Concentration Distribution Learning from Label Distributions
Authors: Jiawei Tang
Yuheng Jia
Venue: ICML 2025 poster (2025)
Keywords: Label distribution learning
background concentration
concentration distribution learning
Primary area: general_machine_learning->supervised_learning
TL;DR: This paper propose a novel label distribution learning model that can predict the background concentration.

Abstract: Label distribution learning (LDL) is an effective method to predict the relative label description degree (a.k.a. label distribution) of a sample. However, the label distribution is not a complete representation of an instance because it overlooks the absolute intensity of each label. Specifically, it's impossible to obtain the total description degree of hidden labels that not in the label space, which leads to the loss of information and confusion in instances. To solve the above problem, we come up with a new concept named background concentration to serve as the absolute description degree term of the label distribution and introduce it into the LDL process, forming the improved paradigm of concentration distribution learning. Moreover, we propose a novel model by probabilistic methods and neural networks to learn label distributions and background concentrations from existing LDL datasets. Extensive experiments prove that the proposed approach is able to extract background concentrations from label distributions while producing more accurate prediction results than the state-of-the-art LDL methods. The code is available in https://github.com/seutjw/CDL-LD.

Concentration Distribution Learning from Label Distributions
Jiawei Tang"
Yuheng Jia
Abstract
Person
Boet
Person
Boat
Backgr
Label distribution learning (LDL) is an effective method to predict the relative label description de- gree (a.k.a. label distribution) of sample. How- ever, the label distribution is not complete rep- resentation of an instance because it overlooks the absolute intensity of each label. Specifically, it's impossible to obtain the total description de- gree of hidden labels that not the label space, which leads to the loss of information and con- fusion in instances. To solve the above problem, we come up with new concept named back- ground concentration to serve the absolute description degree term of the label distribution and introduce it into the LDI. process, forming the improved paradigm of concentration distri- bution learning. Moreover, we propose a novel model by probabilistic methods and neural net- works learn label distributions and background concentrations from existing LDL datasets. Ex- tensive experiments prove that the proposed ap- proach is able to extract background concentra- tions from label distributions while producing more accurate prediction results than the state- of-the-art LDL methods. The code is available in http://ggitubbccom/ssjj///DDDDL
(a)
0.4
0.3
0.5
Similar LDs
Different CDs
Person
Beat
Backgr.
(b)
0.5
0.5
0.1
0.1
0.8
Fe
T1
Fe
T1
Unk.
(c)
Same LDs
Different CDs
Unik.
(d)
0.2
0.2
0.6
0.1
0.1
0.3
0.5
Figure I. The LD-CD diagrams of two pairs (a.b and c,d) of pic- tures that share similar or same LDs. After introducing the back- ground concentration, their CDs can be distinguished easily.
binary value. To this end, label distribution learning (LDL) (Geng, 2016) was developed, which uses real numbers to illustrate how important label is to particular sample. All labels' description degrees make up label distribution (LD). Specifically, let d' stand for the description degree of the label to the instance which is governed by the non-negative constraint d' E [0, 1] and the sum-to-one con- straint Σ, d' = 1. Unlike traditional MLL, LDL is more general paradigm that attempts to predict the LD for unseen samples.
1. Introduction
Multi-label learning (MLL) (Tsoumakas & Katakis, 2007:
In LDL, ground-truth LDs are considered complete repre- sentations of the corresponding instances. However, there exist some cases where cannot describe instance per- fectly only with its label distribution. Fig. 1(a) and Fig. 1(b) show two pictures of boating. Although there is signif- icant difference between the sizes of people and boats in the two pictures, similar LDs are assigned to them due to the similar relative proportions of the labels ("Person" and "Boat"), which goes strongly against our intuition. To solve this problem, introduce the concept of background concentration, which represents the description degree of the complementary set of all existing labels. In this case, it can be regarded as the proportion of the background the two pictures, which differs a lot from each other. Append- ing background concentration terms (Backgr. in Fig. ((a)
Zhang & Zhou, 2014; Peng al., 2025; Li al., 2025) is well-researched machine learning paradigm where set of labels is assigned to each sample. In MIL., logical value (0 or I) is used to indicate whether label is capable of describing a sample. But each label's 's relative impor- tance to a sample cannot be accurately described by this
'School of Computer Science and Engineering, Southeast Uni- versity, Nanjing 210096 "Kyy Laboratory of New Generation Artifi cial Intelligence Technology and Its Interdisciplinary Applications (Southcast University), Ministry of Education, China. Correspon- dence to: Yuheng Jia <yhjia @seu. scu.edu..n>..
Proceedings of the ndnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Concentration Distribution Learning from Label Distributions
0.5
0.2
0.2
011
(a) Beam
(b) Label distribution of beam
(c) Concentration distribution of beam
0.-
0.-
0.6
0.6
0.4
04
0.3
03
02
HAP
5AD
BUR
ANG
H6P
34D
SUR
ANS
06
CON
(d) Laugh
(e) Label distribution of laugh
(1) Concentration distribution of laugh
Figure 2. Label and concentration distributions of the images in (a) and (d). The LDs and CDs are shown in bar charts for ease of observation. By introducing background concentration term, i.c., CON (f) and (i), the two images that have identical label
distributions can be distinguished.
and (b)) to the original LDs, get concentration distri- butions (CDs). CDs contain more information than LDs, helping better describe an instance. In this paper, we define concentration distribution learning (CDL) as the process of learning the background concentration j and the label distribution b simultaneously, which aims to learn concen- tration distribution vectors Ca [b, (4] from concentration distribution datasets.
the background concentration term represents the descrip- tion degree of "no emotion", which is abstract and hard to be measured. In other words, the stronger the emotion, the lower the background concentration it should be assigned. Appending background concentration terms to the LDs in Fig. 2(b) and Fig. 2(e), they become concentration distribu- tions in Fig. 2(c) and Fig. 2(f), which help us distinguish the two images in Fig. 2(a) and Fig. 2(d) very well.
In fact, the concept of background concentration is very common and important in reality. For example, two pictures of ilmenite and alien meteorite are shown in Fig. I(c) and Fig. I()). Ilmenite a known mineral on earth, while me- teorite contains 50% of unknown chemical elements (Unk. in Fig. 1(c) and (d)). After detection in proportions of all known chemical elements, they share the same chemical formulas of F2T00;(20% Fe, 20% Ti and 60% O), leading to the same LD, which is obviously unreasonable. In this case, we have no choice but to introduce the background concentration for representing the proportion of unknown elements because they cannot be detected yet. To give an- other example, Fig. 2(a) and Fig 2(d) are two images of human face. Despite they have significant difference in the intensity of emotion, two identical LDs in Fig. 2(b) and Fig. 2(e) are assigned to them due to the similarity of the proportion of each emotions. In this case, each of the labels describes a specific emotion (happiness, sadness, etc.), so
In this paper, come up with novel model, named CDL- LD. With probabilistic methods and neural networks, it can learn concentration distributions from the existing label distribution dataset. The main contributions of our model are summarized follows:
Based on real-world examples, we come up with a new learning paradigm named concentration distribution learning, which overcomes the ambiguity of LDs in traditional LDL methods. In addition, excavating the background concentration makes full use of the infor- mation in the datasets and benefits the downstream tasks.
With the original version of an LDL. dataset, we con- struct the first real-world concentration distribution dataset, which further proves the realistic significance of background concentration and the effectiveness of our method in concentration distribution learning.
2

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Concentration Distribution Learning from Label Distributions
Although concentration distribution learning is an ex- cellent paradigm, there is no existing concentration distribution dataset for learning, Our method learns CDs directly from existing LDL datasets, which im- proves the universality of CDL.
account. Our work is the first to introduce the concept of background concentration traditional label distribution learning and to develop the novel paradigm of concentration distribution learning. Further experiments on various real- world datasets also prove the effectiveness of our method on learning concentration distributions. the proposed method can precisely predict concentration distributions from la- bel distribution datasets, it can better excavate the hidden information in these datasets and benefit the downstream tasks.
We conduct extensive experiments to validate the ad- vantages of our methods over the baseline algorithms on concentration distribution learning on LDL. datasets. Furthermore, by using the Rademacher complexity, we show the generalization bound of the proposed model and theoretically prove that it is possible to directly construct a CDL model from the LDL datasets for the first time.
3. Proposed Model
Notations:
Let n, m and e represent the number of samples, the dimension of features, and the number of labels. Let x E IR denote feature vector and y E I denote its corresponding ground- truth label distribution vector, which satisfies Vi E 21, cl Vi [0, 1] and Σ V/- = 1. The feature matrix and the corresponding ground-truth label dis- tribution matrix can be denoted by X = [21; 025 2n. E R=xm and Y = 1y 32:.... y, E R= respectively. We aim to learn from the dataset D = [X; Y| and predict concentration distribution vectors Cd [b, μ4] E Re+1 for unseen instances. It is composed of the real label distri- bution vector b and the background concentration term p., in which b E R H > 0, vi E [1.2, c), b, E [0, and Σ 4/ + 1=p11
Extensive experiments on the benchmark datasets clearly show that the LD predicted by our method is better than that predicted by state-of-the-art LDL methods, and the recovery results of our method on background concentrations also fit well with reality.
