SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Theorem 1. The square loss function  $\ell$  of  $DPCLS$  can be rewritten as  $\| \mathbf{F}_{\mathbf{G}} + \mathbf{N} - \mathbf{XW}\| _F^2$ , where  $\mathbf{F}_{\mathbf{G}}\in \mathbb{R}^{m\times q}$  and  $\mathbf{N}\in \mathbb{R}^{m\times q}$  are ground-truth label matrix and false-positive label matrix respectively. Let  $\mathcal{H} = \mathbf{W}\times \mathbf{N}$  represent the family of functions for  $DPCLS$ , where the linear function  $(\mathbf{W},\mathbf{N})\in \mathcal{H}$ . Suppose the complexity of  $\mathbf{W}$  and the sparsity of  $\mathbf{N}$  are upper bounded by  $\epsilon_{1}$  and  $\epsilon_{2}$  respectively, i.e.,  $\| \mathbf{W}\| _F\leq \epsilon_1$  and  $\| \mathbf{N}\| _1\leq \epsilon_2$ . The Rademacher complexity of  $DPCLS$  with square loss  $\ell$  is upper bounded as follow
$$
\hat {\mathcal {R}} _ {S} (\ell \circ \mathcal {H}) \leq \frac {2 \sqrt {2} q \left(\sqrt {m q} \epsilon_ {1} + \epsilon_ {2}\right)}{m}. \tag {19}
$$
Lemma 1. [11] Denote  $\mathcal{H}$  be a family of functions and  $S = \{x_{1}, x_{2}, \dots, x_{m}\}$  is a set of fixed samples. Loss function  $\ell$  is upper bounded by  $\Theta \geq 0$ , then for any  $\delta > 0$ , with probability at least  $1 - \delta$ , for all  $h \in \mathcal{H}$  we have
$$
\mathcal {L} (h) \leq \mathcal {L} _ {\mathcal {S}} (h) + \hat {\mathcal {R}} _ {\mathcal {S}} (\ell \circ \mathcal {H}) + 3 \Theta \sqrt {\frac {\log (2 / \delta)}{2 m}}, \tag {20}
$$
where  $\mathcal{L}(h)$  and  $\mathcal{L}_S(h)$  are generalization error and empirical error to  $h$  respectively.
The detailed proof of Theorem 1 is given in the Section B of the supplementary file. According to Lemma 1 and Theorem 1, we have
$$
\mathcal {L} (h) \leq \mathcal {L} _ {\mathcal {S}} (h) + \frac {2 \sqrt {2} q \left(\sqrt {m q} \epsilon_ {1} + \epsilon_ {2}\right)}{m} + 3 \Theta \sqrt {\frac {\log (2 / \delta)}{2 m}}. \tag {21}
$$
The Rademacher complexity is bounded by the sum of the complexity of classifier  $\mathbf{W}$  and the sparsity of false-positive label matrix  $\mathbf{N}$ . When the number of false-positive labels is small, which leads to a better generalization performance. Moreover, more training samples (a larger  $m$ ) will also promote the generalization performance.
