Classify and Generate Reciprocally: Simultaneous Positive-Unlabelled Learning and Conditional Generation with Extra Data
Authors: Bing Yu
Ke Sun
He Wang
Zhouchen Lin
Zhanxing Zhu
Venue:  (2021)

Abstract: The scarcity of class-labeled data is a ubiquitous bottleneck in a wide range of machine learning problems. While abundant unlabeled data normally exist and provide a potential solution, it is extremely challenging to exploit them. In this paper, we address this problem by leveraging Positive-Unlabeled~(PU) classification and conditional generation with extra unlabeled data \emph{simultaneously}, both of which aim to make full use of agnostic unlabeled data to improve classification and generation performances. In particular, we present a novel training framework to jointly target both PU classification and conditional generation when exposing to extra data, especially out-of-distribution unlabeled data, by exploring the interplay between them: 1) enhancing the performance of PU classifiers with the assistance of a novel Conditional Generative Adversarial Network~(CGAN) that is robust to noisy labels, 2) leveraging extra data with predicted labels from a PU classifier to help the generation. Our key contribution is a Classifier-Noise-Invariant Conditional GAN~(CNI-CGAN) that can learn the clean data distribution from noisy labels predicted by a PU classifier. Theoretically, we proved the optimal condition of CNI-CGAN and experimentally, we conducted extensive evaluations on diverse datasets, verifying the simultaneous improvements on both classification and generation.

Under review as a conference paper at ICLR 2021
CLASSIFY AND GENERATE RECIPROCALLY: SIMULTANEOUS POSITIE-UNNABELLED LEARNING AND CONDITIONAL GENERATION WITH EXTRA DATA
Anonymous authors Paper under double-bile blind review
ABSTRACT
The scarcity of class-labeled data is ubiquitous bottleneck in wide range of machine learning problems. While abundant unlabeled data normally exist and provide potential solution, it is extremely challenging to exploit them. In this paper, we address this problem by leveraging tion and conditional generation with extra unlabeled data simulhaneously, both of which aim to make full use of agnostic unlabeled data to improve classification and generation performance. In particular, present novel training framework jointly target both PU classification and conditional generation when exposing to extra data, especially catoo--distribution unlabeled data, by exploring the interplay between them: 1) enhancing the performance of PU classifiers with the assistance of novel Conditional Generative Adversarial Network (CGAN) that robust noisy labels, 2) leveraging extra data with predicted labels from PU classifier to help the generation. Our key contribution is Classifier-Noóis Noise-Invarian Con- ditional GAN (CNI-CGAN) that can learn the clean data distribution from noisy labels predicted by a PU classifier. Theoretically, we proved the optimal condi- tion of CNI-CGAN and experimentally, conducted extensive evaluations diverse datasets, verifying the simultaneous improvements on both classification and generation.
Saative-Unllbeled (PU) classifica-
INTRODUCTION
Existing machine learning methods, particularly deep learning models, typically require big data to pursue remarkable performance. For instance, conditional deep generative models are able to generate high-fidelity and diverse images, but they have to rely on vast amounts labeled data (Lu-) cic al. 2019). Nevertheless, it is often laborious or impractical to collect large-scale accurate class-labeled data real-world scenarios, and thus the label scarcity is ubiquitous. Under such cir- cumstances, the performance of classification and conditional generation (Mirza & Osindero 2014) drops significantly (Lucic et al.) 2019). At the same time, diverse unlabeled data are available in enormous quantities, and therefore key issue is how to take advantage of the extra data enhance the conditional generation or classification.
Within the unlabeled data, both in-distribution and out-of-distribuue data exist, where in- distribution data conform to the distribution of the labeled data while out-of-distribution data do not. Our key insight is harness the out-of-distributio data. In generation with extra data, most related works focus on the in-distribution data (Lucic et al.] 2019 Gui et al., 2020) Donahue & Simonyan 2019). When it comes the out-of-distribttion data, the majority of existing meth- ods (Noguchi & Harada 2019; Yamaguchi et al.) 2019: Zhao et al.) (020) attempt to forcibly train generative models on large number unlabeled data, and then transfer the learned knowledge of the pre-trained generator to the in-distribution data. In classification, a common setting to utilize unlabeled data semi-supervised learning (Miyato et al. 2018 Sun et al. 2019 Berthelot et al.) 2019), which usually assumes that the unlabeled and labeled data come from the same distribution, ignoring their distributional mismatch. In contrast, Positive and Unlabeled (PU) Learning (Bekker & Davis 2018 Kiryo al. 2017) is an elegant way of handling this under-studied problem, where a model only has access to positive examples and unlabeled data. Therefore, it is possible to utilize pseudo labels predicted by PU classifier unlabeled data to guide the conditional generation.