2. Related Works
2.1. Label Distribution Learning
LDL (Kou et al., 2024; 2025; ?: Wang et al., 2025) is a new machine learning paradigm that constructs a model to predict the label distribution of samples. At first, LDL were achieved through problem transformation that transforms LDL. into set of single label learning problems such as PT- SVM, PT-Bayes (Geng, 2016), or through algorithm adapta- tion that adopts the existing machine learning algorithms to LDI., such as AA-KNN and AA-BP (Geng, 2016). SA-IIS (Geng, 2016) is the first model that specially designed for LDL, whose objective function a mixture of maximum en- tropy loss (Berger et al., 1996) and KL-divergenee. Based on SA-IIS, SA-BFGS (Geng, 2016) adopts BFGS to optimize the loss function, which is faster than SA-IIS. In addition, LDILIC (Zheng et al., 2018) leverages local label correla- tion to ensure that prediction distributions between similar instances are as close as possible. LCLR (Ren et al., 2019) first models the global label correlation using a low-rank matrix and then updates the matrix on clusters of samples to consider local label correlation. LDL forests (LDLFs) (Shen et al., 2017) is based on differentiable decision trees and may be combined with representation learning to provide an end-to-end learning framework. LDLLDM (Wang& & Geng, 2023) can handle incompleee label distribution learning and learn the global and local label distribution manifolds to take advantage of label correlations.
First, to relate label distributions and concentration distribu- tions, we define p E R as the apparent label distribution vector of the corresponding concentration distribution vec- tor C. [b, [4] E Ro+1, where Vi E 21, c] Pc E [0, 1] and > P; 1. The relationship between the apparent label distribution vector and the concentration distribution vector can be formulated as:
p p= b 12"
where 14 E R2, Vi E (]. E [] and Σi=1 11" ;-= =
Eq. (1) indicates that the distribution of the background concentration l on the real label distri- bution vector b converts the concentration distributions to the apparent label distributions. In other words, the appar- ent label distribution is affected by both the dataset and the background concentration.
From a perspective of probability, we assume that p obeys the Dirichlet distribution, i.c., p ~ Dir(a),, where a e R is the vector of distribution parameters. According the ex- pectation formula of Dirichlet distribution, the expectation on p; can be written as
E
(2)
2.2. Concentration Distribution Learning
Ej=1 0j
Although the above LDL methods have achieved great suc- cess, none of them take the background concentration into
From the form of Eq. (2), the distribution parameter a; can be regarded as the belief mass on the i-th class, i.e.,
3

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Concentration Distribution Learning from Label Distributions
+1.
Dir
Eq. (8)
Feature
a
P
b
θ
Ca
PcD
R
Update
GT LD
y
Figure 3. The framework of our method. The feature vector and network parameter matrix & produce datasct-side confidence vector by forward propagation of the nerual network, and O is updated by backward propagation with the ground-truth label distribution vector y and the apparent label distribution vector p. p sampled in the Dirichlet distribution of parameters vector + 1., where 1, all-ones vector of size c. With Eq. (8), the real label distribution vector b and the background concentration j. are generated from the confidence vector e. Finally we get the predicted concentration distribution vector ca [b]
the degree of confidence that the corresponding instance should be classified into the i-th class. This confidence comes from two sources, one is the certain part extracted from the dataset, and the other is the hidden part decided by the background concentration, i.e.
In Eq. (1), assuming that the background concentration is evenly spread on each class of the real label distribution vector in probability, i... vi [1.2, ..., c), Ex; #. then
another form of the expectation of ps be expressed as
Epp = b2 + 4 c
ag = e + Us
(3)
Combining Eq. (6) and Eq. (7), the expressions of b, and μ can be obtained as
where e, 0 and u, > represents the degree of confi- dence on the i-th class from the dataset and the background concentration respectively. Denote Oc, 1. E R as an all- zeros vector and an all-ones vector. Based on reality, when there is nothing in the dataset to provide confidence, i.c.,
6, +1
= bi b /
Σ (e: +1)
(8)
Vi E [1, 2, .... c).e e = (e,,ee....,ed Ee] = Oc. p should be a uniform distribution. this case, the vector of distribution parameters 1. and Dir(a:) degrades
6. Σ E 11= Σ e,=
flat Dirichlet distribution. Substitute 0. and 1. in Eq. (3), we have
To obtain the vector of dataset-side confidence e, we apply a confidence network e = (a= on the dataset D = [X; YJ. where x T is instance from X, is the network function and θ is its parameters. Specifically, the sofımax layer of conventional neural network is replaced with an activation function layer (i.e., RELU (Glorot et al., 201 1)) to ensure that the network outputs non-negative values, which are considered as the confidence vector e = [ei, E2, ..e)). Accordingly. the vector of Dirichlet distribution parameters a be obtained.
1. = 0g + u
(4)
u le,
where [w1, U2 ..., ue]. Substitute Eq. (4) Eq. (3), the relation between a, and e, is formulated as
0g = e + 1.
(5)
For each instance, in conventional neural network, the MSE (Mean Square Error) loss is usually employed as
Finally, substitute ar of Eq. (5) in Eq. (2),
6 +1
Ep.
E5 (ez + 1)
LMSF = ly - 212.
(6) where and p are the ground-truth and the predicted label distribution vector of the instance respectively. For our
61 +1+1
Σ5=1 Cj +

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Concentration Distribution Learning from Label Distributions
model, given the degree of dataset-side confidence e of the instance obtained through the confidence network, we can get the parameter (i.e., a; 6 + 1) of the Dirichlet distribution and sample p from Dir(a). After simple modification on Eq. (9), we have the adjusted MSE loss of our model:
Substitute Eq. (11) in Eq. (12), have
((6) (Cs(1) + E
Σ
o; CAMSE (as)
Te
(13)
log 2/5
+ +31
2n
CAMSE(a)
=
110 /11--pl 211
dp
((a)
1=1
According to the second line of Eq. (10) and
( 04))
Ei=1 at there holds that (AMSE(a) Ei )²
(1i
+
8
( 1
(10)
a, (S-0a)) (51) > O. With o; [0, 1J. the expectation term in Eq.
1=1
Lare
Coor
(13) can be simplified as
Di(1 p.)
Σ (i p=)²
S+1
where S Ei= and μ4 = By decomposing the first and second moments, the loss aims to achieve the joint goals of minimizing the predictive error and the variance of the Dirichlet distribution generated by the neural network specifically for each sample in the training set. While doing so, it prioritizes data fit over variance estimation. With the trained neural network e f(x](] () and then substitute e in Eq. 8, we get the predicted concentration distribution vector ea = [b, /4]. The overall prohabilistic graph model of CDL-LD is presented in Fig.
3.
Eng
a CAMSE (ai)
1 S
Σ n
LAMSE (a.)
π1
(yis
0sj 5
)2
at an))
n
(S +1)
(14)
od (1 5.
1
oú )² (uks
5.
S
1c(c+11
3.1. Generalization Bound
Substitute Eq. (14) in Eq. (13), we get
In this subsection, we first provide Rademacher complexity (Mohri et al., 2012) for CDL-LD, which is a commonly used tool for comprehensive analysis of data-dependent risk bounds.
log 2/8
L(h) Shs(h) +
1 1+ 1e(c + 1)
+ +3/
2n
Definition 1. Let H be a family of functions mapping from X to [0.1] and S be set of fixed samples with size n. Then, the empirical Rademacher complexity of H. with respective to S is defined as
(15)
Let n in Eq. (15) tends to infinity:
Rs(H)) E. hEW
sup
Σ
o (2:) 1=1
C(h) S Cs(h) +
1 Aclc +
(16)
n
(II)
bound
<
E.
C.Lsse (ai)
From Eq. (16), we can observe that when the number of instances n tends to infinity, the generalization risk of our proposed model will be upper-bounded by the empirical risk of it with bound of 1e(c+1)* which indicates that this bound shrinks when the number of classes increases. This conclusion intuitive because the background concen- tration tends to zero when tends to infinity, degrading the CDL problem to learnable LDL problem. Combin- ing all equations together, we can draw the conclusion that it is possible to directly construct a CDL model from the LDL datasets, and the concentration distribution learning problem itself is also learnable.
where a; [0, 1] and a; represents the Dirichlet distribu- tion parameter vector of the i-th instance.
