On Calibration of Modern Neural Networks on ShortScience.org

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On Calibration of Modern Neural Networks
Chuan Guo and Geoff Pleiss and Yu Sun and Kilian Q. Weinberger
arXiv e-Print archive - 2017 via Local arXiv
Keywords: cs.LG
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Summaries/Notes 2

[link] Summary by David Stutz 5 years ago

Guo et al. study calibration of deep neural networks as post-processing step. Here, calibration means a correction of the predicted confidence scores as these are commonlz too overconfident in recent deep networks. They consider several state-of-the-art post-processing steps for calibration, but surprisingly, they show that a simple linear mapping, or even scaling, works surprisingly well. So if $z_i$ are the logits of the network, then (the network being fixed) a parameter $T$ is found such that

$\sigma(\frac{z_i}{T})$

is calibrated and minimized the NLL loss on a held-out validation set. Here, the temeratur $T$ either softens or roughens the probability distribution over classes. Interestingly, finding $T$ by optimizing the same training loss helps to reduce over-confidence.

Also find this summary at [davidstutz.de](https://davidstutz.de/category/reading/).

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[link] Summary by elbaro 5 years ago

## Task

A neural network for classification typically has a **softmax** layer and outputs the class with the max probability. However, this probability does not represent the **confidence**. If the average confidence (average of max probs) for a dataset matches the accuracy, it is called **well-calibrated**. Old models like LeNet (1998) was well-calibrated, but modern networks like ResNet (2016) are no longer well-calibrated. This paper explains what caused this and compares various calibration methods.

## Figure - Confidence Histogram

https://i.imgur.com/dMtdWsL.png

The bottom row: group the samples by confidence (max probailities) into bins, and calculates the accuracy (# correct / # bin size) within each bin.

- ECE (Expected Calibration Error): average of |accuracy-confidence| of bins
- MCE (Maximum Calibration Error): max of |accuracy-confidence| of bins

## Analysis - What
The paper experiments how models are mis-calibrated with different factors: (1) model capacity, (2) batch norm, (3) weight decay, (4) NLL.

## Solution - Calibration Methods

Many calibration methods for binary classification and multi-class classification are evaluated. The method that performed the best is **temperature scailing**, which simply multiplies logits before the softmax by some constant. The paper used the validation set to choose the best constant.

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