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However, the predicted signals from the classifier tend to be noisy. Although there are flurry of pa- pers about learning from noisy labels for classification (sung Wei Tsai 2019; Ge et al. 2020 Guo et al. 2019), to our best knowledge, no work has considered to leverage the noisy labels seamlessly in joint classification and generation. Additionally, Hoou et al. (017 leveraged GANs to recover both positive and negative data distribution to step away from overfitting but they never considered the noise-invariant generation or their mutual improvement. Xu et al. (2019) focused on generative- discriminative complementary learning in weakly supervised learning, but we are the first attempt to tackle the (Multi-) Positive and Unlabeled learning setting while developing the method of noise- invariant generation from noisy labels. The discussion about more related works can be found in
Appendix B
In this paper, we focus on the mutual benefits of conditional generation and PU classification, in settings where extra unlabeled data, including out-of-distribution data, are provided although little class-labeled data is available. Firstly, a parallel non-negative multi-class PU estimator is derived to classify both the positive data of all classes and the negative data. Then we design Classifier-Noise- Invariant Conditional Generative Adversarial Network (CNI-CGAN) that is able to learn the clean data distribution on all unlabeled data with noisy labels provided by the PU classifier. Conversely, we also leverage our CNI-CGAN to enhance the performance of the PU classification through data augmentation, demonstrating reciprocal benefit for both generation and classification. We provide the theoretical analysis on the optimal condition of our CNI-CGAN and conduct extensive experi- ments to verify the superiority of our approach.
2
OUR METHOD
2.1
POSITIVE-UNLABELE LEARNING
Traditional Binary Positive-Unlabelee Problem Setting Let X E R and Y E {+1} be the input
and output variables and p(x, 3) is the joint distribution with marginal distribution Pp(x)) = p(z|Y'
+1) and (2) = p(x|y = -1). In particular, we denote p(x) as the distribution of unlabeled data. np. On and n. are the amount of positive, negative and unlabeled data, respectively.
Parallel Non-Nege PU Estimator Vanilla PU learning (Bekker & Davis, 2018: Kiryo et al,
2017 Du Plessis et al., 2014 2015) employs unbiased and consistent estimator. Denote go : R R as the score function parameterized by 0, and 8: R x [+ - IK as the loss function. The risk of go can be approximated by its empirical version denoted as Rpn (go):
Rpn (go) = Pt. (go) ) + nn Ry (90),
where Tp represents the class prior probability, i.e. P(Y = +1), with TD + T. = 1, and R (go) = My Ein (go +1) and R (go) = E E (go (,,",--), As negative data x² are un- available, common strategy is offset R, (go). We also know that (TPm(z) p(x) Tp and hence n., R, (go) R, (go) - R, (go). Then the resulting unbiased risk estimator Rp (go) can be formulated as:
Rpn (go) = xp Rt. (gn) RR (g0) + Ri (ga);
(2)
where RT((0) = - EE l (go (z,), -1) and Rr (ge) ΣT e (ge (x+), -1). The advan- tage of this unbiased risk minimizer is that the optimal solution can be easily obtained if g is linear in 0. However, in real scenarios we tend to leverage more flexible models ge. e.g., deep neural networks. This strategy will push the estimator ting. Hence, we decide to utilize non-negative risk (Kiryo et al., 2017) for our PU learning, which has been verified in (Kiryo et al., (017)) to allow deep neural network to mitigate overfitting. The non-negative PU estimator is formulated as:
point where it starts suffer from overfit-
Apu RT (ge) + max {0, Rí (96) - Rp (36)
In pursue of the parallel implementation of Rpu(go), we replace max {0, Ri (go) - T T. (nn)
with its lower bound 1 Σ max (o. R. (ge; x2) - Tp R (go; x;)} where Xi and X denote as the unlabeled and positive data in the i-th mini-batch, and N is the number of batches.