Lemma 1. Let H be a family of functions. For any 8 >> O, with probability at least 5, for all E H such that
log 2/5
((h) S (s(h) (H) + +3
(12)
2n
where L(h) and (h) are the generalization risk and em- pirical risk with respective to and n represents the number of instances.
5

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Concentration Distribution Learning from Label Distributions
4. Experiments
4.1.2. EVALUATION METRICS
4.1. Experimental Configurations
As suggested in (Geng, 2016), we adopt three distance met- ries (i.e., Chebyshev, Clark and KL) and one similarity met- ric (i.e. Cosine) to evaluate the performances of methods. The formulas of these evaluation metrics are summarized in Table 2.
4. 1.11. EXPERIMENTAL DATASETS
The experiments are carried out on 12 real-world datasets with label distribution. The statistics of these datasets are summarized in Table 1. Among these, the first eight (from Alpha to Spoem) from the clustering analysis of genome- wide expression in Yeast Saccharomyces cerevisiae (Eisen et al., 1998). The SJAFFE is collected from JAFFE (Lyons et al., 1998), and the SBUL3DFE is obtained from BU_3DFE (Yin et al., 2006). The Scene consists of multi-label images, where the label distributions are transformed from rankings (Geng & Xia, 2014). SJA.c (in section 4.2) is the first CDL dataset generated from SIAFFE dataset in this paper. For each dataset, the last class of the ground-truth label distribution is regarded as the background concentration and will be invisible in training.
4.1.3. COMPARISON METHODS
We compare the proposed methods with four baseline LDL methods, including LDLLC, SA-IIS, LCLR, LDLFs, LDLLDM and DLDL, which are briefly introduced be- low.
LDLLC (Zheng al., 2018): LDLLC makes use of local label correlation to guarantee that prediction dis- tributions between comparable instances are as close as possible.
SA-IIS (Geng, 2016): SA-IIS learns the label distribu- tion using KL divergence and the maximum entropy model.
Table 1. Statistics of the 12 datasets
Dataset (abbr.)
# Instances
# Features
Labels
LCLR (Ren et al., 2019): LCLR uses a low-rank ma- trix to model global label correlation first, and then updates the matrix on sample clusters to account for local label correlation.
Alpha (Alp)
2465
24
18
Cdc (Cde)
2465
24
15
Cold (Col)
2465
24
Diau (Dia)
2465
24
LDLFs (Shen et al., 2017): To provide an end-to-end learning framework, LDL forests (LDLFs), which are based on differentiable decision trees, can be coupled with representation learning.
Elu (Elu)
2465
24
14
Hcat (Hea)
2465
24
6
Spo (Spo5)
2465
24
Spo5 (Spo)
2465
24
LDLLDM (Wang & Geng, 2023): LDLLDM learns both the global and local label distribution manifolds in order to take advantage label correlations. is also capable of handling partial label distribution learning.
SJAFFE (SIA)
213
243
SBU_3DFE (SBU)
2500
243
Scene (Sce)
2000
294
SJA (SJAc)
213
243
DLDL (Jia et al., 2024): DLDL unifies label enhance- ment (LE) and LDL into joint model and avoids the drawbacks of the previous LE methods. Furthermore, it theoretically proves that directly learning LDL model from logical labels is feasible.
Table Formulas of the four evaluation metrics. Here indicates that smaller values are better, and t indicates that larger values are better.
The parameters of the methods are as follows. The sug- gested parameters are used for LDLLC, IIS-LLD, LCLR, LDLFs and DLDL. For LDLLDM, A1 A2 and Ag are tuned from {10-3, 10-2, ..., 103), and g is tuned from 14. Note that all the baseline methods are LDL algorithms, they are not able to provide concentration distributions. So, for each instance, ground concentration to the predicted label distribution vec- tor, where g is the ground-truth description degree of the last class and -0.2g < 8 < 0.2g is a random noise to simulate the inaccurate learning of background concentration in the baseline methods. Then normalization will be applied on
Measure
Formula
Chebyshev
Dis D) max,/d; -d)
(d, dd) (d, (d,+ Disa(D, D) Ei=
Clark],
append g
the predicted back-
K14
Disg(D, ()) 25 d, In 4e
Cosinet
Simi (D,
Ei d,ds VEjzi /D
6

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Concentration Distribution Learning from Label Distributions
this concentration distribution vector to ensure that all of its elements up 1. We run each method for ten-fold cross-validation.
with the other baseline algorithms in terms of all the four metrics.
On the concentration distribution dataset (i.e, SJA_c), CDL-LD shows overwhelming superiority to the other baseline algorithms in all of the four metrics. This re- sult proves the effectiveness of CDL-LD in real-world concentration distribution learning problems.
4.2. Construction of CDL dataset
The generation mechanism of the SJAFFE dataset makes it potential concentration distribution dataset. Specifically, the six classes (happy, sad, surprised, angry, disappointed, and fear) of the original SJAFFE dataset are semantic ratings averaged over 60 Japanese female subjects. A 5-level scale was used for each of the six adjectives (5 for highest and for lowest). An example of the rating vector in the original SJAFFE dataset be [3, 4.8, 1.2, 2.4, 1.5), and after normalization, it becomes a label distribution vector Sn
0.6
Groundtruth
Prediction
0.2
3, 3,4.8, 1.2,
n + 4.8 1.2 +.1 2.4 1.5
(17)
[0.2, 0.32, 0.08, 0.14,0.16,
Hap.
Sad.
Sur.
Ang.
Dis.
Fea.
Con.
According the definition of background concentration, have μr 5 1----- - 1m1 8,, where j is regarded the ground-truth -ouund-ruuthaa background concentration and s; is the i-th element of the original SJAFFE rating vector. In the case above, * 6 (3 + 4.8 + 1.2 + 2.1 +.1+2.0 +
15. Appending to the last of the original rating vector and then applying normalization on the new vector, we get a standard concentration distribution vector Cd
15] Cd 3 4.8 2.4 1.5 15
(18)
= [0.1, 0,160.16.000 0.04, 0.07, 0.08, 0.05, 0.5).
Figure 4. The visualization of a typical result of our method on the SIA.c dataset and corresponding image.
Repetition of the steps above on each instance in the SJAFFE dataset gives the ground-truth concentration distributions of them, making it the first concentration distribution dataset named S.A.c.
Additionally, the visualization of typical result the SJA_c dataset is presented in Fig. 4, where the scales on the horizontal axis represent six emotions of happiness, sad- ness, surprise, anger, disappointment, and fear, while the last represents the background concentration. In this figure, we can observe that the predictive result of our method is very close to the ground-truth concentration distribution in the first six classes (the real label distributions of six emo- tions) and in the last class (the background concentration of "no emotion"). Specifically, both the ground -tound-truth -tuth and the predicted CDs indicate the emotion of faint sadness (a peak on sadness with high background concentration), matching the corresponding image very well. This further proves that background concentrations exist in reality and our method has the ability to precisely excavate background concentrations from real-world datasets.
4.3. Results and Discussion
Table presents the experimental results (mean=std) of all the 7 algorithms on 12 datasets in terms of Chebyshev (abbr. Cheby), Clark, KL, and Cosine, with the best results highlighted in boldface. According to the results recorded in Table 3, we observe that
Our method CDL-LD achieves the lowest average rank in terms of all of the four evaluation metrics. Specifi- cally, out of the 48 statistical comparisons, CDL-LD ranks 1st in 93.75% (45 out of 48) cases. In general, CDL-LD performs better than most comparison algo- rithms.
To sum up, the experimental results further support the competitive performance the proposed algorithm, indicat- ing its effectiveness in real-world concentration distribution learning problems.
