[reliable] (paper 4) Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples

Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples

Contents

1. Abstract
2. Introduction
3. Training Confident Neural Classifiers
   1. Confident Classifier
   2. Adversarial Generator
   3. Joint Training of Confident Classifier & Adversarial Generator

0. Abstract

배경 소개

• detect whether a test sample is from in-distribution
• DNN의 문제점 : highly overconfident
• 이에 대한 해결책으로 threshold-based detector가 제안됨

threshold-based detector의 문제점

• highly depend on HOW TO TRAIN the classifiers

  ( \(\because\) only focus on improving inference procedures )

이 논문에서는, novel training method for classifier를 제안함

( inference algorithm이 더 잘 작동하도록! )

기존 (cross entropy) loss에, 2가지 term을 추가할 것을 제안

• 1) first term : force samples from o.o.d to be less confident
• 2) second term : generate most effective training samples for first term

1. Introduction

Notation

• \(P_{\text {out }}(\mathrm{x})\) : o.o.d
• \(P_{\text {in }}(\mathrm{x}, y)\) : i.d

Goal

• determining if input \(\mathrm{x}\) is from \(P_{\text {in }}\) or \(P_{\text {out }}\)

  ( possibly utilizing a well calibrated classifier \(P_{\theta}(y \mid \mathrm{x})\) )

• 즉 detector \(g(\mathrm{x}): \mathcal{X} \rightarrow\{0,1\}\) 만들기!

  • 1 if in distribution
  • 0 if out of distribution

기존의 threshold based detector

• use pre-trained classifier
• input \(\mathrm{x}\)에 대해, confidence score \(q(\mathrm{x})\) 를 ( pre-trained classifier 를 사용하여 ) 계산

• 이 \(q(\mathrm{x})\)와 threshold \(\delta>0\)를 비교하여 o.o.d 판단

• 장점) computationally simple

• 단점) highly depend on pre-trained classifier

  ( fail to work, if classifier does not separate maximum value of predictive distribution well enough! )

Contribution

Goal : detect o.o.d ( + classification 성능 낮추지 않으면서도 )

• 1) confidence loss 제안
  • KL divergence of (1) & (2)
    • (1) predictive distribution of o.o.d samples
    • (2) uniform distribution
• 2) GAN 사용하여 \(P_{\text {out }}(\mathrm{x})\) 를 모델링 한 뒤, o.o.d sample들을 뽑는다.

2. Training Confident Neural Classifiers

2-1) Confident Classifier

아래의 새로운 confidence loss ( = CE loss + KL )를 제안한다.

• \(\min _{\theta} \mathbb{E}_{P_{\text {in }}(\widehat{\mathbf{x}}, \widehat{y})}\left[-\log P_{\theta}(y=\widehat{y} \mid \widehat{\mathbf{x}})\right]+\beta \mathbb{E}_{P_{\text {out }}(\mathbf{x})}\left[K L\left(\mathcal{U}(y) \| P_{\theta}(y \mid \mathbf{x})\right)\right]\).

  • \(\mathcal{U}(y)\) : uniform distribution
  • \(\beta>0\) : penalty parameter

• 직관적 의미 :

  force predictive distribution of o.o.d to be close to UNIFORM

위 loss function의 \(KL\) term을 계산하기 위해서는, o.o.d 분포에서의 샘플들이 매우 많이 필요.

( 하지만 현실에서는 그렇게 구하기 쉽지 않음 )

\(\because\) effective하게 샘플을 모으자!

• effective하다 = in-distribution과 가깝게 o.o.d에서 샘플하자
• 아래의 그림을 통해 직관적인 이해 가능

2-2) Adversarial Generator

o.o.d 를 생성하기 위한 GAN을 모델링한다!

Notation

• Discriminator & Generator : \(D\) & \(G\)
• prior distribution of latent variable \(\mathbf{z}\) : \(P_{\mathrm{pri}}(\mathrm{z})\)
• generated outputs : \(G(\mathbf{z})\)
• in-distribution : \(P_{\mathrm{in}}(x)\)

Loss function ( 목표 : \(P_{G} \approx\) \(P_{\mathrm{in}}\) )

(1) 기존의 Loss function

• \(\min _{G} \max _{D} \mathbb{E}_{P_{\text {in }}(\mathbf{x})}[\log D(\mathbf{x})]+\mathbb{E}_{P_{\text {pri }}(\mathbf{z})}[\log (1-D(G(\mathbf{z})))]\).

(2) 제안한 Loss function

• want to make the generator recover an effective out-of distribution \(P_{\text {out }}\)

  ( 위에서 말했 듯, effective하다 = in-distribution과 가깝게 o.o.d에서 샘플하자 )

• \(\begin{aligned} \min _{G} \max _{D} & \beta \underbrace{\mathbb{E}_{P_{G}(\mathbf{x})}\left[K L\left(\mathcal{U}(y) \| P_{\theta}(y \mid \mathbf{x})\right)\right]}_{(\mathrm{a})} \\ &+\underbrace{\mathbb{E}_{P_{\text {in }}(\mathbf{x})}[\log D(\mathbf{x})]+\mathbb{E}_{P_{G}(\mathbf{x})}[\log (1-D(\mathbf{x}))]}_{(\mathrm{b})} \end{aligned}\).
• 직관적 의미 : (a) + (b)
  • (a) force predictive distribution of o.o.d to be close to UNIFORM
  • (b) 기존의 Loss function ( 위의 (1) 식 )
    • out of distribution이 in distribution과 유사하도록 유도!

2-3) Joint Training of (1) Confident Classifier & (2) Adversarial Generator

위에서 배운 2-1) & 2-2) 두 모델을 jointly train

최종적인 Loss function :

• (1) Confidence Loss ( 빨간색 ) : (c) + (d)

• (2) GAN loss ( 파란색 ) : (d) + (e)

  ( (d)는 (1), (2)의 중첩되는 부분 )

최종적인 Algorithm