N
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From Binary PU to Multi-PU Learning Previous PU learning focuses learning classifier from positive and unlabeled data, and cannot easily be adapted to K +-1 multicllassfficaion tasks where K represents the number of classes in the positive data. Xu et al. (017)) ever developed Multi-Positive and Unlabeled learning, but the proposed algorithm may not allow deep neural networks. Instead, extend binary PU learning to multi-class version in straightforward way by additionally incor- porating cross entropy loss on all the positive data with labels for different classes. More precisely, we consider the K + 1-class classifier Sa as a score function So - (z), fk (f+++(()))) (x)). Af- ter the softmax function, we select the first K positive data to construct cross-entropy loss (CE, i..,, (fF())())))) = log E exp (f(())
(z) where y E [K]. For the PU loss, we consider the composite function h([o(z)) Rdd - where h(-)) conducts a logit transforma- tion on the accumulative probability for the first K classes, i.c., h(fo(z)) In( in which
Σ 2== f=1 exp (fd(x)) E exp (fz(m)) The final mini-batch risk of our PU learning can be presented as:
Rpu (fo:x')) = Tp (h(fo)i + max fo, . RT (m, + R (fo: &p)
(4)
where RCB (fo; = npp El QCE (fo (z))
2.2 CLASSIFIER-NOISER INVARIANT CONDITIONAL GENERATIVE ADVERSARIAL NETWORK
To leverage extra data, i.e., all unlabeled data, deploy our condi-
to benefit the generation, tional generative model on all data with pseudo labels predicted by our PU classifier. However, these predicted labels tend to be noisy, reduc- ing the reliability of the supervision signals and thus worsening the performance for the condi- tional generative model. Besides, the noise de- pends on the accuracy of the given PU classi- fier. To address this issue, we focus on devel- oping novel noise-invariant conditional GAN that is robust to noisy labels provided by a spec- ified classifier, e.g. PU classifier. We call our method Classifier-Noiss Invariant Conditional Generative Adversarial Network (CNI-CGAN) and the architecture is depicted in Figure [ In the following, we elaborate on each part of
Xy
PU
PU(x))
D
Xg
G
y
PU
PU
y
Principle of the Design of CNI-CGAN
Albeit being noisy, the pseudo labels given by the PU classifier still provide rich informa- take
Figure 1: Model architecture of our Classifier- Noise-Invariant Conditional GAN (CNI-CGAN). The output Hg of the conditional generator G is paired with a noisy label ÿ corrupted by the PU- dependent confusion matrix Ò. The discriminator D distinguishes between whether given labeled sample comes from the real data (I,, PUg (x,)) or generated data (xg. 5).
tion that we can exploit. The key the noise generation mechanism into consid- eration during generation. We denote the real data as I, and the predicted hard label through PU classifier as PUg(x,). i.e., (U)(zz) arg max; f/ (x,), as displayed in Figure [ We let the generator "imitate" the noise generation mechanism to generate pseudo labels for the labeled data. With both pseudo and real labels, can leverage the PU classifier fe to estimate confusion matrix Č' to model the label noise from the classifier. During generation, a real label y. while being fed into the generator G, will also be polluted by Ö to compute a noisy label ÿ. which then will be combined with the generated fake sample 2g for the following discrimination. Finally, the discriminator D will distinguish the real samples [x,, (x, out of fake samples [zg. 7) Overall, the noise "generation" mechanism from both sides can be balanced.
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Estimation of Ć The key in the design of Č is to estimate the label noise of the pre-trained PU classifier by considering all the samples of each class. More specifically, the confusion matrix C is k + 1 by k+ ++1 and each entry Čsj represents the probability of generated sample Tg. given label i, being classified as class j by the PU classifier. Mathematically, we denote Cig as:
C..- (1) = jly = i) (ro,
where Tig G( i) and I is the indicator function. Owing to the stochastic optimization nature when training deep neural networks, we incorporate the estimation of Ć in the processing of training by Exponential Moving Average (EMA) method. We formulate the update of C(++) in the 1-th mini-batch as follows:
((++)) = =x²00 + (1- A)
(6)
where 4C, denotes the incremental change of C on the current 1-th mini-batch data X via Eq. is the averaging coefficient in EMA.
