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README.md
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sdk: gradio
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sdk_version: 3.
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app_file: app.py
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pinned: false
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---
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title: MASE
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emoji: 🤗
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colorFrom: blue
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colorTo: red
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sdk: gradio
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sdk_version: 3.0.2
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app_file: app.py
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pinned: false
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tags:
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- evaluate
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- metric
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description: >-
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Mean Absolute Scaled Error (MASE) is the mean absolute error of the forecast values, divided by the mean absolute error of the in-sample one-step naive forecast on the training set.
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---
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# Metric Card for MASE
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## Metric Description
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Mean Absolute Scaled Error (MASE) is the mean absolute error of the forecast values, divided by the mean absolute error of the in-sample one-step naive forecast. For prediction $x_i$ and corresponding ground truth $y_i$ as well as training data $z_t$ with seasonality $p$ the metric is given by:
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![image](https://user-images.githubusercontent.com/8100/200009284-7ce4ccaa-373c-42f0-acbb-f81d52a97512.png)
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This metric is:
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* independent of the scale of the data;
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* has predictable behavior when predicted/ground-truth data is near zero;
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* symmetric;
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* interpretable, as values greater than one indicate that in-sample one-step forecasts from the naïve method perform better than the forecast values under consideration.
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## How to Use
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At minimum, this metric requires predictions, references and training data as inputs.
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```python
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>>> mase_metric = evaluate.load("mase")
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>>> predictions = [2.5, 0.0, 2, 8]
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>>> references = [3, -0.5, 2, 7]
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>>> training = [5, 0.5, 4, 6, 3, 5, 2]
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training)
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```
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### Inputs
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Mandatory inputs:
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- `predictions`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the estimated target values.
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- `references`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the ground truth (correct) target values.
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- `training`: numeric array-like of shape (`n_train_samples,`) or (`n_train_samples`, `n_outputs`), representing the in sample training data.
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Optional arguments:
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- `periodicity`: the seasonal periodicity of training data. The default is 1.
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- `sample_weight`: numeric array-like of shape (`n_samples,`) representing sample weights. The default is `None`.
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- `multioutput`: `raw_values`, `uniform_average` or numeric array-like of shape (`n_outputs,`), which defines the aggregation of multiple output values. The default value is `uniform_average`.
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- `raw_values` returns a full set of errors in case of multioutput input.
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- `uniform_average` means that the errors of all outputs are averaged with uniform weight.
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- the array-like value defines weights used to average errors.
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### Output Values
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This metric outputs a dictionary, containing the mean absolute error score, which is of type:
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- `float`: if multioutput is `uniform_average` or an ndarray of weights, then the weighted average of all output errors is returned.
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- numeric array-like of shape (`n_outputs,`): if multioutput is `raw_values`, then the score is returned for each output separately.
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Each MASE `float` value ranges from `0.0` to `1.0`, with the best value being 0.0.
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Output Example(s):
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```python
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{'mase': 0.5}
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```
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If `multioutput="raw_values"`:
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```python
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{'mase': array([0.5, 1. ])}
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```
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#### Values from Popular Papers
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### Examples
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Example with the `uniform_average` config:
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```python
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>>> mase_metric = evaluate.load("mase")
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>>> predictions = [2.5, 0.0, 2, 8]
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>>> references = [3, -0.5, 2, 7]
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>>> training = [5, 0.5, 4, 6, 3, 5, 2]
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training)
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>>> print(results)
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{'mase': 0.1833...}
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```
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Example with multi-dimensional lists, and the `raw_values` config:
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```python
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>>> mase_metric = evaluate.load("mase", "multilist")
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>>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
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>>> references = [[0.1, 2], [-1, 2], [8, -5]]
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>>> training = [[0.5, 1], [-1, 1], [7, -6]]
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training)
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>>> print(results)
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{'mase': 0.1818...}
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training, multioutput='raw_values')
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>>> print(results)
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{'mase': array([0.1052..., 0.2857...])}
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```
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## Limitations and Bias
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## Citation(s)
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```bibtex
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@article{HYNDMAN2006679,
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title = {Another look at measures of forecast accuracy},
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journal = {International Journal of Forecasting},
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volume = {22},
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number = {4},
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pages = {679--688},
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year = {2006},
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issn = {0169-2070},
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doi = {https://doi.org/10.1016/j.ijforecast.2006.03.001},
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url = {https://www.sciencedirect.com/science/article/pii/S0169207006000239},
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author = {Rob J. Hyndman and Anne B. Koehler},
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}
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```
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## Further References
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- [Mean absolute scaled error - Wikipedia](https://en.wikipedia.org/wiki/Mean_absolute_scaled_errorr)
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app.py
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import evaluate
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from evaluate.utils import launch_gradio_widget
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module = evaluate.load("mase")
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launch_gradio_widget(module)
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mase.py
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# Copyright 2022 The HuggingFace Datasets Authors and the current dataset script contributor.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""MASE - Mean Absolute Scaled Error Metric"""
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import datasets
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import numpy as np
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from sklearn.metrics import mean_absolute_error
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import evaluate
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_CITATION = """\
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@article{HYNDMAN2006679,
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title = {Another look at measures of forecast accuracy},
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journal = {International Journal of Forecasting},
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volume = {22},
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number = {4},
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pages = {679--688},
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year = {2006},
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issn = {0169-2070},
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doi = {https://doi.org/10.1016/j.ijforecast.2006.03.001},
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url = {https://www.sciencedirect.com/science/article/pii/S0169207006000239},
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author = {Rob J. Hyndman and Anne B. Koehler},
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}
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"""
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_DESCRIPTION = """\
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Mean Absolute Scaled Error (MASE) is the mean absolute error of the forecast values, divided by the mean absolute error of the in-sample one-step naive forecast.
