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Tuning models with Optuna#

In this notebook we will see how to tune the hyperparameters of a GlutonTS model using Optuna. For this example, we are going to tune a PyTorch-based DeepAREstimator.

Note: to keep the running time of this example short, here we consider a small-scale dataset, and tune only two hyperparameters over a very small number of tuning rounds (“trials”). In real applications, especially for larger datasets, you will probably need to increase the search space and increase the number of trials.

Data loading and processing#

[1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import json

from gluonts.dataset.repository import get_dataset
from gluonts.dataset.util import to_pandas

[2]:

dataset = get_dataset("m4_hourly")

Extract and split training and test data sets#

In general, the datasets provided by GluonTS are objects that consists of three things:

  • dataset.train is an iterable collection of data entries used for training. Each entry corresponds to one time series

  • dataset.test is an iterable collection of data entries used for inference. The test dataset is an extended version of the train dataset that contains a window in the end of each time series that was not seen during training. This window has length equal to the recommended prediction length.

  • dataset.metadata contains metadata of the dataset such as the frequency of the time series, a recommended prediction horizon, associated features, etc.

We can check details of the dataset.metadata.

[3]:

print(f"Recommended prediction horizon: {dataset.metadata.prediction_length}")
print(f"Frequency of the time series: {dataset.metadata.freq}")

Recommended prediction horizon: 48
Frequency of the time series: H

This is what the data looks like (first training series, first two weeks of data)

[4]:

to_pandas(next(iter(dataset.train)))[: 14 * 24].plot()
plt.grid(which="both")
plt.legend(["train series"], loc="upper left")
plt.show()
../../_images/tutorials_advanced_topics_hp_tuning_with_optuna_6_0.png

Tuning parameters of DeepAR estimator#

[5]:

import optuna
import torch
from gluonts.dataset.split import split
from gluonts.evaluation import Evaluator
from gluonts.torch.model.deepar import DeepAREstimator

/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

We will now tune the DeepAR estimator on our training data using Optuna. We choose two hyperparameters num_layers and hidden_size to optimize.

First, we define a dataentry_to_dataframe method to transform a DataEntry into a pandas.DataFrame. Second, we define an DeepARTuningObjective class used in tuning process of Optuna. The class can be configured with the dataset, prediction length and data frequency, and the metric to be used for evaluating the model. In the __init__ method, we initialize the objective and split the dataset using split method existed in our GluonTS project. - validation_input: the input part used in validation - validation_label: the label part used in validation In the get_params method, we define what hyperparameters to be tuned within given range. In the __call__ method, we define the way the DeepAREstimator is used in training and validation.

[6]:

def dataentry_to_dataframe(entry):
    df = pd.DataFrame(
        entry["target"],
        columns=[entry.get("item_id")],
        index=pd.period_range(
            start=entry["start"], periods=len(entry["target"]), freq=entry["start"].freq
        ),
    )

    return df


class DeepARTuningObjective:
    def __init__(
        self, dataset, prediction_length, freq, metric_type="mean_wQuantileLoss"
    ):
        self.dataset = dataset
        self.prediction_length = prediction_length
        self.freq = freq
        self.metric_type = metric_type

        self.train, test_template = split(dataset, offset=-self.prediction_length)
        validation = test_template.generate_instances(
            prediction_length=prediction_length
        )
        self.validation_input = [entry[0] for entry in validation]
        self.validation_label = [
            dataentry_to_dataframe(entry[1]) for entry in validation
        ]

    def get_params(self, trial) -> dict:
        return {
            "num_layers": trial.suggest_int("num_layers", 1, 5),
            "hidden_size": trial.suggest_int("hidden_size", 10, 50),
        }

    def __call__(self, trial):
        params = self.get_params(trial)
        estimator = DeepAREstimator(
            num_layers=params["num_layers"],
            hidden_size=params["hidden_size"],
            prediction_length=self.prediction_length,
            freq=self.freq,
            trainer_kwargs={
                "enable_progress_bar": False,
                "enable_model_summary": False,
                "max_epochs": 10,
            },
        )

        predictor = estimator.train(self.train, cache_data=True)
        forecast_it = predictor.predict(self.validation_input)

        forecasts = list(forecast_it)

        evaluator = Evaluator(quantiles=[0.1, 0.5, 0.9])
        agg_metrics, item_metrics = evaluator(
            self.validation_label, forecasts, num_series=len(self.dataset)
        )
        return agg_metrics[self.metric_type]

We can now invoke the Optuna tuning process.