A
Theoretical Guarantee of Clean Data Distribution Firstly, we denote (zx) the oracle class of sample x from an oracle classifier (-). Let i = I,... K ++ be the class-prior probability of the class in the multi pulti-postive unlabeled setting. Theorem I proves the optimal condition of CNI-CGAN to guarantee the convergence to the clean data distribution. The proof is provided in Appendix A
Theorem 1. (Optimal Condition of CNI-CGAN) Let Pa be a probabilistic transition matrix where Pi = ((O(s)) = -ily = -) indicates the probability of sample Fg with the oracle label j generated by G with the initial label i. We assume that the conditional sample space of each class is disjoint with each other, then
(1) P9 is a permutation matrix if the generator G in CNI-CGAN is optimal, with the permutation, compared with an identity matrix, only happens on rows r where corresponding nr, r are equal.
(2) If Ps is an identity matrix and the generator G in CNI-CGAN is optimal, then p' y) (x. y) where p" (z. y) and p² y) are the real and the generating joint distribution, respectively.
The Auxiliary Loss The optimal G in CNI-CGAN can only guarantee that (xx y) is close to p' (I, y) as the optimal permutation matrix P9, i.e., permutation matrix, is close to the identity matrix. Hence in practice, to ensure that we can learn an identity matrix for Pa and thus achieve the clean data distribution,
introduce auxiliary loss to encourage larger trace of Pa, i.e., DK+1 P(O(xg) i)ly y = i). As O()) is intractable, we approximate by the current PU classifier (Ul(T Then we obtain the auxiliary loss:
K +1 E. ((((1)
laux(2, max K+1
Σ
where & E (0. 1) is a converge to the identity matrix where CNI-CGAN can learn the clean data distribution even in the presence of noisy labels.
With the support of auxiliary loss, P has the tendency to
Comparison with RCGAN (Thekumparampi) et al.) 2018; Kaneko et al., 2019 The the- oretical property of CNI-CGAN has a major advantage over existing Robust CGAN (RC- GAN) (Thekumparampil et al. 2018 Kaneko al.] 2019), for which the optimal condition can only be achieved when the label confusion matrix is known a priori. Although heuristics can be employed, such as RCGAN-U (Thekumparampil et al. 2018), handle the unknown label noise setting, these approaches still lack the theoretical guarantee to converge to the clean data distribu- tion. Additionally, to guarantee the efficacy of our approach, one implicit and mild assumption that our PU classifier will not overfit on the training data, while our non-negative estimator helps to ensure that it as explained in Section 2.T. should be worthwhile to note that our CNI-CGAN conducts K + classes generation. To further clarify the optimization process of CNI-CGAN, we elaborate the training steps of D and G, respectively.
D-Step: We train D on an adversarial loss from both the real data and the generated (Zg, W), where ÿ is corrupted by č. Öj denotes the y-th row of Č. We formulate the loss of D as:
max E [0(D(z, (U)()))) + DEF z>p(a)
E
[0 DDG((, v)))
Ne0 SNI2.00-P Blywdy
(8)
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where F is family of discriminators and Pz is the distribution of latent space vector e.g., a Normal distribution. Py is a discrete uniform distribution on K + 1] and is the measuring function.
G-Step: We train G additionally on the auxiliary loss taux (2, y) as follows:
min
1Ø(1 - D(G((,)). + Blaux( ())
GEG
6i P. Cy
(9)
where 3 controls the strength auxiliary loss and G is family of generators.
2.3 TRAINING ALGORITIIM
Firstly, we obtain PU classifier fe trained on multi coalti-positiv and unlabeled dataset with the par- allel non-negative estimator derived in Section 22.1 Then we train our CNI-CGAN, described in Section 2.2] on data with pseudo labels predicted by the pre-trained PU classifier. As our CNI- CGAN is robust to noisy labels, we leverage the data generated by CNI-CGAN to conduct data augmentation to improve the PU classifier. Finally, we implement the joint optimization for the training of CNI-CGAN and the data augmentation of the PU classifier. We summarize the details in Algorithm and Appendix C
Simultaneous Improvement PU Learning and Generation with Extra Data From the per- spective of PU classification, due to the theoretical guarantee from Theorem CNI-CGAN capa- ble of learning a clean data distribution of noisy pseudo labels predicted by the pre-trained PU
Algorithm Alternating Minimization for PU Learning and Classifier-Niise-mmee Invariant Generation. 3 > 0, A, (0, 1). Lo and L N+, Initializing ((1) identity matrix. Number of batches N during the training.