On some LDL datasets, our method achieves superior performance. For example, on Col, Dia. Spo and Scene, CDL-LD significantly improves the results compared

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Concentration Distribution Learning from Label Distributions
Metric
CDL-LD
LDLLC
SA-IIS
LCLR
LDLFss
LDLLDM
DLDL
Cheby
(.045::.0002())
(0021))0002(7)
0.0366+.00088()
0.0529:.000 0018(6)
0.0502+:: (005(3)
(0523++0003(())
0.0520+.0000/
Clark
0277771.0009(1 0.458+2.0128(0
0.7340:.0297(7)
0.42534.0006(2) 0.41051.000((5)
0.4365+.02211(4)
0.43184.0049(3)
Alp
KL
0.00981.00001) 0.09142.0018(7)
0.0623+.0187(4)
0.08581.0020G)
0.03651.0025(3) 0.00552.0005(0)
0.0351=.00011()
Cosine
0.98941.0017(1)
0.95601.0011(7)
0.98244+0007((2)
0.9563:.000216)
0.95901.0000(33
0.95701100000(5)
0.95734..001(44)
Cheby
0.0291110002(1I) 0.06194.0068(4)
0.14562.0119(7)
0.05652..002(22)
0.0632+.00033())
0.05991.0008(3)
0.06262.0033(5)
Clark
11891++000000
0.476+
n.4327+-0007 0.0329+0009017
0.4457+-012233) 0.4539+00026(4)
(44611+-008666)
Cdo
KL
0.0122:1.0003(1) 0.1114#
0.09991.0010(1) 0506)7)
0. 0.10312.0007(6)
0.04262.00111(2
00448+.0011100
Cosine
0.9870=1.0005())
0.9485+.0079961
0.8489+.016-1(7
0.947942.000/) 0.9565+.0002((2
()))
0.9530+.0000((3
0.5502+.004474)
Cheby
(.0091)))00091))
0.1606+.007707
0.1561+-0512(6
0.1475++.0884(4)
O. (0000)))
0.1441+-001:3(3)
0.145)+)0060(3)
Clark
0.2073:.0002(1) 0,40622 0181(6)
0.4670=.1168077
0.38491..01550 0.37341.0218(4)
0.3674+.006112
0.3719#
Col
KL
0.0262:1.000/11 0.1051+.000904 0.2421+.0113(()
0.2180:1.011((5)
0.2209110044(()
0.09734.0064(22
0.09835.0100(3)
Cosine
0.9737+-.00044
0.9139++0008877
(22199))))11((2
0.9266++005666)
0.9277+-00022
0,9302+000155 5(3)
0.9289+.0044(44
Cheby
0.0677:1.000<(1)
0,10922.000 ((4)
0.1529+.0755577)
0.11401.000110)
0. 0.1105+.0100(0)
0.10734.0033(3)
0.1072+.0111(2)
Clark
0.2910:1.0001(1)
0.4420110055(6)
0.5501=.0000(7)
0.439411.006((5)
0.4308:.0019(()
(4186))0058((2)
0.4227+.0018833)
Dia
KL
0.0276+t.0003))
0. 0.0707+
0.1721+.0010(7) 0.0961))0200(4)
0.1689+.0111((6
0.0756+.0010(33
0.07722+.0008(()
Cosine
0.97181.000331)
02292200001(000
0.9042:.0077777
0.92591.00011()
0.93154.002512 0.9294:1.0102(4)
0.93442.0105(3)
Cheby
0.0317:
0.0657+10014|00
0.0500).0015((2)
(.004))..003355)
00629:H00011(3)
0.063244.008((4
0.0683+.0003(7)
Clark
0.2740=t.0002(1)
0.4592=..015(00
0.4333+.0016(44 0.6535+..004(77)
1.4273+.0013/2)
0,4316+.0002((3)
14450550000505
Elu
KL
0.0119-1,000((I)
0.1 (1118)+.0028(7)
0.0987
0. 0.1027+.0026(0)
0. 000001110006(5)
0.0433+.00009(2
0.0487+.0001
Cosine
0.9871 +.000(1
094479-0022000
0.9742+.011422
0.9529 (00SS
0.9523+-0001(4)
0,9471 +.000(7)
Cheby
0.0641++.004(I))
0.1183+.003376)
0.1006220891(()
0.1205+.0001(
0.1154+.051((4
0.1276+.00028(7)
0.1138++.0022(3)
Clark
0.239911.002211) 1411221.0131(0
0.3095:..1411(2
0.4112:1.0009(5)
0.397911.010((3
0.42901.0061117)
0.3997:.0000(4)
Hea
KI.
0.0218+.0000 0.1828+000022
0.0419+
0.1800+ (009(())
0.1730+
0.0925+
0.078)+-0037(3)
Cosine
0,9309#.003100 0.007)=t.000((I)
0.9505+.00441(2)
0.9307+.0005(()
(008))
0.9247+.00021(7)
(0337++.0011(3)
Cheby
0.0634+..016(1)
0.1324+-0047(6)
0.1251+.0036(3) 0.1210++.0005(2) 0.2541+
0.12704.0012(6)
0.1254+ 0039(4)
Clark
0.2584+.0035(1)
0.46114-0009// (-00)999)))
0.4228+ 0.6960+-0367(7)
7(2)
0.4364+.011(())
0.4355+.0008(3
0.4439+0018266)
Spo
KL
0.0254:1.000(1) 0.2140:1.0065(7)
0.2130:1.0222(6
0.19141.0025(1)
0.20041.0081(0)
0.0927+.00021122)
0.0981+t00009(3)
Cosine
0.975411.008(1)
..9190).0044(66)
0.8423:2.0168(7)
0.9301:1.011((2)
0.9265.1.0028(3)
0.92531.002884
0.9241+.0001(55)
Cheby
0.39361.00722 0.31011.0011(1)
0.3850: (275
0.3207:10072((3)
0.3202+L.003((2)
0.3287=.006544
0.34891.0003((3)
Clark
0.7726 H )0044(())
0.9373++0049(()
0.8799 (6624(6)
0.8372+.0123/
0.8393+
$88548+0004455
0.7924
Spo5
KL.
0.4343:..01511)
(.6749.00566(7)
0.7430:1.0877(3)
0.8877:1.0336(6)
0.8850+..019(6)
0.6660+..0054(2)
0.765)L.0852(4)
Cosine
0.8133+.0011(1)
0.7542+.0058(7)
0.882)+..155665
0.8112++.005((2)
0.8095++.005(()
0.80634 (065(3)
0,7844+.008886)
Cheby
0.4335+.00002 +.0002(7)
0.3484+.0433(3
0.3686+-0026(4)
0.3734+.0119(5)
0.3790+.021606
Clark
0.999221.00021) 1.194==00991(7)
1.09764 (1)
1.0373+ 07222(2)
(.1600+.026666)
1.1088+.076665
SJA
KL
0.0841).0007(1)
L.8555..045(7)
0.73081.0122(2)
0.76531..011833)
L181152.01590) 0.757)).1415(4)
0.932)+..0007(5))
Cosine
0.81611.0013(1))
0.7211=.0125(()
1.7088:.031677
0.7478..0021
0.7587+.0110(33
0.7222+.0149((5)
0.7597+.0398(2)
Cheby
0,3362: 0008;3)
0.3688=-.001(66
13511=2.211301
0.2972
0.3123+..019(22
0.3723+.0151(()
0.3823+.0171((7)
Clark
.1914=2.077(())
1.503 (5))
0.979811.0077(3)
0.975711.022(22)
1.16111.0418(6
1.1445:1.0110(4
SBU
KL,
0.4641--00280
1.4267+ (006(()))
0.7209++00003(2
17894440036099
0.82%++-011(()
1.2469+-019005))
1.2848++00211
Cosine
0.6310+-0009(7)
77060+-0044(44
0.7183+-0008(3
07578+J00088
+.049)+
0.704)+.0097(5)
0.6922+.0255(6)
Cheby
0.3948:1.00111)
0.5289:1.0033()
0.5438:1.044((6
0.4789:1.0011
0.4765:..008((2
0.5363:L.015445)
0.54401.0153(7)
Clark
1.9714+1.004(11 2.49927+
2.7042++00992(7)
(00404++.0004(66)
(007(5)
235202++.0065(3)
2.5237++0033(4)
See
KL
0.491811.0010(I) L1354=20008(2)
1.7242# (7)
1.5624 (5)
1.5938#: (6)
12310+21056033
1.2955..0116(4)
Cosine
0.5787+.000 (0048(2)
0.4772+4.0116/0
0,5282+.001 (3)
0.4629:1.0088(7)
0,5187:1.0072(5)
0.019))
Cheby
0.1153:.,003(1)
0.3190-1.0096%
0,3024:t.00144 00014(3)
0.2504:1.0003/2
0.3598-2.0089(7
0.3303++.0148(5)
0.3518+.000566)
Clark
0.533611.048(1I) 0.9786+.0076(55)
08006)10000(33
0.78211.0076(
L.1820 03)1((7
0.9712+1.012444)
0.9983
SlAc
KI.
0.07222+.0020K1 0.7183+
0.2081++0088(22
0.4076++.001
1. 1.0728+.0994(7)
0.4573+.00446(4
0.5089+.0277(55)
Cosine
0.9740+1.0062(1)
0.7459+.01991(1
0.8824+.0192(22
0.7160+ 0.8434+.001633
0.7195+.0151(5)
0.6791+.0072(7)
Table Predictive results (meandsstd) and ranks of our and baseline methods in terms of four metrics on 12 datasets, where the best results are highlighted in boldface.
8

---

Concentration Distribution Learning from Label Distributions
517
147 143
COLLD 30 LOLR
LOLLO 4.3
LOLLO 523
1. LGLR
OLOL
675
L0ITs 48
LO.LMM
BLDL
IB-LDL
XX Lo.Fs
DLDL 522
122 FDLFs
LOLR 432
OLDL
(BADL 522
LDLFs
6x
LOLLOM
482 LOLLOM
(a) Chebyshev
(b) Clark
(c) KL
(d) Cosine
Figure 5. The CD diagram of CDL-LD against other six methods with the Bonferroni- Dunne test (CD = 2.3265 at 0.05 significance level).
