Safeguarded Dynamic Label Regression for Noisy Supervision · Safeguarded Dynamic Label Regression...

Background Literature Review Latent Class-Conditional Noise Model Experiments Conclusion

Safeguarded Dynamic Label Regression for

Noisy Supervision

Jiangchao Yao†,‡, Hao Wu†, Ya Zhang†

Ivor W. Tsang‡, Jun Sun††Shanghai Jiao Tong University‡University of Technology Sydney

November 14, 2018

Safeguarded Dynamic Label Regression for Noisy Supervision 1/28


Outline

1 Background

2 Literature Review

3 Latent Class-Conditional Noise Model

4 Experiments

5 Conclusion



Background

Low Expensive Noisy Data Meets Deep Learning

Inexhaustible social images with annotations on websites.

Fine-grained annotations from crowdsourcing platforms.

Rich medical diagnosis by numerous levels of doctors.

Large amount of unreliable stock labels for revenue.

Learning with Noisy Supervision Brings Robustness

Existing deep learning based methods,

Learning with Noise Transition

Learning with Sample Re-weighting

Learning with Model Regularization



Outline

1 Background

2 Literature Review


4 Experiments

5 Conclusion



Probabilistic ModelingLearning with Noise Transition

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lnP(y |x) = ln∑

z

P(y |z , x)︸︷︷︸Noise transition

P(z |x)︸︷︷︸Classifier

(1)

Classification Risk:

Ex ,z [− lnP(z |x)] 6= Ex ,y [− lnP(y |x)] if z 6≡ y .



Probabilistic ModelingLearning with Noise Transition





If it is given the class-conditional noise, i.e.,

P(y |z , x) = P(y |z) = Tzy (given and invertible),

we have the following theorem for parameter estimation,

arg minθ

Ex ,z [− lnP(z |x)] = arg minθ

Ex ,y [− lnP(y |x)] .



Probabilistic ModelingLearning with Sample Re-weighting





Ex ,z

− lnP(z |x)︸︷︷︸classifier

= Ex ,y

− Pc(x , z)

Pn(x , y)

∣∣∣∣z=y︸︷︷︸

weight

lnP(y |x)︸︷︷︸classifier

= Ex ,y

− β(x , y)︸︷︷︸weight

lnP(y |x)︸︷︷︸classifier

(2)



Probabilistic ModelingLearning with Sample Re-weighting




Typically, the weight can be estimated with small clean data,

β(x , y) =Pc(x , y)

Pn(x , y)=

Pc(y |x)

Pn(y |x).

A simpler way is based on the classifier itself motivated by theperceptual consistency, i.e., bootstrapping,

β(x , y) = α + (1− α)P(y |x)

Pn(y |x), where α ∈ [0, 1].



Probabilistic ModelingLearning with Model Regularization




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lnP(y |x) = ln∑

z

P(y |z , s)︸︷︷︸Noise transition

P(z |x)︸︷︷︸Classifier

(3)

Explicitly introduce a noise source to apportion the reasoningfrom z to y , which alleviates the uncertain effect on classifier



Probabilistic ModelingLearning with Model Regularization



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Roughly treat z=y and the following conjecture is quite useful,i.e., deep neural networks memorize physic patterns ♠ in order.

Conjecture: simple ♠simple (x ,y)

∣∣ hard(x ,y)−−−−−−−−−−−−−−→

memorizing orderhard ♠

Since most simple clean data belongs to simple (x , y), we candetain memorizing in the early phase by dropout regularization.



Outline

1 Background

2 Literature Review


4 Experiments

5 Conclusion



Motivation

In this work, we focus on learning with noise transition.

noisy labelsimages classifier network

Wolf

Car

Mouse

Roseestimated transition

forward correction

backward correction

Backward correction

min T−1︸︷︷︸fixed

∗` (y, P(y|x))

Forward correction

min− ln

T︸︷︷︸fixed

∗P(y|x)

Noise adaptation

min− ln

φ︸︷︷︸tunable

∗P(y|x)

noisy labelsimages classifier network Noise modeling

Wolf

Car

Mouse

Rose

forward correction



Motivation

Problems

Forward and backward corrections critically depends onthe accurate estimation of noise transition, which isimpractical via a finite anchor set in real-world scenarios.