Input: Training data (Xp, Xx). Batch size M and
Output: Model parameter for generator G, and for the PU classifier fg.
1: * Pre-train PU classifier Jo
2: for to N do
3: Update I' by descending its stochastic gradient of Rpn (Jo; via Eq.
4: end for
5: repeat
6: 1* Update CNI-CGAN #/
7:
for to T. do
8:
Sample {21,..,, ZMr, [yI,..,,yr) and (.., xM) from Pz, Py and all training data, respectively, and then sample 17.,..., through the current Č(.), Update the discrimi- nator D by ascending its stochastic gradient of
1
M DiO(D(x, PU, + 6(1 D(G((Z.).)..)))
9: Sample {2i, .... 2m3 and tyi,..., y from Pz and Pv. and then sample (5,,.., through the current O()) Update the generator G by descending its stochastic gradient of
M
1
Io 3.) + 3laxx 2:)]-
M
if Lo then Compute A
EM M
[(Ptt(((e..)))l)) via Eq. 5 and then estimate by ((+1) xO + (1 A)
end if end for
13:
Update PU classifier via Data Augmentation * Sample {Zi,... ZM and Ly.,..., } from Pz and Py, respectively, and then update the PU classifier fo by descending its stochastic gradient of
15:
CB (fo (G(z..)))
16: until convergence
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classifier. Hence, the following data augmentation has the potential to improve the generalization of PU classification regardless of the specific form of the PU estimator. From the perspective of gener- ation with extra data, the predicted labels unlabeled data from the PU classifier can provide the CNI-CGAN with more supervision signals, thus further improving the quality of generation. Due to the joint optimization, both the PU classification and the conditional generative models are able to improve each other reciprocally, as demonstrated in the following experiments.
EXPERIMENT
Experimental Setup We perform our approaches and several baselines on MNIST, Fashion-MNIST and CIFAR-10. We select the first 5 classes on MNIST and 5 non-clothes classes on Fashion- MNIST, respectively, for K + classification (K = 5). To verify the consistent effectiveness of our method in the standard binary PU setting, we pick the categories of transportation tools in CIFAR- 10 as the one-class positive dataset. As for the baselines, the first is CGAN-P, where a Vanilla CGAN (Mirza& & Osindero 2014) is trained only on limited positive data. Another natural baseline is CGAN-A where a Vanilla CGAN is trained on all data with labels given by the PU classifier. The last baseline is RCGAN-U (Thekumparampil al. 2018) where the confusion matrix is totally learnable while training. For fair comparisons, we choose the same GAN architecture, and more details about parameersss can be found in Appendix D
Evaluation For MNIST and Fashion-MNIST racy (Thekumparampil al. 2018) and PU Accuracy to evaluate the quality of generated images. Generator Label Accuracy compares specified y from CGANs to the true class of the generated ex- amples through a pre-trained (almost) oracle classifier f. In experiments, we pre-trained two K +1 classifiers with 99. 99.28% and 98.23% accuracy on the two datasets, respectively. Additionally, the increased PU Accurucy measures the closeness between generated data distribution and test (almost real) data distribution for the PU classification, serving as key indicator to reflect the quality of generated images. For CIFAR 10, we take the Inception Score into consideration.
we mainly use Generator Label Accu-
3.1 GENERATION AND CLASSIFICATION PERFORMANCE
We set the whole training dataset as the unlabeled data and select certain amount of positive data with the ratio of Positive Rate. Figure presents the trend of Generator Label Accuracy, Inception Score and PU Accuracy as the Positive Rate increases. It turns out that CNI-CGAN outperforms CGAN-P and CGAN-A consistently especially when the Positive Rate is small, i.e. little positive data. Remarkably, our approach enhances the PU accuracy greatly when exposed to low positive
Generztor Label Accuracy
MNIST
Generator Label Aceurncy
Fashice-MNiS
CIFAR-10
1:00
300
Inception Score
CGAN-P COAN-A
CGAN-P COAN-A
CGANP
20
CGAN-A
01
15c
10"
16
101
18
MNIST
MNIST
CIFAR-10
PU Accurncy (%))
Aecuracy
Koemayy UU
MLD
2 22 a
$7.5
Original CGAN-A
Original PU
Original
35.0
COAN-A
OGAN-A
6.