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"""
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_KWARGS_DESCRIPTION = """
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Args:
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predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)
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Estimated target values.
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references: array-like of shape (n_samples,) or (n_samples, n_outputs)
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Ground truth (correct) target values.
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training: array-like of shape (n_train_samples,) or (n_train_samples, n_outputs)
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In sample training data for naive forecast.
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periodicity: int, default=1
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Seasonal periodicity of training data.
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sample_weight: array-like of shape (n_samples,), default=None
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Sample weights.
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multioutput: {"raw_values", "uniform_average"} or array-like of shape (n_outputs,), default="uniform_average"
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Defines aggregating of multiple output values. Array-like value defines weights used to average errors.
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"raw_values" : Returns a full set of errors in case of multioutput input.
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"uniform_average" : Errors of all outputs are averaged with uniform weight.
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Returns:
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mase : mean absolute scaled error.
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If multioutput is "raw_values", then mean absolute percentage error is returned for each output separately. If multioutput is "uniform_average" or an ndarray of weights, then the weighted average of all output errors is returned.
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MASE output is non-negative floating point. The best value is 0.0.
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Examples:
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>>> mase_metric = evaluate.load("mase")
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>>> predictions = [2.5, 0.0, 2, 8, 1.25]
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>>> references = [3, -0.5, 2, 7, 2]
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>>> training = [5, 0.5, 4, 6, 3, 5, 2]
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training)
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>>> print(results)
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{'mase': 0.18333333333333335}
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If you're using multi-dimensional lists, then set the config as follows :
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>>> mase_metric = evaluate.load("mase", "multilist")
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>>> predictions = [[0, 2], [-1, 2], [8, -5]]
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>>> references = [[0.5, 1], [-1, 1], [7, -6]]
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>>> training = [[0.5, 1], [-1, 1], [7, -6]]
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training)
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>>> print(results)
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{'mase': 0.18181818181818182}
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training, multioutput='raw_values')
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>>> print(results)
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{'mase': array([0.10526316, 0.28571429])}
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>>> results = mase_metric.compute(predictions=predictions, references=references, training=training, multioutput=[0.3, 0.7])
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>>> print(results)
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{'mase': 0.21935483870967742}
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"""
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@evaluate.utils.file_utils.add_start_docstrings(_DESCRIPTION, _KWARGS_DESCRIPTION)
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class Mase(evaluate.Metric):
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def _info(self):
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return evaluate.MetricInfo(
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description=_DESCRIPTION,
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citation=_CITATION,
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inputs_description=_KWARGS_DESCRIPTION,
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features=datasets.Features(self._get_feature_types()),
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reference_urls=["https://otexts.com/fpp3/accuracy.html#scaled-errors"],
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)
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def _get_feature_types(self):
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if self.config_name == "multilist":
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return {
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"predictions": datasets.Sequence(datasets.Value("float")),
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"references": datasets.Sequence(datasets.Value("float")),
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}
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else:
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return {
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"predictions": datasets.Value("float"),
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"references": datasets.Value("float"),
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}
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def _compute(
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self,
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predictions,
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references,
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training,
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periodicity=1,
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sample_weight=None,
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multioutput="uniform_average",
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):
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y_pred_naive = training[:-periodicity]
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mae_naive = mean_absolute_error(training[periodicity:], y_pred_naive, multioutput=multioutput)
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mae_score = mean_absolute_error(
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references,
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predictions,
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sample_weight=sample_weight,
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multioutput=multioutput,
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)
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epsilon = np.finfo(np.float64).eps
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mase_score = mae_score / np.maximum(mae_naive, epsilon)
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return {"mase": mase_score}
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requirements.txt
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git+https://github.com/huggingface/evaluate@7e21410f9bcff651452f188b702cc80ecd3530e6
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sklearn
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