Theorem 2. Denote  $\mathbf{F} \in \{0,1\}^{m \times q}$  and  $\mathbf{D} \in \{0,1\}^{m \times m}$  the partial label matrix and the to be optimized semantic dissimilarity matrix. Let  $\mathbf{F}_{\mathbf{G}}$  and  $\hat{\mathbf{D}}$  be the ground-truth label matrix and the ground-truth dissimilarity matrix. Suppose the smallest eigenvalue of  $\hat{\mathbf{D}}$  and  $\mathbf{L}$  are  $\lambda_{\hat{\mathbf{D}}}$  and  $\lambda_{\mathbf{L}}$  respectively ( $\lambda_{\hat{\mathbf{D}}} \geq 0$ ,  $\lambda_{\mathbf{L}} \geq 0$ ). Let  $\left\| \bar{\Delta}_{\mathbf{F}} \right\|_F$  be the average distance of each sample between  $\mathbf{F}_{\mathbf{G}}$  and  $\mathbf{F}$  (i.e.,  $\left\| \bar{\Delta}_{\mathbf{F}} \right\|_F = \frac{1}{m} \left\| \mathbf{F}_{\mathbf{G}} - \mathbf{F} \right\|_F$ ) and  $\left\| \bar{\Delta}_{\mathbf{D}} \right\|_F$  be the average distance of each corresponding position between  $\hat{\mathbf{D}}$  and  $\mathbf{D}$  (i.e.,  $\left\| \bar{\Delta}_{\mathbf{D}} \right\|_F = \frac{1}{m^2} \left\| \hat{\mathbf{D}} - \mathbf{D} \right\|_F$ ). Then we have
$$
\left\| \bar {\boldsymbol {\Delta}} _ {\mathbf {F}} \right\| _ {F} \leq \frac {q}{\lambda_ {\hat {\mathbf {D}}}} \left\| \mathbf {D} - \hat {\mathbf {D}} \right\| _ {F} + \frac {2 \sqrt {q}}{\lambda_ {\hat {\mathbf {D}}} \sqrt {m}} \left\| \hat {\mathbf {D}} \right\| _ {F}, \tag {22}
$$
$$
\left\| \bar {\boldsymbol {\Delta}} _ {\mathbf {D}} \right\| _ {F} \leq \frac {1}{\lambda_ {\mathbf {L}} m} \left\| \mathbf {F} \mathbf {F} ^ {\intercal} - \mathbf {F} _ {\mathbf {G}} \mathbf {F} _ {\mathbf {G}} ^ {\intercal} \right\| _ {F} + \frac {2}{\lambda_ {\mathbf {L}} m} \left\| \mathbf {L} \right\| _ {F} + \frac {1}{\lambda_ {\mathbf {L}} m}.
$$
The proof can be found in Section B of the supplementary file. From Theorem 2, we can find that as the number of samples  $m$  increases, the upper bound of  $\left\| \bar{\Delta}_{\mathbf{F}} \right\|_F$  decreases, which indicates that more training samples will push the partial label matrix to be close to the ground-truth one and achieve better PLL performance. Moreover, a smaller error between  $\mathbf{D}$  and  $\hat{\mathbf{D}}$  implies a smaller upper bound of  $\left\| \bar{\Delta}_{\mathbf{F}} \right\|_F$ , which indicates a better dissimilarity matrix can help achieve a better label matrix. Similarly, a larger number of training samples will reduce the distance between  $\mathbf{D}$  and  $\hat{\mathbf{D}}$ , and a smaller error between  $\mathbf{F}$  and  $\mathbf{F}_{\mathbf{G}}$  implies a smaller upper bound of  $\left\| \bar{\Delta}_{\mathbf{D}} \right\|_F$ , suggesting a better dissimilarity matrix. As a summary, we prove that, under some general assumptions, a better dissimilarity matrix will help produce a better label matrix, and vice versa. Therefore, the rationality of the proposed adversarial prior is theoretically proved.
5 Experiment and Analysis
To demonstrate the effectiveness of the proposed model, we compared DPCLS with eight shallow PLL algorithms, which were configured by the suggested parameters in the literature, i.e., CLPL [1], PL-SVM [12], PL-KNN [5], PL-DA [18], IPAL [22], AGGD [16], PL-CLA [13], SDIM [2]. Those methods were evaluated on 10 synthetic data sets and 7 real-world data sets, whose details can be found in Section C of the supplementary file. Three deep learning PLL methods RC [4], PRODEN [10], and CAVL [21] were also evaluated as comparison on the real-world data sets. Ten runs of  $50\% / 50\%$  random train/test splits were performed on each data set, and the average classification accuracy and the standard deviation were recorded.