Ous
10
16"
Positive Rate
Positive Rate
Positive Rate
Figure 2: Generation and classification performance of CGAN-P, CGAN-A and Ours on three datasets. Results of CGAN-P on PU accuracy do not exist since CGAN-P generates only K classes data rather than K + 1 categories that the PU classifier needs.

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MNIST: Positive Rate 0.2%, Initial PU: 69.14%
CNI-CGAN
CGAN-A
RCGAN-U
CNI-CGAN
Fashion-MNe
MNNIST
CIFAR-10
Q
0
O
0
O
0
0
0
0 O
O
O
O
O
D
/
1
/
1 2 3 4 5
1 2 3 4 8
5
8
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7-
2 3 3
22
2 3
7 6 4 9
7 5 4
2 2 3
2 3
2 3
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4 3 9
2
7
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2
3 7
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4
4 4 5
4
4 9
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Generator Label Accuracy
39.67%
81.58
96.33%
Figure 3: Visualization of generated samples on three datasets. Rows below the red line represent the negative class. We highlight the erroneously generated images with red boxes MNIST.
rates, while CGAN-A even worsens the original PU classifier sometimes in this scenario due to the existence of too much label noise given by less accurate PU classifier. Meanwhile, when more su- pervised positive data are given, the PU classifier generalizes better and then provides more accurate labels, conversely leading to more consistent and better performance for all methods. Besides, note that even though the CGAN-P achieves comparable generator label accuracy on MNIST, it results in lower Inception Score. We demonstrate this in Appendix D
Table 1: PU classification accuracy of RCGAN-U and Ours across three datasets. Final PU accuracy represents the accuracy of PU classifier after the data augmentation.
Final PU Accuracy Positive Rates (%)
0.2%
0.3%
1.0%
10.0%
Original PU
68.86
76.75
86.94
95.88
MNIST
ROGAN-U
87,95
95.24
95.86
97,80
Ours
96.33
96.43
96.71
97.82
Original PU
80.68
88.25
93.05
95.99
Fashico-MNIST
ROGAN-U
89.21
92.05
94.59
97.24
Ours
89.23
93.82
95.16
97.33
Original PD
76.79
80.63
85.33
88.43
CIFAR-I0 10
ROGAN-U
83.13
86.22
88.22
90.45
Ours
87.64
87.92
88.60
90.69
To verify the advantage of theoretical property for our CNI-CGAN, we further compare it with RCGCN-U (Thekumparampil et al. 2018: Kaneko et al., 2019), the heuristic version of robust gen- eration against unknown noisy labels setting without the theoretical guarantee of optimal condition. As observed in Table D our method outperforms RCGAN-U especially when the positive rate is low, and when the number of positive labeled data is relatively large, e.g., 10.0%, both Ours and RCGAN-U obtain comparable performance.
Visualization To further demonstrate the superiority of CNI-CGAN compared with the other base- lines, we present some generated images within + classes from CGAN-A, RCGAN-U and CNI- CGAN on MNIST, and high-quality images from CNI-CGAN on Fashion-MNIST and CIFAR-IO. in Figure 3 In particular, we choose the positive rate as 0.2% on MNIST, yielding the initial PU classifier with 69.14% accuracy. Given the noisy labels on all data, our CNI-CGAN can generate more accurate images of each class visually compared with CGAN-A and RCGAN-U. Results of Fashion-MNIST and comparison with CGAN-P CIFAR-IO can refer Appendix
3.2 ROBUSTNESS OF OUR APPROACH
Robustness against the Initial PU accuracy The auxiliary loss can help the CNI-CGAN to learn the clean data distribution regardless of the initial accuracy PU classifiers. To verify that, select distinct positive rates, yielding the pre- pre-trained PU classifiers with different initial accuracies. Then perform method based these PU classifiers. Figure 4 suggests that although better initial PU accuracy can be beneficial to the initial generation performance, our approach under different PU accuracies can still attain the similar generation quality after sufficient training.