[7]:

import time

start_time = time.time()
study = optuna.create_study(direction="minimize")
study.optimize(
    DeepARTuningObjective(
        dataset.train, dataset.metadata.prediction_length, dataset.metadata.freq
    ),
    n_trials=5,
)

print("Number of finished trials: {}".format(len(study.trials)))

print("Best trial:")
trial = study.best_trial

print("  Value: {}".format(trial.value))

print("  Params: ")
for key, value in trial.params.items():
    print("    {}: {}".format(key, value))
print(time.time() - start_time)

[I 2024-05-31 18:25:30,746] A new study created in memory with name: no-name-33a5f099-a6bc-49b7-ae60-e8db6064e006
INFO: GPU available: False, used: False
INFO:lightning.pytorch.utilities.rank_zero:GPU available: False, used: False
INFO: TPU available: False, using: 0 TPU cores
INFO:lightning.pytorch.utilities.rank_zero:TPU available: False, using: 0 TPU cores
INFO: IPU available: False, using: 0 IPUs
INFO:lightning.pytorch.utilities.rank_zero:IPU available: False, using: 0 IPUs
INFO: HPU available: False, using: 0 HPUs
INFO:lightning.pytorch.utilities.rank_zero:HPU available: False, using: 0 HPUs
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/connectors/logger_connector/logger_connector.py:67: Starting from v1.9.0, `tensorboardX` has been removed as a dependency of the `lightning.pytorch` package, due to potential conflicts with other packages in the ML ecosystem. For this reason, `logger=True` will use `CSVLogger` as the default logger, unless the `tensorboard` or `tensorboardX` packages are found. Please `pip install lightning[extra]` or one of them to enable TensorBoard support by default
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/configuration_validator.py:74: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
INFO: Epoch 0, global step 50: 'train_loss' reached 5.97729 (best 5.97729), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 0, global step 50: 'train_loss' reached 5.97729 (best 5.97729), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO: Epoch 1, global step 100: 'train_loss' reached 5.08986 (best 5.08986), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 1, global step 100: 'train_loss' reached 5.08986 (best 5.08986), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO: Epoch 2, global step 150: 'train_loss' reached 4.82337 (best 4.82337), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 2, global step 150: 'train_loss' reached 4.82337 (best 4.82337), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO: Epoch 3, global step 200: 'train_loss' reached 4.66130 (best 4.66130), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 3, global step 200: 'train_loss' reached 4.66130 (best 4.66130), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO: Epoch 4, global step 250: 'train_loss' reached 4.65298 (best 4.65298), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 4, global step 250: 'train_loss' reached 4.65298 (best 4.65298), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO: Epoch 5, global step 300: 'train_loss' reached 4.45146 (best 4.45146), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 5, global step 300: 'train_loss' reached 4.45146 (best 4.45146), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO: Epoch 6, global step 350: 'train_loss' reached 4.43675 (best 4.43675), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=6-step=350.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 6, global step 350: 'train_loss' reached 4.43675 (best 4.43675), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=6-step=350.ckpt' as top 1
INFO: Epoch 7, global step 400: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 7, global step 400: 'train_loss' was not in top 1
INFO: Epoch 8, global step 450: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 8, global step 450: 'train_loss' was not in top 1
INFO: Epoch 9, global step 500: 'train_loss' reached 4.42556 (best 4.42556), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=9-step=500.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 9, global step 500: 'train_loss' reached 4.42556 (best 4.42556), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_1/checkpoints/epoch=9-step=500.ckpt' as top 1
INFO: `Trainer.fit` stopped: `max_epochs=10` reached.
INFO:lightning.pytorch.utilities.rank_zero:`Trainer.fit` stopped: `max_epochs=10` reached.
Running evaluation: 100%|██████████| 414/414 [00:00<00:00, 8080.46it/s]
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
[I 2024-05-31 18:25:46,776] Trial 0 finished with value: 0.12650161257328987 and parameters: {'num_layers': 2, 'hidden_size': 23}. Best is trial 0 with value: 0.12650161257328987.
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/torch/nn/modules/rnn.py:83: UserWarning: dropout option adds dropout after all but last recurrent layer, so non-zero dropout expects num_layers greater than 1, but got dropout=0.1 and num_layers=1