Stochastic approximation to EM learning between theclassifier and the noise model via a noise adaptation layeris not rigorous and suffers from instability in tuning.

Solutions

Learning on posterior labels along with learning the noisetransition is more reliable than that on noisy labels.

Gibbs sampling for Bayesian class-conditional noise modelcan reduce computational costs and avoid tweaking issues.



Latent Class-Conditional Noise Model




Learning on Posterior Labels

zm ∼ P(zm|xm, ym)︸︷︷︸Posterior

∝ P(zm|xm)︸︷︷︸Classifier

P(ym|xm, zm)︸︷︷︸Noise transition

(4)

Explicitly Decoupled Minimization:

minEx ,z [− lnP(z |x)] and minEx ,z,y [− lnP(y |x , z)] (5)

Classification Risk:

Ex ,z [− lnP(z |x)]← Ex ,z [− lnP(z |x)] if P(x , z)← P(x , z)



Latent Class-Conditional Noise ModelDynamic Label Regression




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Dynamic Label Regression

If it is the latent class-conditional noise (LCCN), i.e.,

P(y |z , x) = P(y |z) = φzy ,

the noise model can degrade to a nonparametric counting nzy .We then simplify the computation with the Gibbs sampling,

zm|Z¬(m) ∼ P(zm|xm)︸︷︷︸Classifier

αym + n¬zmym∑k ′(αk ′) + n¬zmk ′︸︷︷︸Noise transition

. (6)



Latent Class-Conditional Noise ModelSafeguarded Transition Update

Theorem

Suppose αi is a positive smoothing scalar, Ni is the current samplenumber of the ith category (i=1,. . . ,K ), Mi is the sum of thesample numbers newly allocated into (positive) and removed from(negative) the ith category after a batch of training samples, andMi is its absolute sum of such two cases. Then, for the transitionvector φi of the ith category, its variation via a training batch ischaracterized by the following equation,

∣∣φnewi − φold

i

∣∣ ≤ |ri |+ ri1 + ri

where ri = Mi

Ni +∑K

j=1 αjand ri = Mi

Ni +∑K

j=1 αj. According to the

definition, we have ri > −1, ri ≥ 0 and ri ≥ |ri |.



Latent Class-Conditional Noise ModelSafeguarded Dynamic Label Regression

Algorithm 1 Dynamic Label Regression for LCCN

Require: A noisy dataset D = {(xn, yn)}Nn=1, a classifier P(·|x) modeled by DNN fθ,

warming-up steps δ, the running epoch number L and the batch-size M.1: Directly pretrain the classifier fθ on the noisy dataset D.2: Compute the warming-up noise transition matrix φ′.3: for epoch i = 1 to L do4: for batch j = 1 to dN/Me do5: Let step=i×dN/Me+j and hook a batch of samples.6: if step < δ then7: Substitute the transition in Equation (6) with φ′, and sample zn.8: else9: Sample zn with Equation (6) for the batch.

10: end if11: Update the confusion matrix N(·)(·) based on observations {(zn, yn)}.12: Optimize Equation (5) to learn fθ and estimate φ.13: end for14: end for15: Output the classifier fθ and the noise transition φ.



Latent Class-Conditional Noise Model

Complexity Analysis

Stochastic training a DNN model involves two steps, the forwardand backward computations. In each mini-batch update, its timecomplexity is O(MΛ), where M is the mini-batch size and Λ is theparameter size. Here, in Algorithm 1, we additionally add asampling operation via Equation (6) whose complexity isO(M + K 2) (K is the class size). Note that, the first term in theRHS of Equation (6) has been computed in the forward procedure.So the extra cost for the sampling is negligible compared toO(MΛ). An optimization for noise modeling is also negligible,which involves the normalization of a confusion matrix only andthe complexity is O(K 2). Since the big-O complexity of eachmini-batch remains the same, our method is scalable to big data.