5.1 Performance on Synthetic Data Sets
Following the widely-used partial label data generation protocol [1], 10 synthetic data sets were used to generate artificial partial label data sets. Specifically, three parameters  $r, p, \epsilon$  control the generation process, i.e.,  $p$  controls the proportion of partial label examples,  $r$  controls the number of false-positive labels, and  $\epsilon$  controls the probability of a specific false-positive label co-occurs with the ground-truth label.
Fig. 1 illustrates the classification accuracy of six data sets (Glass, Steel, Ecoli, Yeast, Optdigits and Usps) as the co-occurring probability  $\epsilon$  varies from 0.1 to 0.7 with step-size 0.1 ( $p = 1$ ,  $r = 1$ ). In general, the proposed model clearly exceeds the compared methods with different  $\epsilon$ , and achieves the highest accuracy in 33 out of 36 cases. Moreover, as  $\epsilon$  increases, it is more difficult to distinguish the
(a) Glass  $(p = 1, r = 1)$
(b) Steel  $(p = 1, r = 1)$
(c) Ecoli  $(p = 1, r = 1)$
(d) Yeast  $(p = 1, r = 1)$
(e) Optdigits  $(p = 1, r = 1)$
(f) Usps  $(p = 1, r = 1)$
Figure 1: The classification accuracy of each algorithm as  $\epsilon$  increases from 0.1 to 0.7 with  $p = 1$ ,  $r = 1$ .
Table 1: Classification accuracy (mean±std) of each comparing algorithm on four synthetic data sets as  $r$  increases from 3 to 6.  $\bullet / \circ$  indicates whether the accuracy of DPCLS is statistically superior/inferior to the compared algorithm according to the pairwise t-test at 0.05 significance level.
Data set	r	DPCLS	CLPL	PL-SVM	PL-KNN	PL-DA	IPAL	AGGD	PL-CLA	SDIM
Isolet	3	.912±.008	.604±.023●	.668±.034●	.695±.025●	.782±.020●	.793±.018●	.898±.011●	.880±.007●	.917±.007
4	.899±.011	.594±.023●	.577±.057●	.661±.026●	.768±.022●	.772±.017●	.880±.013●	.855±.011●	.891±.015
5	.880±.012	.535±.015●	.543±.070●	.668±.018●	.751±.016●	.790±.010●	.855±.017●	.845±.018●	.849±.017●
6	.858±.017	.525±.020●	.452±.062●	.645±.020●	.733±.020●	.776±.011●	.824±.015●	.824±.015●	.824±.018●
Orl	3	.807±.040	.780±.037	.262±.034●	.247±.033●	.347±.061●	.715±.064●	.764±.054	.735±.055●	.744±.044●
4	.776±.049	.743±.031	.196±.052●	.216±.030●	.287±.042●	.665±.065●	.730±.065	.673±.066●	.692±.067●
5	.736±.041	.704±.032	.158±.029●	.189±.027●	.247±.040●	.594±.045●	.677±.067●	.607±.049●	.622±.056●
6	.669±.042	.660±.045	.114±.024●	.159±.025●	.218±.029●	.536±.047●	.646±.073	.545±.050●	.556±.053●
Amazon	3	.062±.007	.058±.007	.041±.006●	.021±.004●	.022±.004●	.060±.009	.056±.010	.055±.008●	.047±.006●
4	.057±.007	.055±.007	.043±.005●	.020±.005●	.021±.005●	.055±.009	.054±.009	.053±.007	.045±.005●
5	.055±.009	.050±.007	.043±.005●	.020±.005●	.022±.005●	.050±.009	.047±.008●	.044±.009●	.037±.007●
6	.048±.009	.042±.007	.029±.007●	.020±.003●	.020±.003●	.046±.009	.043±.008	.041±.006●	.032±.006●
Bookmark	3	.337±.007	.248±.007●	.208±.013●	.115±.017●	.178±.014●	.286±.012●	.333±.009	.291±.009●	.305±.010●
4	.326±.008	.244±.009●	.190±.020●	.121±.028●	.170±.013●	.282±.010●	.325±.007	.284±.011●	.300±.011●
5	.323±.009	.240±.010●	.169±.019●	.116±.025●	.189±.051●	.278±.009●	.319±.005	.278±.010●	.298±.011●
6	.322±.009	.240±.010●	.148±.013●	.103±.029●	.186±.043●	.270±.009●	.316±.007	.276±.009●	.295±.007●
false-positive label and the ground-truth label, and PLL becomes harder. Accordingly, the accuracies of all the PLL algorithms decrease, but the performance advantage of the proposed method over the compared ones becomes more salient such as on Glass and Ecoli, which proves that our method is skilled in more challenging PLL tasks.