  warnings.warn("dropout option adds dropout after all but last "
INFO: GPU available: False, used: False
INFO:lightning.pytorch.utilities.rank_zero:GPU available: False, used: False
INFO: TPU available: False, using: 0 TPU cores
INFO:lightning.pytorch.utilities.rank_zero:TPU available: False, using: 0 TPU cores
INFO: IPU available: False, using: 0 IPUs
INFO:lightning.pytorch.utilities.rank_zero:IPU available: False, using: 0 IPUs
INFO: HPU available: False, using: 0 HPUs
INFO:lightning.pytorch.utilities.rank_zero:HPU available: False, using: 0 HPUs
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/configuration_validator.py:74: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
INFO: Epoch 0, global step 50: 'train_loss' reached 5.95037 (best 5.95037), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 0, global step 50: 'train_loss' reached 5.95037 (best 5.95037), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO: Epoch 1, global step 100: 'train_loss' reached 5.34065 (best 5.34065), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 1, global step 100: 'train_loss' reached 5.34065 (best 5.34065), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO: Epoch 2, global step 150: 'train_loss' reached 4.51309 (best 4.51309), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 2, global step 150: 'train_loss' reached 4.51309 (best 4.51309), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO: Epoch 3, global step 200: 'train_loss' reached 4.33170 (best 4.33170), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 3, global step 200: 'train_loss' reached 4.33170 (best 4.33170), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO: Epoch 4, global step 250: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 4, global step 250: 'train_loss' was not in top 1
INFO: Epoch 5, global step 300: 'train_loss' reached 4.28196 (best 4.28196), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 5, global step 300: 'train_loss' reached 4.28196 (best 4.28196), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO: Epoch 6, global step 350: 'train_loss' reached 4.17429 (best 4.17429), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=6-step=350.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 6, global step 350: 'train_loss' reached 4.17429 (best 4.17429), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=6-step=350.ckpt' as top 1
INFO: Epoch 7, global step 400: 'train_loss' reached 4.03278 (best 4.03278), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 7, global step 400: 'train_loss' reached 4.03278 (best 4.03278), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_2/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO: Epoch 8, global step 450: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 8, global step 450: 'train_loss' was not in top 1
INFO: Epoch 9, global step 500: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 9, global step 500: 'train_loss' was not in top 1
INFO: `Trainer.fit` stopped: `max_epochs=10` reached.
INFO:lightning.pytorch.utilities.rank_zero:`Trainer.fit` stopped: `max_epochs=10` reached.
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/torch/nn/modules/rnn.py:83: UserWarning: dropout option adds dropout after all but last recurrent layer, so non-zero dropout expects num_layers greater than 1, but got dropout=0.1 and num_layers=1
  warnings.warn("dropout option adds dropout after all but last "
Running evaluation: 100%|██████████| 414/414 [00:00<00:00, 7625.91it/s]
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
[I 2024-05-31 18:25:56,608] Trial 1 finished with value: 0.08251994522973598 and parameters: {'num_layers': 1, 'hidden_size': 20}. Best is trial 1 with value: 0.08251994522973598.
INFO: GPU available: False, used: False
INFO:lightning.pytorch.utilities.rank_zero:GPU available: False, used: False
INFO: TPU available: False, using: 0 TPU cores
INFO:lightning.pytorch.utilities.rank_zero:TPU available: False, using: 0 TPU cores
INFO: IPU available: False, using: 0 IPUs
INFO:lightning.pytorch.utilities.rank_zero:IPU available: False, using: 0 IPUs
INFO: HPU available: False, using: 0 HPUs
INFO:lightning.pytorch.utilities.rank_zero:HPU available: False, using: 0 HPUs
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/configuration_validator.py:74: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