Outline

1 Background

2 Literature Review


4 Experiments

5 Conclusion



Experiments

Asymmetric Noise & Wild Noise

(1) Inject asymmetric noise manually

CIFAR-10: trkr−→ atm, brd

r−→ apl , deerr−→ horse, cat

r−→ dog

CIFAR-100: oner−→ the next circularly within the superclass

(2) Totally agnostic wild noiseClothing1M: 14 predefined clothing classes.WebVision17: 1000 classes same to those of ImageNet.



Experiments

Experimental Setup

CIFAR-10 and CIFAR-100:

Resnet-32 and data augmentation

mo=0.9, weight-decay=1e-4, batch-size=128

40 (lr=0.5), 80 (lr=0.1), 120 (lr=0.01) epochs

Clothing1M and WebVision17:

Resnet-50 (ImageNet pretrained) and data augmentation

lr=0.01, mo=0.9, weight-decay=1e-3, batch-size=32

10 epochs (lr is divided by 10 after each 5 epochs)

Baselines:CE, Forward, S-adaptation, Bootstrapping, Joint Optimization.



ExperimentsCIFAR-10 and CIFAR-100

Dataset CIFAR-10

# Method \ Noise Ratio 0.1 0.3 0.5 0.7 0.91 CE 90.10 88.12 76.93 59.01 56.852 Bootstrapping 90.73 88.12 76.29 57.04 56.793 Forward 90.86 89.03 82.47 67.11 57.294 S-adaptation 91.02 88.83 86.79 72.74 60.925 LCCN 91.35 89.33 88.41 79.48 64.82

6 CE with the clean data 91.63

Table: The average accuracy(%) over 5 trials on noisy CIFAR-10.




Dataset CIFAR-100

# Method \ Noise Ratio 0.1 0.2 0.3 0.4 0.51 CE 66.15 64.31 60.11 51.68 33.372 Bootstrapping 66.48 64.61 63.01 55.27 34.523 Forward 65.43 62.72 61.28 52.64 33.824 S-adaptation 65.52 64.11 62.39 52.74 30.075 LCCN 67.83 67.63 66.86 65.52 33.71


Table: The average accuracy(%) over 5 trials on noisy CIFAR-100.




0

0.5

1

1.5

2

2.5

0 10000 20000 30000 40000 50000

BCCN

S-adaption

0.55

0.65

0.75

0.85

0.95

0 10000 20000 30000 40000 50000

LCCN

S-adaption

LCCN

S-adaption

Figure: Test accuracy of LCCN andS-adaptation on CIFAR-10 with r=0.5 (left),and the corresponding histogram (right) forthe variation of φ via a batch of samples.

0.5

0.6

0.7

0.8

0.9

1

0 10000 20000 30000 40000 50000

labe

l cor

rect

ion

ratio

horse car

car car

truck truck

car ship

plane car

truck Frog

Figure: The colormap for the confusion matrix on CIFAR-10 with r=0.5. We use the log-scale of eachentry in the confusion matrix for fine-grained visualization. The left three maps are gradually learned byLCCN and the right one is the groudtruth.



Experiments

# Method Accuracy

1 CE 68.942 Bootstrapping 69.123 Forward 69.844 S-adaptation 70.365 Joint Optimization 72.236 LCCN 73.07


# Method Accuracy@1 Accuracy@5

1 CE 63.11 83.692 Bootstrapping 63.20 83.813 Forward 63.10 83.784 S-adaptation 62.54 81.735 LCCN 63.52 84.27

Table: Results on Clothing1M (top) and WebVision (bottom).



Outline

1 Background

2 Literature Review


4 Experiments

5 Conclusion



Conclusion

Summary

We present a Latent Class-Conditional Noise model tosolve the issues when training the classifier and modelingthe noise transition together in previous models .

A dynamic label regression method is deduced for LCCN.Theoretical analysis guarantees the safeguarded transitionupdate and introduces the negligible computational cost.

Experiments on CIFAR-10, CIFAR-100 datasets and thereal-world noisy datasets, confirm the superiority of ourmodel compared with some state-of-the-art methods.

More future works based on LCCN can be extended todeal with general multiple sources of noise in practise.



Q&AThank you!


Safeguarded Dynamic Label Regression for Noisy Supervision · Safeguarded Dynamic Label Regression...

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