Table 1 reports the classification accuracies of different algorithms as  $r$  varies from 3 to 6 on four data sets (Isolet, Orl, Amazon, Bookmark) with more than 20 classes. Our method ranks first in 11 out of 12 cases, and ranks second in the remaining case. The improvements brought by our method are significant. For example, on Isolet with  $r = 6$ , our method improves the classification accuracy of the best comparison from 0.824 to 0.858. According to the pairwise t-test, our method significantly surpasses the compared ones in 103 out of 128 cases. Moreover, different methods have different characteristics and may fit different data sets. For example, CLPL performs satisfactorily on Orl and Amazon, but badly on Isolet and Bookmark; AGGD is good at Bookmark, but not at Orl.
DPCLS CLPL - PL-SVM - PL-KNN - PL-DA - IPAL AGGD - PL-CLA SDIM
Table 2: Classification accuracy (mean±std) of each algorithm on real-world partial label data sets.  $\bullet /0$  indicates whether the accuracy of DPCLS is statistically superior/inferior to the compared algorithm according to the pairwise t-test at 0.05 significance level. "S" and "D" indicate shallow and deep PLL methods respectively.
Type	Method	FG-NET	FG-NET3	FG-NET5	Lost	MSRCv2	BirdSong	Malagasy	Soccer Player	Yahoo! News
S	DPCLS	.077±.009	.436±.017	.586±.011	.770±.024	.557±.014	.751±.009	.676±.004	.532±.002	.626±.003
CLPL	.058±.009	.383±.016	.538±.017	.665±.019	.371±.010	.610±.012	.675±.016	.497±.002	.544±.004
PL-SVM	.052±.010	.357±.022	.511±.026	.578±.078	.310±.060	.682±.023	.564±.061	.500±.002	.546±.006
PL-KNN	.038±.005	.287±.022	.433±.019	.334±.021	.391±.023	.657±.014	.573±.007	.493±.002	.383±.003
PL-DA	.042±.004	.166±.050	.255±.070	.309±.069	.416±.022	.690±.013	.606±.008	.495±.003	.397±.004
IPAL	.052±.006	.347±.015	.510±.016	.610±.020	.494±.024	.722±.006	.621±.017	.530±.005	.618±.007
AGGD	.075±.010	.423±.016	.568±.018	.702±.024	.477±.019	.722±.014	.593±.050	.527±.003	.616±.004
PL-CLA	.074±.011	.424±.020	.571±.015	.696±.021	.470±.016	.722±.012	.654±.005	.525±.003	.606±.004
SDIM	.073±.009	.423±.022	.568±.019	.736±.023	.475±.016	.724±.012	.643±.007	.524±.003	.607±.004
D	RC	.072±.009	.391±.012	.488±.020	.740±.026	.446±.019	.715±.007	.664±.004	.532±.004	.620±.003
PRODEN	.071±.009	.415±.016	.567±.025	.712±.032	.430±.019	.704±.013	.665±.017	.528±.004	.620±.003
CAVL	.071±.006	.365±.020	.488±.021	.747±.060	.444±.013	.695±.017	.668±.039	.510±.004	.628±.004
Table 3: Win/tie/loss counts on the classification performance of DPCLS against each comparing algorithm on all data sets. D-PLL indicates the summary of deep learning PLL methods RC, PRODEN and CAVL. (I), (II) indicate the summaries on synthetic data sets and on real-world data sets respectively. "Total" denotes the summary on all the data sets.