INFO: Epoch 0, global step 50: 'train_loss' reached 5.85761 (best 5.85761), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 0, global step 50: 'train_loss' reached 5.85761 (best 5.85761), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO: Epoch 1, global step 100: 'train_loss' reached 5.25142 (best 5.25142), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 1, global step 100: 'train_loss' reached 5.25142 (best 5.25142), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO: Epoch 2, global step 150: 'train_loss' reached 5.13679 (best 5.13679), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 2, global step 150: 'train_loss' reached 5.13679 (best 5.13679), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO: Epoch 3, global step 200: 'train_loss' reached 4.94917 (best 4.94917), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 3, global step 200: 'train_loss' reached 4.94917 (best 4.94917), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO: Epoch 4, global step 250: 'train_loss' reached 4.53793 (best 4.53793), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 4, global step 250: 'train_loss' reached 4.53793 (best 4.53793), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO: Epoch 5, global step 300: 'train_loss' reached 4.51407 (best 4.51407), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 5, global step 300: 'train_loss' reached 4.51407 (best 4.51407), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO: Epoch 6, global step 350: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 6, global step 350: 'train_loss' was not in top 1
INFO: Epoch 7, global step 400: 'train_loss' reached 4.43576 (best 4.43576), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 7, global step 400: 'train_loss' reached 4.43576 (best 4.43576), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO: Epoch 8, global step 450: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 8, global step 450: 'train_loss' was not in top 1
INFO: Epoch 9, global step 500: 'train_loss' reached 4.08463 (best 4.08463), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=9-step=500.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 9, global step 500: 'train_loss' reached 4.08463 (best 4.08463), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_3/checkpoints/epoch=9-step=500.ckpt' as top 1
INFO: `Trainer.fit` stopped: `max_epochs=10` reached.
INFO:lightning.pytorch.utilities.rank_zero:`Trainer.fit` stopped: `max_epochs=10` reached.
Running evaluation: 100%|██████████| 414/414 [00:00<00:00, 7966.97it/s]
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
[I 2024-05-31 18:26:09,527] Trial 2 finished with value: 0.11560589914025643 and parameters: {'num_layers': 3, 'hidden_size': 18}. Best is trial 1 with value: 0.08251994522973598.
INFO: GPU available: False, used: False
INFO:lightning.pytorch.utilities.rank_zero:GPU available: False, used: False
INFO: TPU available: False, using: 0 TPU cores
INFO:lightning.pytorch.utilities.rank_zero:TPU available: False, using: 0 TPU cores
INFO: IPU available: False, using: 0 IPUs
INFO:lightning.pytorch.utilities.rank_zero:IPU available: False, using: 0 IPUs
INFO: HPU available: False, using: 0 HPUs
INFO:lightning.pytorch.utilities.rank_zero:HPU available: False, using: 0 HPUs
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/configuration_validator.py:74: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
INFO: Epoch 0, global step 50: 'train_loss' reached 5.95401 (best 5.95401), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 0, global step 50: 'train_loss' reached 5.95401 (best 5.95401), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO: Epoch 1, global step 100: 'train_loss' reached 5.16907 (best 5.16907), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 1, global step 100: 'train_loss' reached 5.16907 (best 5.16907), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO: Epoch 2, global step 150: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 2, global step 150: 'train_loss' was not in top 1
INFO: Epoch 3, global step 200: 'train_loss' reached 4.60087 (best 4.60087), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 3, global step 200: 'train_loss' reached 4.60087 (best 4.60087), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO: Epoch 4, global step 250: 'train_loss' reached 4.36051 (best 4.36051), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 4, global step 250: 'train_loss' reached 4.36051 (best 4.36051), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO: Epoch 5, global step 300: 'train_loss' reached 4.25172 (best 4.25172), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 5, global step 300: 'train_loss' reached 4.25172 (best 4.25172), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO: Epoch 6, global step 350: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 6, global step 350: 'train_loss' was not in top 1
INFO: Epoch 7, global step 400: 'train_loss' reached 4.12659 (best 4.12659), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 7, global step 400: 'train_loss' reached 4.12659 (best 4.12659), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO: Epoch 8, global step 450: 'train_loss' reached 4.12235 (best 4.12235), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=8-step=450.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 8, global step 450: 'train_loss' reached 4.12235 (best 4.12235), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_4/checkpoints/epoch=8-step=450.ckpt' as top 1