CDL-LD
LDLLC
SA-IIS
LCLR
LDLFs
LDLLDM
DLDL
CDL-LD if its average rank differs from that of CDL-LD by at least one critical difference.
Chehy
1.6(1)
5.17(7)
4.67(5)
3.42(2)
3.92()
4,25(4)
4.92(6)
1.001))
5.83(7)
5.75(6)
3.67(2)
3,67(2)
4.004)
4.08(5)
KL
1,001)
6,33(7)
3.92(4)
4.83(5)
5.08(6)
3,17(2)
3,67(5)
The results are shown in Fig. 5. If the average rank of a comparing algorithm is within one CD to that of CDL- LD, they are connected with a thick line; otherwise, is considered have a significantly different performance from CDL-LD. It is impressive that CDL-LD achieves the lowest rank in terms of all four evaluation metries, and the effectiveness of it is also more significant than all the other baseline methods based on Clark and Cosine. and the effectiveness of is also more significant than all the other baseline methods based on Clark and Cosine.
Cosine
1.50(1)
5,3377)
4.33(5)
3.83(2)
4.17(3
4.25(4)
4,866)
Table Average ranks and their ranks of our and baseline methods in terms of four metries all the datascts, where the best average ranks are highlighted in boldface.
Critical Value
Evalusice metric
Chehyshev
Cosine
2913
Friedman Statistics Fy
22.2645
40.2058
43.9416
21.8687
4.5. Time Complexity Analysis
Table Summary of the Friedman statistics FF in terms of four evaluation metries, with the critical value significance level of 0.05 (7 algorithms on 12 datasets)
In this section, three large datasets are selected from all the training datasets. We compare the running time of all the algorithms, and the results are shown in Table 6. The hardware configuration of the test machine is as follows: AMD EPYC 7K62 48- 18-Cores CPU, 377G running memory and NVIDIA GeForce RTX 3090 GPU. It can be observed from the results that the proposed model CDL-LD is much lower in terms of time cost than all other baseline algorithms, further proving the superiority of it.
CDL-LD
LDLLC
SA-IIS
LCLR
LDLFs
LDULDM
DLDL
Alp
10.45(1)
177.12/0)
69.34/2)
78.75(3)
136.8915)
114.36(4)
180.7107)
SBU
29.96(1)
189.8115)
100.2912)
123.57(3)
158.09(4
197,38(6)
241.150)
See
17.23(1)
18635866)
92,62(3
92,03()
143.62(4)
172.5155
234.02())
Table 6. Average ranks and their ranks of our and haseline methods terms running time (unit: second) on three large datasets, where the best average ranks are highlighted in boldface.
5. Conclusion
This paper presents novel paradigm called concentration distribution learning (CDL). Specifically, concentration dis- tributions are constructed by introducing background con- centration terms in label distributions. Due to the lack of concentration distribution learning datasets, we propose an algorithm to learn concentration distribution from traditional label distribution learning (LDL) datasets. Extensive exper- iments validate the advantage of CDL-LD against other baseline algorithms in concentration distribution learning, confirming the effectiveness of our method in training a CDL model from LDL datasets. Moreover, we build the first CDL dataset, that is, SJA e from the original SJAFFE dataset, and further prove the ability of our method to solve real-world CDL problems. Future work will continue to explore this innovative direction, focusing on concentration distribution learning.
4.4. Significance Tests
In this subsection, the average ranks of all methods are presented in Table 4. First, we conduct the Friedman test (Demšar, 2006) to study the comparative performance of all methods. Table 5 shows the Friedman statistics for each metric and the critical value. At the confidence level of 0.05, the null hypothesis that all algorithms have equal per- formance is rejected. Then we apply a post-hoc test, that is, the Bonferroni-Dumm test (Demšar, 2006) at the 0.05 significance level to test whether CDL-LD achieves signif- icantly better performance compared to other algorithms. We use CDL-LD as the control algorithm with a critical dif- ference (CD) (Demšar, 2006) to correct for the difference in mean level with the comparison algorithms. An algorithm is deemed achieve significantly different performance from

---

Concentration Distribution Learning from Label Distributions
Impact Statement
Lyons, M. J., Akamatsu, S., Kamachi, M., and Gyoba, J. Coding facial expressions with gabor wavelets. In 3rd International Conference on Face & Gesture Recognition (FG '98), pp. 200-205, 1998.
This paper presents work which comes up with a novel paradigm of concentration distribution learning and aims to advance the field of label distribution learning Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Mohri, M., Rostamizadeh, A., and Talwalkar, A. Founda- tions of Machine Learning MIT Press, Cambridge, MA, 2012. ISBN 9780262018258.
Peng, X., Jia, Y., Yang, F., Wang, R., and Zhang, M. Noise separation guided candidate label reconstruction for noisy partial label learning. In The Thirteenth International Conference Learning Representations, ICLR 2025, Singapore, April 24-28, 2025, 2025.
Funding Information
This work was supported by the National Natural Science Foundation of China under Grant U24A20322 and the Big Data Computing Center of Southeast University.
Ren, T., Jia, X., Li, W. Chen, L., and Li, Z. Label distribu- tion learning with label-specific features. In Proceedings of the Eventy-Eighthe International Joint Conference Artificial Intelligence, IJCAI 2019, pp. 3318-3324, 2019.
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Yin, L., Wei, X., Sun, Y., Wang. J., and Rosato, M. J. A 3d facial expression database for facial behavior research. In Seventh IEEE International Conference on Automatic Face and Gesture Recognition (FGR 2006), pp. 211-216, 2006.
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Zheng, X., Jia, X., and Li, W. Label distribution learning by exploiting sample correlations locally. pp. 4556-4563, 2018.
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10


Reviews:
[{"review_id": "iKyGC7QGml", "reviewer": "Reviewer_3FJ2", "summary": "This paper proposes Concentration Distribution Learning (CDL), which introduces background concentration to address the limitation of Label Distribution Learning (LDL) in capturing hidden information. The authors designed the CDL-LD model based on the Dirichlet distribution, combining confidence and background concentration to generate concentration distributions. They also constructed the SJA c dataset to validate the approach. Experiments demonstrate that CDL-LD outperforms existing methods across multiple metrics, especially in concentration distribution tasks.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "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": "Thanks for your valuable reviews, and your suggestions will effectively help us improve our work. Below are our responses to your **questions**.\n\n**Claims And Evidence 1 \\& 2: Why does the paper assume that each $alpha\\_i$ is composed of the sum of the dataset $e\\_i$ and the background concentration $u\\_i$, instead of treating the background as a whole?**\n\nThe paradigm of concentration distribution learning is a new concept raised by this paper. Since we have no further prior knowledge about the background concentration distribution pattern, the assumption that it is evenly spread across each class of the real label distribution is general. Furthermore, the experimental results also validate the rationality of this assumption. By defining $\\alpha_i=e_i+u_i$, we make the problem mathematically computable and finally draw the conclusion that all $u_i$ equal to one, which indicates that we should treat background concentrations as a whole. In other words, without initially dividing the background concentrations, the value of $u$ cannot be decided. \n\n**Methods And Evaluation Criteria 1: The paper uses MSE loss in a way that seems somewhat unreasonable. Have you tried using CE loss instead?**\n\nBy applying MSE loss, the final loss function can be arranged in the form of Eq. (10) in the paper, which minimizes the predictive square error ($(y_i-\\frac{\\alpha_i}{S})^2$) and the variance of the Dirichlet distribution ($\\frac{\\alpha_i(S-\\alpha_i)}{S^2(S+1)}$) simultaneously. Optimizing these two terms makes our experimental results more precise and stable. The CE loss, however, does not have this property.\n\n**Relation To Broader Scientific Literature: The paper studies label distribution learning, but only ancient references are cited.**\n\nThank you for your pointing out our shortcoming. We will incorporate some recent works in the final version of our paper.\n\n**Disadvantage 1: Some of the theoretical assumptions in the paper lack proper analysis or proof.**\n\nThank you for pointing out our shorcoming. We apply rademacher complexity to explain the theoretical bound of our proposed model.\n\nLet $\\mathcal{H}$ be a family of functions. For any $\\delta>0$, with probability at least $1-\\delta$, for all $h \\in \\mathcal{H}$ such that\n\n$$\n \\mathcal{L}(h) \\leq \\mathcal{L}\\_{S}(h)+\\widehat{\\mathcal{R}}\\_{S}(\\mathcal{H})+3\\sqrt{\\frac{\\log 2 / \\delta}{2 n}},\n$$\n\nwhere $\\mathcal{L}(h)$ and $\\mathcal{L}\\_{S}(h)$ are the generalization risk and empirical risk with respective to h, and $\\widehat{\\mathcal{R}}\\_{S}$ is the empirical rademacher complexity bounded by $(\\mathcal{H})\\leq\\mathbb{E}\\_{\\boldsymbol{\\sigma}}\\left[ \\frac{1}{n} \\sum\\_{i=1}^{n} \\sigma\\_{i} \\mathcal{L}\\_{AMSE}(\\mathbf{\\alpha}\\_i) \\right]$ with $\\sigma\\_{i}\\in[0,1]$. $n$ represents the number of instances.\n\nBecause $\\mathcal{L}\\_{AMSE}(\\mathbf{\\alpha})=\\sum^c\\_{i=1}(y\\_i-\\frac{\\alpha\\_i}{S})^2+\\frac{\\alpha\\_i(S-\\alpha\\_i)}{S^2(S+1)}>0$, we get\n\n$$\n        \\mathcal{L}(h)- \\mathcal{L}\\_{S}(h) \\leq \\mathbb{E}\\_{\\boldsymbol{\\sigma}}\\left[ \\frac{1}{n} \\sum\\_{i=1}^{n} \\sigma\\_{i} \\mathcal{L}\\_{AMSE}(\\mathbf{\\alpha}\\_i) \\right]+3\\sqrt{\\frac{\\log 2 / \\delta}{2 n}}\n        \\leq \\frac{1}{n} \\sum\\_{i=1}^{n} \\sum^c\\_{j=1} \\left[(y\\_{ij}-\\frac{\\alpha\\_{ij}}{S\\_i})^2+\\frac{\\alpha\\_{ij}(S\\_i-\\alpha\\_{ij})}{S\\_i^2(S\\_i+1)}\\right]+3\\sqrt{\\frac{\\log 2 / \\delta}{2 n}},\n$$\n\nin which $c$ is the number of classes. We assume that the neural network gives $e>0$ for every instance, then $\\forall i,j, \\alpha\\_{ij}>1, S\\_i>c$. So we have\n\n$$\n        \\mathcal{L}(h)- \\mathcal{L}\\_{S}(h) \\leq  \\frac{1}{n} \\sum\\_{i=1}^{n} \\sum^c\\_{j=1} \\left[(y\\_{ij}-\\frac{\\alpha\\_{ij}}{S\\_i})^2+\\frac{\\frac{\\alpha\\_{ij}}{S\\_i}(1-\\frac{\\alpha\\_{ij}}{S\\_i})}{S\\_i(S\\_i+1)}\\right]+3\\sqrt{\\frac{\\log 2 / \\delta}{2 n}}\n        \\leq \\frac{1}{n} \\sum\\_{i=1}^{n}  \\left[1+\\frac{1}{4c(c+1)}\\right]+3\\sqrt{\\frac{\\log 2 / \\delta}{2 n}}.