CLPL	PL-SVM	PL-KNN	PL-DA	IPAL	AGGD	PL-CLA	SDIM	D-PLL
(I)	44/8/0	51/1/0	52/0/0	47/5/0	46/6/0	23/29/0	38/14/0	30/22/0	-
(II)	8/1/0	9/0/0	9/0/0	9/0/0	8/1/0	7/2/0	7/2/0	7/2/0	21/6/0
Total	52/9/0	60/1/0	61/0/0	56/5/0	54/7/0	30/31/0	45/16/0	37/24/0	21/6/0
Different from them, the proposed method produces excellent performance on all the evaluated data sets, suggesting its robustness to different data sets.
Table 3 (row (I)) reports win/tie/loss counts between DPCLS and eight comparing algorithms on the synthetic data sets according to the pairwise t-test at the significance level of 0.05, where we can find that DPCLS statistically outperforms other algorithms in  $79.6\%$  cases (331 out of 416) and none of the algorithms can beat DPCLS significantly.
5.2 Performance on Real-world Data Sets
Real-world data sets were collected from various tasks and domains. As the average size of the candidate label set of FG-NET is large, which will cause low classification accuracy on the test set. Following [2, 16] we employed the mean absolute error (MAE) to further calculate two extra evaluation indicators MAE3 and MAE5 on FG-NET, i.e., the test examples are considered to be correctly classified if the difference between the predicted age and the ground-truth age is no more than 3/5 years.
Table 2 demonstrates the classification accuracies of different methods on the real-world data sets. It is obvious that our method ranks first in all cases when compared with shallow PLL algorithms. Moreover, according to the pairwise t-test, our method statistically outperforms PL-SVM, PL-KNN and PL-DA on all real-world data sets and statistically surpasses AGGD, PL-CLA and SDIM on six data sets except FG-NET. Furthermore, compared with the best comparisons, our method improves the classification accuracy from 0.494 to 0.557 on MSRCv2 and from 0.747 to 0.770 on Lost.
We also compare the classification accuracies of our method with three deep learning PLL methods RC, PRODEN, CAVL on the real-world data sets. Our method ranks first on six the data sets except Yahoo! News. Specifically, according to the pairwise t-test, our method statistically outperforms RC, PRODEN and CAVL on three real-world data sets (Lost, MSRCv2 and BirdSong). Furthermore, compared with the best comparisons of deep leraning PLL methods, our method improves the classification accuracy from 0.446 to 0.557 on MSRCv2 and from 0.715 to 0.751 on BirdSong. Therefore, we can conclude that our method shows competitive performance compared with the deep learning PLL methods.
Table 4: Ablation study of our method on the real-world partial label data sets.
FG-NET	Lost	MSRCv2	BirdSong	Malagasy	Soccer Player	Yahoo! News
DPCLS	.077±.009	.770±.024	.557±.014	.751±.009	.676±.004	.532±.002	.626±.003
DPCLS-LM	.067±.009•	.652±.023•	.357±.009•	.577±.012•	.587±.014•	.492±.002•	.447±.004•
DPCLS-KE	.068±.009•	.701±.023•	.388±.014•	.595±.014•	.674±.009	.495±.002•	.463±.004•
DPCLS-DP	.073±.010	.687±.027•	.466±.018•	.721±.014•	.612±.011•	.524±.003•	.604±.004•
(a) Ideal  $\mathbf{F}\mathbf{F}^{\top}$
(b) Original  $\mathbf{FF}^{\mathrm{T}}$
Figure 2: Visual comparison of the similarity matrix and the semantic dissimilarity matrix on data set Ecoli  $(p = 1, r = 1, \epsilon = 0.8)$ . (a), (d) Ideal similarity matrix and semantic dissimilarity matrix; (b), (e) Initial similarity matrix  $\mathbf{F}\mathbf{F}^{\top}$  and semantic dissimilarity matrix  $\mathbf{D}_0$ ; (c), (f) The similarity matrix  $\mathbf{F}\mathbf{F}^{\top}$  and the dissimilarity matrix  $\mathbf{D}$  produced by DPCLS. The brighter color indicates a larger value.