INFO: Epoch 9, global step 500: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 9, global step 500: 'train_loss' was not in top 1
INFO: `Trainer.fit` stopped: `max_epochs=10` reached.
INFO:lightning.pytorch.utilities.rank_zero:`Trainer.fit` stopped: `max_epochs=10` reached.
Running evaluation: 100%|██████████| 414/414 [00:00<00:00, 7639.46it/s]
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
[I 2024-05-31 18:26:36,714] Trial 3 finished with value: 0.06051118673905025 and parameters: {'num_layers': 4, 'hidden_size': 46}. Best is trial 3 with value: 0.06051118673905025.
INFO: GPU available: False, used: False
INFO:lightning.pytorch.utilities.rank_zero:GPU available: False, used: False
INFO: TPU available: False, using: 0 TPU cores
INFO:lightning.pytorch.utilities.rank_zero:TPU available: False, using: 0 TPU cores
INFO: IPU available: False, using: 0 IPUs
INFO:lightning.pytorch.utilities.rank_zero:IPU available: False, using: 0 IPUs
INFO: HPU available: False, using: 0 HPUs
INFO:lightning.pytorch.utilities.rank_zero:HPU available: False, using: 0 HPUs
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/configuration_validator.py:74: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
INFO: Epoch 0, global step 50: 'train_loss' reached 5.75196 (best 5.75196), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 0, global step 50: 'train_loss' reached 5.75196 (best 5.75196), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO: Epoch 1, global step 100: 'train_loss' reached 5.26680 (best 5.26680), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 1, global step 100: 'train_loss' reached 5.26680 (best 5.26680), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO: Epoch 2, global step 150: 'train_loss' reached 5.14737 (best 5.14737), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 2, global step 150: 'train_loss' reached 5.14737 (best 5.14737), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO: Epoch 3, global step 200: 'train_loss' reached 4.99823 (best 4.99823), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 3, global step 200: 'train_loss' reached 4.99823 (best 4.99823), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO: Epoch 4, global step 250: 'train_loss' reached 4.85785 (best 4.85785), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 4, global step 250: 'train_loss' reached 4.85785 (best 4.85785), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO: Epoch 5, global step 300: 'train_loss' reached 4.74995 (best 4.74995), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 5, global step 300: 'train_loss' reached 4.74995 (best 4.74995), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO: Epoch 6, global step 350: 'train_loss' reached 4.57844 (best 4.57844), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=6-step=350.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 6, global step 350: 'train_loss' reached 4.57844 (best 4.57844), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=6-step=350.ckpt' as top 1
INFO: Epoch 7, global step 400: 'train_loss' reached 4.34586 (best 4.34586), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 7, global step 400: 'train_loss' reached 4.34586 (best 4.34586), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO: Epoch 8, global step 450: 'train_loss' reached 4.28116 (best 4.28116), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=8-step=450.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 8, global step 450: 'train_loss' reached 4.28116 (best 4.28116), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=8-step=450.ckpt' as top 1
INFO: Epoch 9, global step 500: 'train_loss' reached 4.26179 (best 4.26179), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=9-step=500.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 9, global step 500: 'train_loss' reached 4.26179 (best 4.26179), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_5/checkpoints/epoch=9-step=500.ckpt' as top 1
INFO: `Trainer.fit` stopped: `max_epochs=10` reached.
INFO:lightning.pytorch.utilities.rank_zero:`Trainer.fit` stopped: `max_epochs=10` reached.
Running evaluation: 100%|██████████| 414/414 [00:00<00:00, 7385.91it/s]
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/pandas/core/dtypes/astype.py:138: UserWarning: Warning: converting a masked element to nan.
  return arr.astype(dtype, copy=True)
[I 2024-05-31 18:26:51,459] Trial 4 finished with value: 0.08992057277146621 and parameters: {'num_layers': 4, 'hidden_size': 18}. Best is trial 3 with value: 0.06051118673905025.