\n$$\n\nWhen the number of instances $n$ tends to infinity, the bound finally becomes $1+\\frac{1}{4c(c+1)}$, which indicates that this bound shrinks when the number of classes $c$ increases. **This conclusion is intuitive because the background concentration tends to zero when $c$ tends to infinity, degrading the CDL problem to learnable LDL problem.**\n\n**Experimental Designs Or Analyses \\& Disadvantage 3: The paper provides a detailed introduction to the experimental design and analysis, but the datasets used seem relatively small. Have you tried testing on larger datasets? \\& The datasets used in the experimental section are relatively small, and no experiments have been conducted on larger datasets.**\n\nThank you for your advice. We carry out further experiments on the human gene dataset (with 17,892 instances). The results are listed as in the response of **Weakness 2** to Reviewer 7WaC due to the character limit, which further proves the superiority of the proposed CDL-LD.", "claims_and_evidence": "1.Why does the paper assume that each alpha_i is composed of the sum of the dataset e_i and the background concentration u_i, instead of treating the background as a whole? Specifically, why not define αi = e_i, with the sum of alpha_i plus a single overall u equaling 1? The authors' method seems inconsistent with the idea presented in the introduction.\n2.Why does the paper assume that the background concentration is evenly spread across each class of the real label distribution? There is neither theoretical nor intuitive justification for this assumption.", "methods_and_evaluation_criteria": "The paper uses MSE loss in a way that seems somewhat unreasonable. Have you tried using CE loss instead?  \nThe idea in the paper is relatively novel, the method is somewhat simplistic.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "The paper provides a detailed introduction to the experimental design and analysis, but the datasets used seem relatively small. Have you tried testing on larger datasets?", "relation_to_broader_scientific_literature": "The paper is related to label distribution learning, concentration distribution learning,  and face expression recogintion.", "essential_references_not_discussed": "More comprehensive discussion over related works from the last 2-3 years should be incorporated.", "other_strengths_and_weaknesses": "Advantages:  \nThe paper presents a novel and relatively reasonable approach.  \nThe introduction to related work and the explanation of the experimental section are quite detailed.  \n\nDisadvantages: \nSome of the theoretical assumptions in the paper lack proper analysis or proof.  \nThe datasets used in the experimental section are relatively small, and no experiments have been conducted on larger datasets.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "The authors should carefully address the above-mentioned issues.", "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": "", "extra_scores": {}}, {"review_id": "NXlTlj1J8J", "reviewer": "Reviewer_7WaC", "summary": "The paper introduces a novel concept called concentration distribution learning (CDL), which extends traditional label distribution learning (LDL) by incorporating a background concentration term. This term represents the absolute description degree of labels not present in the existing label space. The authors propose a method called CDLLD that uses probabilistic methods and neural networks to learn both label distributions and background concentrations from existing LDL datasets. The paper demonstrates the effectiveness of this approach through extensive experiments on multiple real-world datasets demonstrate the effectiveness of the proposed method. ## update after rebuttal. Most of my concerns are addressed, the authors have conducted experiments on larger datasets and clarified the unclear parts, thus I have decided to retain my positive score.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "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": "Thanks for your valuable reviews, and your suggestions will effectively help us improve our work. Below are our responses to your **questions**.\n\n**Claims And Evidence: The authors claim that \"excavating the background concentration makes full use of the information in the datasets and benefits the downstream tasks\", however, the experiments are not conducted on several downstream tasks, I suggest the authors should be cautious when making such a statement.**\n\nThank you for your advice. We think that in the experiments on the real-world CDL dataset, our model exvacates the hidden strength of emotions and helps us distinguish the images better, which can also be regarded as a downstream task. So we drew the conclusion that our proposed model can benefit the downstream tasks, which is reasonable.\n\n**Essential References Not Discussed: There is one essential reference that should be discussed, that is [1] \"Label distribution changing learning with sample space expanding.\" Journal of Machine Learning Research 24.36 (2023): 1-48.**\n\nThanks for pointing out our missing reference. We will add this to the final version of this paper.\n\n**Theoretical Claims: No theoretical claim is provided in this paper.**\n\nPlease refer to the response of **Weakness 1** to reviewer 3FJ2.\n\n**Weakness 2: Datasets used in the experiments are small, larger datasets should be considered.**\n\nThank you for your advice. We carry out further experiments on the human gene dataset (with 17,892 instances). The results are listed as below, with the best result of each metric shown in boldface. The extensive experiment further proves the superiority of the proposed CDL-LD.\n\n|        |      Cheby↓      |      Clark↓      |       LCLR       |      Cosine↑     |\n|:------:|:----------------:|:----------------:|:----------------:|:----------------:|\n| CDL-LD | **0.5735±.0090** | **3.6863±.0288** | **1.0830±.0160** | **0.7757±.0025** |\n|  LDLLC |   0.6745±.0039   |   3.9021±.0226   |   2.2932±.0206   |   0.6199±.0179   |\n| SA-IIS |   0.6948±.0121   |   3.7957±.0359   |   2.1820±.0337   |   0.6114±.0483   |\n|  LCLR  |   0.6148±.0178   |   3.5548±.0387   |   2.3030±.0228   |   0.6514±.0150   |\n|  LDLFs |   0.6383±.0467   |   3.7784±.0700   |   2.7793±.0261   |   0.6248±.0140   |\n| LDLLDM |   0.6549±.0283   |   3.8324±.0307   |   2.4558±.0193   |   0.6719±.0248   |\n|  DLDL  |   0.6056±.0259   |   3.7024±.0076   |   2.1174±.0328   |   0.6854±.0144   |\n\n**Question 1: Why do you choose the Dirichlet distribution(line 149 ), please give the reasons behind.**\n\nDirichlet distribution is a probability distribution on a multidimensional space and the sum of its components is 1, which makes it suitable for representing the probability distribution of multiple mutually exclusive events. Label distributions represent the probability distribution of multiple labels which are mutually exclusive, so we choose Dirichlet distribution in this paper.\n\n**Question 2: In Eq. (1), assuming that the background concentration is evenly spread on each class of the real label distribution vector b in probability.\" Is this assumption reasonable?**\n\nThe paradigm of concentration distribution learning is a new concept raised by this paper. Since we have no further prior knowledge about the background concentration distribution pattern, the assumption that it is evenly spread across each class of the real label distribution is general. Furthermore, the experimental results also validate the rationality of this assumption.\n\n**Question 3: Why define Eq.(10) in such a form? Can you make a detailed explanation?**\n\n$\\vert\\vert\\boldsymbol{y}-\\boldsymbol{p}\\vert\\vert_2^2$ is the MSE loss mentioned above in the paper, and $\\frac{1}{B(\\boldsymbol{\\alpha})}\\prod^c_{i=1}p_i^{\\alpha_i-1}$ is the probability density function of Dirichlet distribution. Integrating the product of these two terms gives the final loss function of the neural network, which aims to minimize the average value of MSE loss over the whole Dirichlet distribution.", "claims_and_evidence": "The authors claim that \"excavating the background concentration makes full use of the information in the datasets and benefits the downstream tasks\", however, the experiments are not conducted on several downstream tasks, I suggest the authors should be cautious when making such a statement.", "methods_and_evaluation_criteria": "Yes, the proposed method and evaluation criteria in this paper are well-suited for the problem of label distribution learning.", "theoretical_claims": "No theoretical claim is provided in this paper.", "experimental_designs_or_analyses": "Yes, I have checked the experimental parts, the experiments in this paper are useful for validating the effectiveness of the proposed method.", "relation_to_broader_scientific_literature": "The key contributions of the tempered sigmoid proposed in this paper are closely related to several areas of the broader scientific literature, particularly in the fields of label distribution learning, facial expression recognition, and emotion recognition.", "essential_references_not_discussed": "Yes, there is one essential reference that should be discussed.\n\n[1] \"Label distribution changing learning with sample space expanding.\" Journal of Machine Learning Research 24.36 (2023): 1-48.", "other_strengths_and_weaknesses": "Strengths:\n1. The problem studied in this paper is interesting and important in the label distribution learning area.\n2. The proposed method is effective according to the experimental results.\n3. The authors construct the first real-world concentration distribution dataset.\n\nWeaknesses:\n1. Some parts of the paper are not easy to understand and need further explanation. See the question parts below.