(c)  $\mathbf{F}\mathbf{F}^{\top}$  by DPCLS
(d) Ideal D
(e) Original  $\mathbf{D}_0$
(f)  $\mathbf{D}$  by DPCLS
Table 3 (row (II)) presents the win/tie/loss counts of the proposed method against the compared ones on real-world data sets according to the pairwise t-test at significance level of 0.05. On all the real-world data sets, DPCLS achieves significantly superior performance in  $85.9\%$  cases, and gets comparable performance in the remaining cases against the comparing algorithms. Taking both the synthetic data sets and real-world data sets into account, our method accomplishes significantly better performance in  $80.8\%$  cases, which indicates the excellent classification ability of our method.
Visualization Fig. 2 visually compares the ideal, the original and the enhanced similarity matrix and semantic dissimilarity matrices on data set Ecoli  $(p = 1, r = 1, \epsilon = 0.8)$ . Compared with the ideal similarity matrix, the value of each element in the original similarity matrix  $\mathbf{F}\mathbf{F}^{\top}$  is relatively small with many incorrect connections. Compared with the ideal dissimilarity matrix, the original dissimilarity matrix  $\mathbf{D}_0$  is relatively sparse, and many positive elements are missed in  $\mathbf{D}_0$ . On the contrary, the similarity matrix and the dissimilarity matrix produced by DPCLS become denser, which are quite close to the ideal ones. Especially, when checking the areas highlighted by the red rectangle boxes, DPCLS can effectively recover the similarity relationship between samples in  $\mathbf{F}\mathbf{F}^{\top}$ , and many positive elements missed by  $\mathbf{D}_0$  have been recovered by our method. The visual comparison illustrates that our method can produce much higher-quality similarity and dissimilarity matrices, which is useful to find a high-quality label confidence matrix  $\mathbf{F}$  and promote the performance of PLL.
Ablation Study In Table 4, we conduct an ablation study on the real-world data sets to check the necessity of the involved terms of our method. Specifically, DPCLS-LM denotes DPCLS without Dissimilarity Propagation and Kernel Extension, and DPCLS-KE and DPCLS-DP indicate DPCLS without Kernel Extension and without Dissimilarity Propagation respectively. From Table 4, we can find that both the kernel extension and the dissimilarity propagation are helpful in improving classification accuracy and taking both of them into account is the best choice.
In this paper, we have presented a novel PLL method. Specifically, we first construct a similarity matrix based on the multiplication of the label confidence matrix and its transpose. Then, we develop a dissimilarity matrix by exploiting the label space, and further utilize the local geometric structure of the samples to enhance the dissimilarity matrix, i.e., propagating the initial semantic dissimilarity relationships to the whole data set. The similarity and dissimilarity matrices form an adversarial relation, and the proposed model takes advantage of this novel adversarial prior to shrink the solution space of the label confidence matrix, which contributes to find the correct label in the candidate label set. Extensive experiments and comparisons on artificial and real-world partial label data sets have validated the effectiveness of our approach.
This work was supported in part by the National Natural Science Foundation of China under Grant 62106044 and 62072100, in part by the Natural Science Foundation of Jiangsu Province under Grant BK20210221, and in part by the ZhiShan Youth Scholar Program from Southeast University under Grant 2242022R40015.
[1] Timothée Cour, Benjamin Sapp, and Ben Taskar. Learning from partial labels. Journal of Machine Learning Research, 12:1501-1536, 2011.
[2] Lei Feng and Bo An. Partial label learning by semantic difference maximization. In International Joint Conference on Artificial Intelligence, pages 2294-2300, 2019.
[3] Lei Feng and Bo An. Partial label learning with self-guided retraining. In AAAI Conference on Artificial Intelligence, pages 3542-3549, 2019.
