---
title: ECE
datasets:
-  
tags:
- evaluate
- metric
description: binned estimator of expected calibration error
sdk: gradio
sdk_version: 3.0.2
app_file: app.py
pinned: false
---

# Metric Card for ECE

## Metric Description
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*Give a brief overview of this metric, including what task(s) it is usually used for, if any.*
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Expected Calibration Error *ECE* is a popular metric to evaluate top-1 prediction miscalibration. 
It measures the L^p norm difference between a model’s posterior and the true likelihood of being correct.

![ECE definition](https://huggingface.co/spaces/jordyvl/ece/resolve/main/ECE_definition.jpg)

It is generally implemented as a binned estimator that discretizes predicted probabilities into ranges of possible values (bins) for which conditional expectation can be estimated.


## How to Use
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*Give general statement of how to use the metric*
*Provide simplest possible example for using the metric*
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```
>>> metric = evaluate.load("jordyvl/ece")
>>> results = metric.compute(references=[0, 1, 2], predictions=[[0.6, 0.2, 0.2], [0, 0.95, 0.05], [0.7, 0.1 ,0.2]])
>>> print(results)
{'ECE': 0.1333333333333334}
```

For valid model comparisons, ensure to use the same keyword arguments.


### Inputs
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*List all input arguments in the format below*
- **input_field** *(type): Definition of input, with explanation if necessary. State any default value(s).*
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### Output Values
<!--- 
*Explain what this metric outputs and provide an example of what the metric output looks like. Modules should return a dictionary with one or multiple key-value pairs, e.g. {"bleu" : 6.02}*

*State the range of possible values that the metric's output can take, as well as what in that range is considered good. For example: "This metric can take on any value between 0 and 100, inclusive. Higher scores are better."*

#### Values from Popular Papers
*Give examples, preferrably with links to leaderboards or publications, to papers that have reported this metric, along with the values they have reported.*
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As a metric of calibration *error*, it holds that the lower, the better calibrated a model is. Depending on the L^p norm, ECE will either take value between 0 and 1 (p=2) or between 0 and \infty_+.
The module returns dictionary with a key value pair, e.g., {"ECE": 0.64}.


### Examples
<!--- 
*Give code examples of the metric being used. Try to include examples that clear up any potential ambiguity left from the metric description above. If possible, provide a range of examples that show both typical and atypical results, as well as examples where a variety of input parameters are passed.*
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```python
N = 10  # N evaluation instances {(x_i,y_i)}_{i=1}^N
K = 5  # K class problem

def random_mc_instance(concentration=1, onehot=False):
    reference = np.argmax(
        np.random.dirichlet(([concentration for _ in range(K)])), -1
    )  # class targets
    prediction = np.random.dirichlet(([concentration for _ in range(K)]))  # probabilities
    if onehot:
        reference = np.eye(K)[np.argmax(reference, -1)]
    return reference, prediction

references, predictions = list(zip(*[random_mc_instance() for i in range(N)]))
references = np.array(references, dtype=np.int64)
predictions = np.array(predictions, dtype=np.float32)
res = ECE()._compute(predictions, references)  # {'ECE': float}
```


## Limitations and Bias
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*Note any known limitations or biases that the metric has, with links and references if possible.*
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See [3],[4] and [5].

## Citation
[1] Naeini, M.P., Cooper, G. and Hauskrecht, M., 2015, February. Obtaining well calibrated probabilities using bayesian binning. In Twenty-Ninth AAAI Conference on Artificial Intelligence.

[2] Guo, C., Pleiss, G., Sun, Y. and Weinberger, K.Q., 2017, July. On calibration of modern neural networks. In International Conference on Machine Learning (pp. 1321-1330). PMLR.

[3] Nixon, J., Dusenberry, M.W., Zhang, L., Jerfel, G. and Tran, D., 2019, June. Measuring Calibration in Deep Learning. In CVPR Workshops (Vol. 2, No. 7).

[4] Kumar, A., Liang, P.S. and Ma, T., 2019. Verified uncertainty calibration. Advances in Neural Information Processing Systems, 32.

[5] Vaicenavicius, J., Widmann, D., Andersson, C., Lindsten, F., Roll, J. and Schön, T., 2019, April. Evaluating model calibration in classification. In The 22nd International Conference on Artificial Intelligence and Statistics (pp. 3459-3467). PMLR.

[6] Allen-Zhu, Z., Li, Y. and Liang, Y., 2019. Learning and generalization in overparameterized neural networks, going beyond two layers. Advances in neural information processing systems, 32.

## Further References
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*Add any useful further references.*
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