Robustness against the Unlabeled data In real scenarios, we are more likely to have little knowl- edge about the extra data have. To further verify the robustness of CNI-CGAN against the
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GAN: Generator Accuracy (%)
MNIST
GAN: Generstor Label Accurecy (%g
Fashion MNIST
CIFAR
1000
100
90
8.8
80-
80
PI] Accuracy(
866
60
60
84
40-
40
82
Initill PC 77 77.67%
Initial PU 88 27%
Inkial PD 79 49%
20
Initaal PU 64.57%
20
Initaal PU 91.01%
Initaal PC 82.51%
Initial PU 91.28%
Inttial PU 54,02%
78
Inttal PU 45.45%
10"
10"
10"
10"
10"
10
10"
10"
Number of Troining Iterations
Number of Trinnin Iterations
Number of Training Iterations
Figure 4: Tendency of generation performance as the training iterations increaseon three datasets.
unknown distribution of extra data, we test different approaches across different amounts and dis- tributions of the unlabeled data. Particularly, we consider two different types of distributions for unlabeled data. Type is 1 '+11'- K+1 K+1 where the number of data in each class, including the negative data, is even, while type is 2K ..."K' 1 where the negative data makes up half of all unlabeled data. In experiments,
focus the PÚ Accuracy to evaluate both the generation
quality and the improvement of PU learning. For MNIST, we choose 1% and 0.5% for two settings while we opt for 0.5% and 0.2% both Fashion-MNIST and CIFAR-10.
Disiiictoo Type PU Aco50)
DissErctou Taee PU Au4N0
Fadian-MNISS
Distiactes Type Acor5
CIFAR-10
75
16'
16
16"
Din Draiiia Type 2.U Ava77))
Din Rrabic Sy0 2 PU Av076))
Bastac Lyps A30750
98
23
Ouard
Numbor of Unitibeeed Dep
Nembvr erthiieeled Dats
Numbertlniieee Dats
Figure 5: PU Classification accuracy of CGAN-A. RCGAN-U and Ours after joint optimization across different amounts and distribution types of unlabeled data.
Figure manifests that the accuracy of PU classifier exhibits slight ascending tendency with the increasing of the number of unlabeled data. More importantly, our CNI-CGAN almost consistently outperforms other baselines across different amount of unlabeled data as well as distinct distributions of unlabeled data. This verifies the robustness of our proposal to the situation of extra data.
DISCUSSION AND CONCLUSION
In this paper, we proposed new method, CNI-CGAN, to jointly exploit PU classification and conditional generation. is, to our best knowledge, the first method of such kind to break the ceiling of class-label scarcity, by combining two promising yet separate methodologies to gain massive mutual improvements. CNI-CGAN can learn the clean data distribution from noisy labels given by a PU classifier, and then enhance the performance of PU classification through data augmentation in various settings. We have demonstrated, both theoretically and experimentally, the superiority of our proposal on diverse benchmark datasets in an exhaustive and comprehensive manner. In the future, it will be promising to investigate learning strategies imbalanced data, e.g., cost-sensitive learning (Elkan 200T), to extend our approach to broader settings, which will further cater to real- world scenarios where only highly unbalanced data available.
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10


Reviews:
[{"review_id": "YUfm2Oq0UuW", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This work proposes to optimize PU classifiers and conditional generative models jointly. A CNI-CGAN framework is proposed, in which the generated examples and pseudo labels are applied to PU classifications and the conditional generation, respectively.\n\nThe leverage of noisy labels in the joint optimization across classification and generation seems interesting. Especially, both PU classification and conditional generation can benefit from such a joint optimization.\n\nI have some concerns about the details of this work.\n1. This work extends binary PU learning to a multi-class version so that deep neural networks can be applied. In the proposed CNI-CGAN framework, to my understanding, any PU classifier can be applied here, not necessarily a differentiable one. The multi-PU classifier proposed in [1] can also be applied. It might also work on MNIST and FMNIST.\n\n2. Another question is about PU(X_r) and y_tilde in Figure 1. They are one-hot coding in this work. A trivial but promising choice is to use soft labels. Any special reason for choosing one-hot encoding?\n\n3. Towards the estimation of C_tilde: it is updated with Exponential Moving Average (EMA). Why use the moment-based update instead of the instantaneous update? The noise label corresponding to the newest PU classifier can be obtained with the instantaneous update. Or it just stabilizes the training process?\n\n4. It is expensive to estimate k + 1 by k + 1 confusion matrix C_tilde. The estimation is conducted (L-L_0) times in each update. Its efficiency should be discussed, especially when compared to the cost of the whole training process.