[4] Lei Feng, Jiaqi Lv, Bo Han, Miao Xu, Gang Niu, Xin Geng, Bo An, and Masashi Sugiyama. Provably consistent partial-label learning. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems, 2020.
[5] Eyke Hüllermeier and Jürgen Beringer. Learning from ambiguously labeled examples. Intelligent Data Analysis, 10(5):419-439, 2006.
[6] Rong Jin and Zoubin Ghahramani. Learning with multiple labels. In Advances in Neural Information Processing Systems 15, pages 897-904, 2002.
[7] Changchun Li, Ximing Li, and Jihong Ouyang. Learning with noisy partial labels by simultaneously leveraging global and local consistencies. In ACM International Conference on Information and Knowledge Management, pages 725-734, 2020.
[8] Li-Ping Liu and Thomas G. Dietterich. A conditional multinomial mixture model for superset label learning. In Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems, pages 557-565, 2012.
[9] Jie Luo and Francesco Orabona. Learning from candidate labeling sets. In Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems, pages 1504-1512, 2010.
[10] Jiaqi Lv, Miao Xu, Lei Feng, Gang Niu, Xin Geng, and Masashi Sugiyama. Progressive identification of true labels for partial-label learning. In International Conference on Machine Learning, volume 119, pages 6500-6510, 2020.
[11] Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. Foundations of Machine Learning. The MIT Press, 2nd edition, 2018.
[12] Nam Nguyen and Rich Caruana. Classification with partial labels. In ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 551-559, 2008.
[13] Peng Ni, Suyun Zhao, Zhi-Gang Dai, Hong Chen, and Cui-Ping Li. Partial label learning via conditional-label-aware disambiguation. J. Comput. Sci. Technol., 36(3):590-605, 2021.
[14] Cai-Zhi Tang and Min-Ling Zhang. Confidence-rated discriminative partial label learning. In Satinder Singh and Shaul Markovitch, editors, AAAI Conference on Artificial Intelligence, pages 2611-2617, 2017.
[15] Yingjie Tian, Xiaotong Yu, and Saiji Fu. Partial label learning: Taxonomy, analysis and outlook. Neural Networks, 161:708-734, 2023.
[16] Deng-Bao Wang, Min-Ling Zhang, and Li Li. Adaptive graph guided disambiguation for partial label learning. IEEE Trans. Pattern Anal. Mach. Intell., 44(12):8796-8811, 2022.
[17] Haobo Wang, Ruixuan Xiao, Yixuan Li, Lei Feng, Gang Niu, Gang Chen, and Junbo Zhao. Pico: Contrastive label disambiguation for partial label learning. In International Conference on Learning Representations, 2022.
[18] Wei Wang and Min-Ling Zhang. Partial label learning with discrimination augmentation. In ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 1920-1928, 2022.
[19] Ning Xu, Jiaqi Lv, and Xin Geng. Partial label learning via label enhancement. In AAAI Conference on Artificial Intelligence, pages 5557-5564, 2019.
[20] Zinan Zeng, Shijie Xiao, Kui Jia, Tsung-Han Chan, Shenghua Gao, Dong Xu, and Yi Ma. Learning by associating ambiguously labeled images. In IEEE Conference on Computer Vision and Pattern Recognition, pages 708-715, 2013.
[21] Fei Zhang, Lei Feng, Bo Han, Tongliang Liu, Gang Niu, Tao Qin, and Masashi Sugiyama. Exploiting class activation value for partial-label learning. In International Conference on Learning Representations, 2022.
[22] Min-Ling Zhang and Fei Yu. Solving the partial label learning problem: An instance-based approach. In International Joint Conference on Artificial Intelligence, pages 4048-4054, 2015.
[23] Min-Ling Zhang, Bin-Bin Zhou, and Xu-Ying Liu. Partial label learning via feature-aware disambiguation. In ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 1335-1344, 2016.