---
title: sMAPE
emoji: 🤗 
colorFrom: blue
colorTo: red
sdk: gradio
sdk_version: 3.19.1
app_file: app.py
pinned: false
tags:
- evaluate
- metric
description: >-
  Symmetric Mean Absolute Percentage Error (sMAPE) is the symmetric mean percentage error difference between the predicted and actual values defined by Chen and Yang (2004).
---

# Metric Card for sMAPE


## Metric Description

Symmetric Mean Absolute Error (sMAPE) is the symmetric mean of the percentage error of difference between the predicted $x_i$ and actual $y_i$ numeric values:

![image](https://user-images.githubusercontent.com/8100/200009801-ae8be6c8-facf-401b-8df0-3f80a458b9f4.png)


## How to Use

At minimum, this metric requires predictions and references as inputs.

```python
>>> smape_metric = evaluate.load("smape")
>>> predictions = [2.5, 0.0, 2, 8]
>>> references = [3, -0.5, 2, 7]
>>> results = smape_metric.compute(predictions=predictions, references=references)
```

### Inputs

Mandatory inputs: 
- `predictions`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the estimated target values.
- `references`: numeric array-like of shape (`n_samples,`) or (`n_samples`, `n_outputs`), representing the ground truth (correct) target values.

Optional arguments:
- `sample_weight`: numeric array-like of shape (`n_samples,`) representing sample weights. The default is `None`.
- `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`.
  - `raw_values` returns a full set of errors in case of multioutput input.
  - `uniform_average` means that the errors of all outputs are averaged with uniform weight. 
  - the array-like value defines weights used to average errors.

### Output Values
This metric outputs a dictionary, containing the mean absolute error score, which is of type:
- `float`: if multioutput is `uniform_average` or an ndarray of weights, then the weighted average of all output errors is returned.
- numeric array-like of shape (`n_outputs,`): if multioutput is `raw_values`, then the score is returned for each output separately. 

Each sMAPE `float` value ranges from `0.0` to `2.0`, with the best value being 0.0.

Output Example(s):
```python
{'smape': 0.5}
```

If `multioutput="raw_values"`:
```python
{'smape': array([0.5, 1.5 ])}
```

#### Values from Popular Papers


### Examples

Example with the `uniform_average` config:
```python
>>> smape_metric = evaluate.load("smape")
>>> predictions = [2.5, 0.0, 2, 8]
>>> references = [3, -0.5, 2, 7]
>>> results = smape_metric.compute(predictions=predictions, references=references)
>>> print(results)
{'smape': 0.5787...}
```

Example with multi-dimensional lists, and the `raw_values` config:
```python
>>> smape_metric = evaluate.load("smape", "multilist")
>>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
>>> references = [[0.1, 2], [-1, 2], [8, -5]]
>>> results = smape_metric.compute(predictions=predictions, references=references)
>>> print(results)
{'smape': 0.8874...}
>>> results = smape_metric.compute(predictions=predictions, references=references, multioutput='raw_values')
>>> print(results)
{'smape': array([1.3749..., 0.4])}
```

## Limitations and Bias
This metric is called a measure of "percentage error" even though there is no multiplier of 100. The range is between (0, 2) with it being two when the target and prediction are both zero. 

## Citation(s)

```bibtex
@article{article,
    author = {Chen, Zhuo and Yang, Yuhong},
    year = {2004},
    month = {04},
    pages = {},
    title = {Assessing forecast accuracy measures}
}
```

## Further References
- [Symmetric Mean absolute percentage error - Wikipedia](https://en.wikipedia.org/wiki/Symmetric_mean_absolute_percentage_error)