\n2. Datasets used in the experiments are small, larger datasets should be considered.", "other_comments_or_suggestions": "Some parts need further explanation. See the question parts below.", "questions_for_authors": "1. Why do you choose the Dirichlet distribution(line 149 ), please give the reasons behind.\n2. \"In Eq. (1), assuming that the background concentration is evenly spread on each class of the real label distribution vector b in probability.\" Is this assumption reasonable? Maybe it is better to consider uneven spread.\n3. Why define Eq.(10) in such a form? Can you make a detailed explanation?", "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": "", "extra_scores": {}}, {"review_id": "MX5XdKN14k", "reviewer": "Reviewer_5CcH", "summary": "The paper proposes a new label distribution learning method based on a novel hypothesis. Hypothesis: In existing label distribution learning, there is an issue where the current labels within the label set cannot adequately describe the samples. Based on this hypothesis, the authors suggest that concentration can be used to describe the extent to which existing labels describe the samples, and accordingly, the label distribution is augmented and expanded. The authors, based on this hypothesis, expand and augment the label distribution and then design a label distribution learning algorithm tailored to this hypothesis, setting concentration as a part of all label distributions. Experiments show that the algorithm proposed in the paper performs well on almost all datasets used, possessing the optimal average ranking, and the gap in the average ranking metric with other comparison algorithms used is quite significant.\n\n## update after rebuttal\nAfter discussing with the authors, I believe the research problem addressed in this paper is important and the methodology employed demonstrates novelty. However, some aspects of the presentation remain unclear. Taking these factors into consideration, I have decided to raise my score to 3.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "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": "Thank you for your precious suggestions. After careful consideration, our responses to the **questions** you mentioned are listed as follows.\n\n**Claims And Evidence: The authors believe that in the existing label distribution learning, the labels in the label space are insufficient to describe the samples, which contradicts the basic assumption in the consensus definition of label distribution learning.\n\nThe assumption that \"the labels in the label space can fully describe each sample\" is correct in the cases of label distribution learning, which aims to learn the relative description level of each sample. However, in concentration distribution learning, we focus on learning the absolute description level. In these cases, the labels in the label space are insufficient to describe the samples because they overlook the existence of background concentration. In other words, CDL is an extension of LDL, which are not contradicted with each other.\n\n**Methods And Evaluation Criteria: I am rather skeptical about the significance of comparing the experiments in this paper, which involve label distribution learning with concentration terms, to traditional label distribution datasets that do not include concentration terms.**\n\nThe paradigm of concentration distribution learning is a new concept, so there are no available CDL datasets. To this end, we construct the first real-world CDL dataset in our paper and conduct experiments on it to verify the effectiveness of our model of exvacating background concentration. And by hiding the last dimension of LDL datasets, we transform LDL datasets into CDL datasets. If our model can recover this hidden dimension, which is regarded as the background concentration, its ability to learn concentration distribution can be proved.\n\n**Experimental Designs Or Analyses: Would it be better to add a two-tailed t-test to verify the superiority or inferiority against each comparison algorithm?**\n\nThank you for pointing out our shortcoming. The following is the result of the two-tailed t-test. In the significance level of $\\alpha=0.01$, the null hypotheses that \"there is no significant difference between the ranks of our proposed CDL-LD and the baseline algorithm\" are all rejected, which means that the control model CDL-LD is significantly different to all the other baseline algorithms in rank. This result further proves the effectiveness of the proposed model.\n\n| p-value | LDLLC     | SA-IIS    | LCLR      | LDLFs     | LDLLDM    | DLDL      |\n|---------|-----------|-----------|-----------|-----------|-----------|-----------|\n| CDL-LD  | 8.5504e-6 | 2.2121e-4 | 2.9684e-4 | 1.6835e-4 | 1.4473e-4 | 8.7229e-5 |\n\n**Weakness 1: The real-world examples used by the authors to illustrate the role of concentration are inappropriate; both sets of examples could resolve the mismatch in descriptive strength by adding extra labels, which is not convincing.**\n\nThe concept of background concentration cannot be replaced by simply adding extra labels. In Fig. 1(a) and (b), background concentration can be interpreted as the background of the image. However, it's hard to describe the background by adding labels like “mountain” or “water” since there are lots of contents in the background except mountain and water. Even if we make out all objects in the background, the label distribution of them is still costly and time-consuming to obtain. For other cases of Fig. 1(c), (d) and Fig.2, the meaning of background concentration is too abstract that it's impossible to be labeled. So we have no choice but to introduce the concept of background concentration.\n\n**Weakness 2: The validation of the algorithm’s performance should not be considered as one of the contributions of the entire paper.**\n\nOur contribution is mainly reflected in coming up with the concentration distribution learning paradigm, constructing the first real-world CDL dataset and proposing a model to learn CDs from LDL datasets. We will rearrange the part of contribution in the final version of this paper.\n\n**Weakness 3: No theoretical analysis or claims are provided to further validate the robustness and effectiveness of the proposal.**\n\nPlease refer to the response of **Weakness 1** to reviewer 3FJ2.\n\n**Other Comments Or Suggestions: The authors should use appropriate examples to match the methods of solving the problem with the issues and motivations they propose, and they should avoid giving the impression that contradicts the fundamental assumption of label distribution learning.**\n\nPlease refer to **Claims And Evidence** and **Weakness 1** of this response.\n\n**Questions For Authors: If an additional labels, such as “mountain” or “water,” is added to make the label set meet the condition of “being able to fully describe each sample,” does the issue discussed by the authors no longer exist in the example they used?**\n\nPlease refer to **Weakness 1** of this response.", "claims_and_evidence": "I raise doubts about the label distribution assumption proposed in the paper. The authors believe that in the existing label distribution learning, the labels in the label space are insufficient to describe the samples, which contradicts the basic assumption in the consensus definition of label distribution learning that ‘the labels in the label space can fully describe each sample.’ The approach taken in this paper is to add an extra ‘concentration’ to each label distribution component, meaning that each label distribution component in the dataset requires an additional quantity to correctly describe each sample. Therefore, in my opinion, the issue raised by this paper points to the difference between the relative description level of label distribution description and the absolute description level of the original description.", "methods_and_evaluation_criteria": "I am rather skeptical about the significance of comparing the experiments in this paper, which involve label distribution learning with concentration terms, to traditional label distribution datasets that do not include concentration terms.", "theoretical_claims": "This paper does not provide any proofs or theoretical analysis.", "experimental_designs_or_analyses": "Yes, I suspect that it is not sufficient to test the effectiveness of the algorithm solely through the Friedman test on the average ranking, as this is influenced by the number of comparison algorithms and the quantity of datasets. Would it be better to add a two-tailed t-test to verify the superiority or inferiority against each comparison algorithm?", "relation_to_broader_scientific_literature": "This paper points out a new issue related to label distribution learning, which has not been considered before.", "essential_references_not_discussed": "After my review, I believe that the paper has adequately cited and discussed the prior work related to its key contributions. I have not identified any uncited or undiscussed work that is essential for understanding the context or the key contributions of the paper.", "other_strengths_and_weaknesses": "Strengths:\n1. The issue addressed in the paper is indeed one of the problems in label distribution learning, namely, the inconsistency in the intensity of the original label descriptions and the label distribution descriptions after normalization. The authors introduce a new concept of concentration in label distribution to address the mismatch in descriptive strength between the relative description level of label distribution and the absolute description level of labels.\n2. The authors propose a new framework for label distribution learning based on the concept of concentration, offering new methods and perspectives for label distribution learning.\n\nWeaknesses:\n1. The real-world examples used by the authors to illustrate the role of concentration are inappropriate; both sets of examples could resolve the mismatch in descriptive strength by adding extra labels, which is not convincing.\n2. The validation of the algorithm’s performance should not be considered as one of the contributions of the entire paper.