N_FOLDS,
aggregate_metrics=True,
n_jobs=2,
)[0].iloc[:, 1:]
voting_ensamble_metrics.index = ["voting ensemble"]
voting_ensamble_metrics
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[10]:
| MAE | MSE | SMAPE | MAPE | |
|---|---|---|---|---|
| voting ensemble | 1972.207943 | 6.685831e+06 | 8.172377 | 8.299714 |
3.2 StackingEnsemble#
StackingEnsemble forecasts future using the metamodel to combine the forecasts of it’s pipelines.
[11]:
from etna.ensembles import StackingEnsemble
By default, StackingEnsemble uses only the pipelines’ forecasts as features for the final_model. However, you can specify the additional features using the features_to_use parameter. The following values are possible:
None - use only the pipelines’ forecasts(default)
List[str] - use the pipelines’ forecasts + features from the list
“all” - use all the available features
Note: It is possible to use only the features available for the base models.
[12]:
stacking_ensemble_unfeatured = StackingEnsemble(pipelines=pipelines, n_folds=10, n_jobs=4)
[13]:
stacking_ensamble_metrics = stacking_ensemble_unfeatured.backtest(
ts=ts,
metrics=[MAE(), MSE(), SMAPE(), MAPE()],
n_folds=N_FOLDS,
aggregate_metrics=True,
n_jobs=2,
)[0].iloc[:, 1:]
stacking_ensamble_metrics.index = ["stacking ensemble"]
stacking_ensamble_metrics
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[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.6s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.6s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.6s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.8s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 20.5s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 20.5s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 20.6s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 20.6s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.3s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.3s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.3s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.1s
[Parallel(n_jobs=2)]: Done 1 tasks | elapsed: 22.0s
[Parallel(n_jobs=2)]: Done 2 tasks | elapsed: 22.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 1.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 1.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 2.3s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 2.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 1.6s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 1.7s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 3.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 3.4s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 4.8s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 5.2s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 6.6s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 6.8s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 7.8s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 8.5s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 9.8s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 10.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 11.5s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 11.9s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 13.4s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 13.4s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 14.8s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 15.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 16.6s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 16.6s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.6s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 17.5s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 17.5s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.8s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.9s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.9s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 1.0s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 1.0s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.6s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.7s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 20.5s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 20.5s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.5s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 21.2s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 21.2s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.7s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.7s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=2)]: Done 3 out of 5 | elapsed: 44.4s remaining: 29.6s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.6s
[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 1.6s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 1.2s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.4s
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 2.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.8s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 1.8s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 2.7s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 3.5s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 4.5s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 5.5s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 6.5s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 7.5s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 8.4s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 9.3s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 9.3s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 4 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 5 tasks | elapsed: 0.4s
[Parallel(n_jobs=1)]: Done 6 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 7 tasks | elapsed: 0.5s
[Parallel(n_jobs=1)]: Done 8 tasks | elapsed: 0.6s
[Parallel(n_jobs=1)]: Done 9 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 10 tasks | elapsed: 0.7s
[Parallel(n_jobs=1)]: Done 1 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 2 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 3 tasks | elapsed: 0.1s
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[Parallel(n_jobs=4)]: Done 3 tasks | elapsed: 12.8s
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[Parallel(n_jobs=4)]: Done 1 tasks | elapsed: 0.0s
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[Parallel(n_jobs=2)]: Done 5 out of 5 | elapsed: 58.2s finished
[Parallel(n_jobs=2)]: Using backend MultiprocessingBackend with 2 concurrent workers.
[Parallel(n_jobs=4)]: Done 2 tasks | elapsed: 0.1s
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[Parallel(n_jobs=2)]: Done 3 out of 5 | elapsed: 0.6s remaining: 0.4s
[Parallel(n_jobs=2)]: Done 5 out of 5 | elapsed: 0.7s finished
[Parallel(n_jobs=2)]: Using backend MultiprocessingBackend with 2 concurrent workers.
[Parallel(n_jobs=2)]: Done 1 tasks | elapsed: 0.2s
[Parallel(n_jobs=2)]: Done 2 tasks | elapsed: 0.3s
[Parallel(n_jobs=2)]: Done 3 tasks | elapsed: 0.3s
[Parallel(n_jobs=2)]: Done 5 out of 5 | elapsed: 0.4s finished
[13]:
| MAE | MSE | SMAPE | MAPE | |
|---|---|---|---|---|
| stacking ensemble | 1986.453478 | 7.309679e+06 | 8.276998 | 8.328746 |
In addition, it is also possible to specify the final_model. You can use any regression model with the sklearn interface for this purpose.
3.3 Results#
Finally, let’s take a look at the results of our experiments
[14]:
metrics = pd.concat([metrics, voting_ensamble_metrics, stacking_ensamble_metrics])
metrics
[14]:
| MAE | MSE | SMAPE | MAPE | |
|---|---|---|---|---|
| naive | 2437.466667 | 1.089199e+07 | 9.949886 | 10.222106 |
| moving average | 1913.826667 | 6.113701e+06 | 7.897570 | 7.824056 |
| catboost | 2271.766726 | 8.923741e+06 | 9.376638 | 10.013138 |
| voting ensemble | 1972.207943 | 6.685831e+06 | 8.172377 | 8.299714 |
| stacking ensemble | 1986.453478 | 7.309679e+06 | 8.276998 | 8.328746 |