Number of finished trials: 5
Best trial:
  Value: 0.06051118673905025
  Params:
    num_layers: 4
    hidden_size: 46
80.71679067611694

Re-training the model#

After getting the best hyperparameters by optuna, you can set them into the DeepAR estimator to re-train the model on the whole training subset we consider here.

[8]:

estimator = DeepAREstimator(
    num_layers=trial.params["num_layers"],
    hidden_size=trial.params["hidden_size"],
    prediction_length=dataset.metadata.prediction_length,
    context_length=100,
    freq=dataset.metadata.freq,
    trainer_kwargs={
        "enable_progress_bar": False,
        "enable_model_summary": False,
        "max_epochs": 10,
    },
)

After specifying our estimator with all the necessary hyperparameters we can train it using our training dataset train_subset by invoking the train method of the estimator. The training algorithm returns a fitted model (or a Predictor in GluonTS parlance) that can be used to obtain forecasts.

[9]:

predictor = estimator.train(dataset.train, cache_data=True)

INFO: GPU available: False, used: False
INFO:lightning.pytorch.utilities.rank_zero:GPU available: False, used: False
INFO: TPU available: False, using: 0 TPU cores
INFO:lightning.pytorch.utilities.rank_zero:TPU available: False, using: 0 TPU cores
INFO: IPU available: False, using: 0 IPUs
INFO:lightning.pytorch.utilities.rank_zero:IPU available: False, using: 0 IPUs
INFO: HPU available: False, using: 0 HPUs
INFO:lightning.pytorch.utilities.rank_zero:HPU available: False, using: 0 HPUs
/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/lightning/pytorch/trainer/configuration_validator.py:74: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.
INFO: Epoch 0, global step 50: 'train_loss' reached 5.43426 (best 5.43426), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 0, global step 50: 'train_loss' reached 5.43426 (best 5.43426), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=0-step=50.ckpt' as top 1
INFO: Epoch 1, global step 100: 'train_loss' reached 5.19284 (best 5.19284), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 1, global step 100: 'train_loss' reached 5.19284 (best 5.19284), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=1-step=100.ckpt' as top 1
INFO: Epoch 2, global step 150: 'train_loss' reached 5.03852 (best 5.03852), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 2, global step 150: 'train_loss' reached 5.03852 (best 5.03852), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=2-step=150.ckpt' as top 1
INFO: Epoch 3, global step 200: 'train_loss' reached 4.74886 (best 4.74886), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 3, global step 200: 'train_loss' reached 4.74886 (best 4.74886), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=3-step=200.ckpt' as top 1
INFO: Epoch 4, global step 250: 'train_loss' reached 4.52917 (best 4.52917), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 4, global step 250: 'train_loss' reached 4.52917 (best 4.52917), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=4-step=250.ckpt' as top 1
INFO: Epoch 5, global step 300: 'train_loss' reached 4.33903 (best 4.33903), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 5, global step 300: 'train_loss' reached 4.33903 (best 4.33903), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=5-step=300.ckpt' as top 1
INFO: Epoch 6, global step 350: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 6, global step 350: 'train_loss' was not in top 1
INFO: Epoch 7, global step 400: 'train_loss' reached 3.88879 (best 3.88879), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 7, global step 400: 'train_loss' reached 3.88879 (best 3.88879), saving model to '/home/runner/work/gluonts/gluonts/lightning_logs/version_6/checkpoints/epoch=7-step=400.ckpt' as top 1
INFO: Epoch 8, global step 450: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 8, global step 450: 'train_loss' was not in top 1
INFO: Epoch 9, global step 500: 'train_loss' was not in top 1
INFO:lightning.pytorch.utilities.rank_zero:Epoch 9, global step 500: 'train_loss' was not in top 1
INFO: `Trainer.fit` stopped: `max_epochs=10` reached.
INFO:lightning.pytorch.utilities.rank_zero:`Trainer.fit` stopped: `max_epochs=10` reached.

Visualize and evaluate forecasts#

With a predictor in hand, we can now predict the last window of the test dataset and evaluate our model’s performance.

GluonTS comes with the make_evaluation_predictions function that automates the process of prediction and model evaluation. Roughly, this function performs the following steps:

  • Removes the final window of length prediction_length of the test dataset that we want to predict

  • The estimator uses the remaining data to predict (in the form of sample paths) the “future” window that was just removed

  • The forecasts are returned, together with ground truth values for the same time range (as python generator objects)

[10]:

from gluonts.evaluation import make_evaluation_predictions

forecast_it, ts_it = make_evaluation_predictions(
    dataset=dataset.test,
    predictor=predictor,
)

First, we can convert these generators to lists to ease the subsequent computations.

[11]:

forecasts = list(forecast_it)
tss = list(ts_it)

Forecast objects have a plot method that can summarize the forecast paths as the mean, prediction intervals, etc. The prediction intervals are shaded in different colors as a “fan chart”.