\n3. No theoretical analysis or claims are provided to further validate the robustness and effectiveness of the proposal.", "other_comments_or_suggestions": "The authors should use appropriate examples in the Introduction section to match the methods of solving the problem with the issues and motivations they propose. The example of emotional intensity used by the authors is a good illustration, as it appropriately reveals that the same label distribution may correspond to completely different levels of emotional intensity. The examples used in the Introduction can also be resolved by adding labels and other means. \nThe authors should also be mindful of the perspective from which they articulate the problem, ensuring that it does not lead to ambiguity for the readers. They should avoid giving the impression that “the issue pointed out by the authors is that the existing labels in the label space of label distribution learning cannot fully describe the samples,” as this would contradict the fundamental assumption of label distribution learning.", "questions_for_authors": "In the example used by the authors in the motivation part, such as the example about the boat, if an additional labels, such as “mountain” or “water,” is added to make the label set meet the condition of “being able to fully describe each sample,” does the issue discussed by the authors no longer exist in the example they used?", "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": "", "extra_scores": {}}, {"review_id": "XSOhbrrl9T", "reviewer": "Reviewer_uvxc", "summary": "This paper proposes Concentration Distribution Learning (CDL), a new variant of Label Distribution Learning (LDL). In CDL, in addition to the common label distribution that represents the descriptions of each class, there is a dimension that represents the background information. Based on an assumption about the generation process of the concentration distribution, an estimation method is proposed to determine the concentration distribution. Experimental results validate the effectiveness of the proposed method, and a new CDL dataset is also proposed.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "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": "Thank you for your time and effort on reviewing our paper. In what follows, we will address your **questions** in detail.\n\n**Experimental Designs Or Analyses 1: The traditional LDL experimental datasets may differ from real-world scenarios because the last dimension may not serve as the background and its generation assumption may not be consistent with the assumption proposed in this paper (Eq. (1)).**\n\nThe paradigm of concentration distribution learning is a new concept, so there are no available CDL datasets. To this end, we construct the first real-world CDL dataset in our paper and conduct experiments on it to verify the effectiveness of our model of exvacating background concentration. And by hiding the last dimension of LDL datasets, we transform LDL datasets into CDL datasets. If our model can recover this hidden dimension, which is regarded as the background concentration, its ability to learn concentration distribution can be proved.\n\n**Experimental Designs Or Analyses 2: Can the authors elaborate more on the success of the proposed method on the CDL dataset? Also, it might be helpful to include more experimental results on more data points.**\n\nThanks for your advice. In the final version of this paper, we will present more results on the constructed CDL dataset and some other data points.\n\n**Weakness 1 \\& 2: The writing of the paper needs to be improved. There are some typos and unclear expressions in the paper, and some equations seem to be redundant.**\n\nThanks for pointing out our shortcomings. In the final version of our paper, we will carefully correct these errors and simplify our equations.\n\n**Weakness 3: The assumption of the background vector generation process is too simple, which may limit the applications in the real-world scenarios.**\n\nThe paradigm of concentration distribution learning is a new concept raised by this paper. Since we have no further prior knowledge about the background concentration distribution pattern, the assumption that it is evenly spread across each class of the real label distribution is general. Furthermore, the experimental results also validate the rationality of this assumption.\n\n**Other Comments Or Suggestions 1: The writing of the paper can be improved and revised to be clearer.**\n\nThanks for your advise. This paper will be carefully revised in its final version.\n\n**Other Comments Or Suggestions 2: More justification of the data generation model and its practicality in real-world applications should be given.**\n\nFor the data generation model, please refer to **Weakness 3** of this response. Additionally, in the final version of this paper, we will present more real-world applications of concentration distribution learning.\n\n**Other Comments Or Suggestions 3: Theoretical analysis of the proposed method can be done to improve the paper.**\n\nPlease refer to the response of **Weakness 1** to reviewer 3FJ2.\n\n**Question: Fig. 2 is not similar because the difference, i.e. the expression, may not correspond to the background. It is the main object of the image. Therefore, I am not sure that the core idea of the paper that the background of the image is important can be applied.**\n\nThe \"background concentration\" is named after the background, but it is an abstract concept and does not actually refer to the background of the image. In the case of facial expression, the background concentration doesn't refer to any expression, and it represents the description degree of “no emotion”. In other words, the stronger the emotion is, the lower the background concentration it should be assigned.", "claims_and_evidence": "The claim that traditional label distribution learning does not take the background into account is novel in the literature and also makes sense. It is reasonable that two images with different backgrounds may have similar label distributions, and traditional label distributions may not describe the images well. Therefore, I think the novelty of the proposed setting is good", "methods_and_evaluation_criteria": "- The proposed method can learn a good label distribution under the proposed assumption. However, I think that the proposed assumption may be a bit strong. First, it assumes that the background vector is an all-one vector, which may be a bit easy since the contribution of the background to each class may be equal.\n\n- Second, it assumes that the concentration distribution is an addition of the previous label distribution and the new concentration distribution. This may be more complex in real applications. I think this point needs to be clarified.", "theoretical_claims": "No theoretical claims are made in this paper.", "experimental_designs_or_analyses": "- The experiments consist mainly of two parts. The first part is a synthetic experiment, where traditional LDL experimental datasets are used and the last dimension is considered as a background. Such an experimental setting may differ from real-world scenarios because the last dimension may not serve as the background and its generation assumption may not be consistent with the assumption proposed in this paper (Eq. (1)). \n\n- For the second part, a new CDL dataset is constructed, and it is surprising to see that the results of the proposed method are very similar to the ground-truth label (Fig. (4)). I am curious with these good experimental results. Can the authors elaborate more on the success of the proposed method on this dataset? Also, it might be helpful to include more experimental results on more data points.", "relation_to_broader_scientific_literature": "Not available.", "essential_references_not_discussed": "There are no essential references that need to be discussed.", "other_strengths_and_weaknesses": "### Strengths\n- The novelty of the new CDL setting is good and practical for LDL literature. This may open new research directions for LDL.\n- The proposed method is simple and effective, validated by extensive experimental results.\n\n### Weaknesses\n- The writing of the paper needs to be improved. There are some typos and unclear expressions in the paper. For example, the word \"are\" is missing in line 18 of the abstract. There are some similar problems in the main text, which should be carefully reviewed and revised. \n\n- Some equations seem to be redundant. For example, the left column on page 4 contains some equations that can be greatly simplified, since only simple calculations are performed.\n\n- The assumption of the background vector generation process is too simple, which may limit the applications in the real-world scenarios.", "other_comments_or_suggestions": "- The writing of the paper can be improved and revised to be clearer.\n\n- More justification of the data generation model and its practicality in real-world applications should be given.\n\n- Theoretical analysis of the proposed method can be done to improve the paper.\n\nI am willing to increase my score if my concerns can be addressed properly.", "questions_for_authors": "- I have a question about the CDL examples in the introduction. Fig. 1 is quite intuitive that different images with significant differences in the background should have different label distributions. Fig. 2 is not similar because the difference, i.e. the expression, may not correspond to the background. It is the main object of the image. Therefore, I am not sure that the core idea of the paper that the background of the image is important can be applied.", "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": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper introduces a novel technique for label distribution learning, specifically concentration distribution learning, which incorporates a background concentration term. The experimental results demonstrate that the proposed method is effective on existing benchmark datasets. During the rebuttal phase, the authors addressed most concerns raised by the reviewers, and all reviewers now support the acceptance of this paper. Therefore, I recommend accepting this paper. The authors should revise the manuscript according to the reviewers' feedback.
Decision: Accept (poster)