\n\n\n[1] Yixing Xu, Chang Xu, Chao Xu, and Dacheng Tao. Multi-positive and unlabeled learning. In IJCAI, pp. 3182–3188, 2017. ", "extra_scores": {}, "extra_text": {}}, {"review_id": "TBfp1faS0M", "reviewer": "AnonReviewer5", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Summary:\nThis paper proposed the combination of two techniques for improved learning with unlabelled data: 1)  Positive-Unlabelled (PU) classifier, and 2) class-conditional GAN (cGAN). The idea is that the PU classifier can help produce more accurate pseudo labels for training of a cGAN, and with the improved cGAN, the generated images can be used in turn to further improve the PU classifier. The idea looks interesting and the empirical results verified its effectiveness. \n\nThe major weakness of this paper is the presentation. \n1. The paper is hard to read. The problems are not well defined and connected. The exact learning setting is vague. What is the main problem the authors try to solve here? The classification problem or the generation problem? \n2. The technical contribution to PU classification is very limited. The proposed learning pipeline is basically: 1) training PU classifier, 2) using the classifier do something else, then 3) retraining the classifier with more data. This does not seem to be a solid contribution.\n3.  On the other hand, what is the contribution to generative modelling with extra unlabelled data? Using a more accurate predictor (PU classifier) to obtain high-quality pseudo labels is also trivial.\n4. Why the proposed approach helps learning with out-of-distribution data? How does OOD data help GAN learning? In other words, what is the goal of OOD GAN?\n5. Why PU data is a practical way for using web data?  Why not simply use a pre-trained models to do pseudo labelling, along with open-set or OOD learning strategies? The experiments were only run on small datasets MNIST, Fashion MNIST and CIFAR-10. I am not convinced what the authors proposed in this paper is useful for dealing with real-world web data like WebVision. \n6. Is PU Acc a fair performance metric for baseline methods? \n7. Many typos needed to be fixed.\n\nComments after rebuttal:\n-------------\nThank the authors for the clarifications. I will raise my score to 5. Theoretical analysis of the proposed method is nice. But I still think the proposed approach was not well justified or motivated. Why is it the best option? And how are other simple baselines for improving both (not standalone) settings? ", "extra_scores": {}, "extra_text": {}}, {"review_id": "SrTVWPnBVKd", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The topic of the work is interesting. It uses a joint training system to improve two divergent techniques in a novel way which jointly bootstraps better performance on the problems that they demonstrate. They extend their comparisons in ways to increase the data imbalance problem and show robustness to even that. The tests they do show are convincing that there is definitely something of value here, however, in the next paragraph, I will discuss some problems I find with the work and comparisons themselves.\n\nDid every technique get the same number of iterations to converge, or did the authors use early stopping? The authors state that \"[they] take the Inception Score into consideration,\" what does that mean? How did they take it into consideration? The table of their results lists a percentage, and inception score is not a percentage. The authors state they use an \"almost oracle\" for MNIST and Fashion-MNIST, but they do not state how they got percentages for CIFAR-10, nor, if they used an oracle, what the accuracy metrics are for the CIFAR-10 oracle. How does the model hold up on more than 10 classes? There is no discussion on that topic (many real world problems deal with more than 10 classes). What about data imbalance worse than 2:1 (also shows up all the time in real world problems)? How long did training take in clock time vs these other techniques? What about number of parameters used for the different models? It would also be nice to see how well it performs on slightly harder datasets with larger samples.\n\nThere were some clarity issues as well: variables and notation are often used before they are explained, and there are gaps in explaining how exactly one would implement these results: what hyperparameters did the authors use for $L_0$, $\\lambda$, $\\beta$, and $\\kappa$ for their results? Poor grammar throughout the paper also causes some confusion when reading. A summary of the proof of theorem 1 would be nice, as appendix A is not released so is not verifiable to this reviewer.\n\nOne small issue is that the paper seems to cite a lot of survey papers and not the original work itself, however, there is nothing majorly concerning on that front and it is well supported.\n\n\nOverall, the paper seems original and decently significant, however, it would be a much stronger submission if some of the issues here were addressed. As it stands, it is a 6/10.", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper studies the problem of leveraging Positive-Unlabeled~(PU) classification and conditional generation with extra unlabeled data simultaneously in one learning framework. Some major review concerns on the weaknesses include limited novel technical contributions, poor presentation and weak experimental results (e.g., experiments were mostly conducted on small toy datasets). Overall, the paper has some interesting idea, but the work is clearly below the ICLR acceptance bar. 
Decision: Reject