[12]:

plt.plot(tss[0][-150:].to_timestamp())
forecasts[0].plot(show_label=True)
plt.legend()

[12]:

<matplotlib.legend.Legend at 0x7f6eeaf53040>
../../_images/tutorials_advanced_topics_hp_tuning_with_optuna_22_1.png

We can also evaluate the quality of our forecasts numerically. In GluonTS, the Evaluator class can compute aggregate performance metrics, as well as metrics per time series (which can be useful for analyzing performance across heterogeneous time series).

[13]:

from gluonts.evaluation import Evaluator

[14]:

evaluator = Evaluator(quantiles=[0.1, 0.5, 0.9])
agg_metrics, item_metrics = evaluator(tss, forecasts)

Running evaluation: 414it [00:00, 7500.25it/s]

Aggregate metrics aggregate both across time-steps and across time series.

[15]:

print(json.dumps(agg_metrics, indent=4))

{
    "MSE": 2904649.6919837557,
    "abs_error": 7130449.606354713,
    "abs_target_sum": 145558863.59960938,
    "abs_target_mean": 7324.822041043146,
    "seasonal_error": 336.9046924038305,
    "MASE": 2.7545853877072,
    "MAPE": 0.22468119902887207,
    "sMAPE": 0.16241664783474233,
    "MSIS": 28.85744362749451,
    "num_masked_target_values": 0.0,
    "QuantileLoss[0.1]": 3311120.5242288597,
    "Coverage[0.1]": 0.07830112721417071,
    "QuantileLoss[0.5]": 7130449.615060806,
    "Coverage[0.5]": 0.40247584541062803,
    "QuantileLoss[0.9]": 3864508.7020874014,
    "Coverage[0.9]": 0.8110909822866345,
    "RMSE": 1704.3032863853064,
    "NRMSE": 0.23267504341205705,
    "ND": 0.04898670840113545,
    "wQuantileLoss[0.1]": 0.022747639287270072,
    "wQuantileLoss[0.5]": 0.048986708460946944,
    "wQuantileLoss[0.9]": 0.026549456395301044,
    "mean_absolute_QuantileLoss": 4768692.947125689,
    "mean_wQuantileLoss": 0.032761268047839354,
    "MAE_Coverage": 0.37036366076221156,
    "OWA": NaN
}

Individual metrics are aggregated only across time-steps.

[16]:

item_metrics.head()

[16]:
item_id forecast_start MSE abs_error abs_target_sum abs_target_mean seasonal_error MASE MAPE sMAPE num_masked_target_values ND MSIS QuantileLoss[0.1] Coverage[0.1] QuantileLoss[0.5] Coverage[0.5] QuantileLoss[0.9] Coverage[0.9]
0 0 1750-01-30 04:00 1641.944499 1555.849609 31644.0 659.250000 42.371302 0.764988 0.048947 0.048178 0.0 0.049167 5.675331 668.749005 0.104167 1555.849579 0.666667 742.963159 1.000000
1 1 1750-01-30 04:00 167186.770833 18859.820312 124149.0 2586.437500 165.107988 2.379733 0.150390 0.139492 0.0 0.151913 13.140830 12771.814990 0.812500 18859.821777 1.000000 6181.971582 1.000000
2 2 1750-01-30 04:00 65984.177083 10269.212891 65030.0 1354.791667 78.889053 2.711934 0.147278 0.162526 0.0 0.157915 41.837951 2931.179285 0.000000 10269.212341 0.000000 11613.746228 0.250000
3 3 1750-01-30 04:00 199187.416667 16794.406250 235783.0 4912.145833 258.982249 1.350994 0.070886 0.070058 0.0 0.071228 8.733110 9183.591992 0.166667 16794.407471 0.437500 6128.578857 0.750000
4 4 1750-01-30 04:00 89862.916667 11872.976562 131088.0 2731.000000 200.494083 1.233721 0.090101 0.095563 0.0 0.090573 8.756501 4312.656763 0.020833 11872.977051 0.187500 8194.775342 0.520833 
[17]:

item_metrics.plot(x="sMAPE", y="MASE", kind="scatter")
plt.grid(which="both")
plt.show()
../../_images/tutorials_advanced_topics_hp_tuning_with_optuna_30_0.png