Table of Links Abstract & Introduction


Proposal

Classification Target
Masked Conditional Density Estimation (MaCoDE)



Theoretical Results

With Missing Data



Experiments


Results

Related Works
Conclusions and Limitations
References



A1 Proof of Theorem 1

A2 Proof of Proposition 1
A3 Dataset Descriptions



A4 Missing Mechanism

A5 Experimental Settings for Reproduction



A6 Additional Experiments


A7 Detailed Experimental Results 2.3 Theoretical Results Remark 2. Since we constrain the values of continuous columns to the interval [0, 1], our proposed approach and Theorem 1 can be seen as similar to the copula density estimation method [22, 27, 9, 2]. However, given the heterogeneous nature of tabular data [3, 43], handling categorical variables is essential, and the categorical marginal distributions do not guarantee the uniqueness of the copula [44]. Therefore, instead of utilizing the copula density estimation method, we adopt a multi-class classification approach for density estimation. 2.4 With Missing Data In (6), the missingness pattern is described by min(m, r), indicating that the missing data model is determined by the joint distribution p(m, r|x). Thus, as the masking vector defined in Definition 2 satisfies the conditions in Proposition 1, the missingness pattern of our proposed model also conforms to the MAR mechanism according to Proposition 1 if the given data is MAR. It implies that our inference strategies based on the observed dataset can be justified [34]. However, we empirically demonstrate in Section 3 that our proposed model is also applicable to other missing data scenarios. Authors:
(1) Seunghwan An, Department of Statistical Data Science, University of Seoul, S. Korea (dkstmdghks79@uos.ac.kr);
(2) Gyeongdong Woo, Department of Statistical Data Science, University of Seoul, S. Korea (dngudxor23@uos.ac.kr);
(3) Jaesung Lim, Department of Statistical Data Science, University of Seoul, S. Korea (wotjd1410@uos.ac.kr);
(4) ChangHyun Kim, Department of Statistical Data Science, University of Seoul, S. Korea (hahaha503@uos.ac.kr);
(5) Sungchul Hong, Department of Statistics, University of Seoul, S. Korea (shong@uos.ac.kr);
(6) Jong-June Jeon (corresponding author), Department of Statistics, University of Seoul, S. Korea (jj.jeon@uos.ac.kr). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Table of Links Abstract & Introduction Proposal

Classification Target
Masked Conditional Density Estimation (MaCoDE) Theoretical Results

With Missing Data Experiments Results

Related Works
Conclusions and Limitations
References A1 Proof of Theorem 1

A2 Proof of Proposition 1
A3 Dataset Descriptions A4 Missing Mechanism

A5 Experimental Settings for Reproduction A6 Additional Experiments A7 Detailed Experimental Results Abstract & Introduction Abstract & Introduction Abstract & Introduction Proposal Classification Target
Masked Conditional Density Estimation (MaCoDE) Proposal Proposal Classification Target Masked Conditional Density Estimation (MaCoDE) Classification Target Masked Conditional Density Estimation (MaCoDE) Theoretical Results With Missing Data Theoretical Results Theoretical Results With Missing Data With Missing Data Experiments Experiments Experiments Results Related Works
Conclusions and Limitations
References Results Results Related Works Conclusions and Limitations References Related Works Conclusions and Limitations References A1 Proof of Theorem 1 A2 Proof of Proposition 1
A3 Dataset Descriptions A1 Proof of Theorem 1 A1 Proof of Theorem 1 A2 Proof of Proposition 1 A3 Dataset Descriptions A2 Proof of Proposition 1 A3 Dataset Descriptions A4 Missing Mechanism A5 Experimental Settings for Reproduction A4 Missing Mechanism A4 Missing Mechanism A5 Experimental Settings for Reproduction A5 Experimental Settings for Reproduction A6 Additional Experiments A6 Additional Experiments A6 Additional Experiments A7 Detailed Experimental Results A7 Detailed Experimental Results A7 Detailed Experimental Results 2.3 Theoretical Results Remark 2. Since we constrain the values of continuous columns to the interval [0, 1] , our proposed approach and Theorem 1 can be seen as similar to the copula density estimation method [22, 27, 9, 2]. However, given the heterogeneous nature of tabular data [3, 43], handling categorical variables is essential, and the categorical marginal distributions do not guarantee the uniqueness of the copula [44]. Therefore, instead of utilizing the copula density estimation method, we adopt a multi-class classification approach for density estimation. Remark 2. Since we constrain the values of continuous columns to the interval , our proposed approach and Theorem 1 can be seen as similar to the copula density estimation method [22, 27, 9, 2]. However, given the heterogeneous nature of tabular data [3, 43], handling categorical variables is essential, and the categorical marginal distributions do not guarantee the uniqueness of the copula [44]. Therefore, instead of utilizing the copula density estimation method, we adopt a multi-class classification approach for density estimation. 2.4 With Missing Data In (6), the missingness pattern is described by min(m, r), indicating that the missing data model is determined by the joint distribution p(m, r|x). Thus, as the masking vector defined in Definition 2 satisfies the conditions in Proposition 1, the missingness pattern of our proposed model also conforms to the MAR mechanism according to Proposition 1 if the given data is MAR. It implies that our inference strategies based on the observed dataset can be justified [34]. However, we empirically demonstrate in Section 3 that our proposed model is also applicable to other missing data scenarios. Authors: (1) Seunghwan An, Department of Statistical Data Science, University of Seoul, S. Korea (dkstmdghks79@uos.ac.kr); (2) Gyeongdong Woo, Department of Statistical Data Science, University of Seoul, S. Korea (dngudxor23@uos.ac.kr); (3) Jaesung Lim, Department of Statistical Data Science, University of Seoul, S. Korea (wotjd1410@uos.ac.kr); (4) ChangHyun Kim, Department of Statistical Data Science, University of Seoul, S. Korea (hahaha503@uos.ac.kr); (5) Sungchul Hong, Department of Statistics, University of Seoul, S. Korea (shong@uos.ac.kr); (6) Jong-June Jeon (corresponding author), Department of Statistics, University of Seoul, S. Korea (jj.jeon@uos.ac.kr). Authors : Authors (1) Seunghwan An, Department of Statistical Data Science, University of Seoul, S. Korea (dkstmdghks79@uos.ac.kr); (2) Gyeongdong Woo, Department of Statistical Data Science, University of Seoul, S. Korea (dngudxor23@uos.ac.kr); (3) Jaesung Lim, Department of Statistical Data Science, University of Seoul, S. Korea (wotjd1410@uos.ac.kr); (4) ChangHyun Kim, Department of Statistical Data Science, University of Seoul, S. Korea (hahaha503@uos.ac.kr); (5) Sungchul Hong, Department of Statistics, University of Seoul, S. Korea (shong@uos.ac.kr); (6) Jong-June Jeon (corresponding author), Department of Statistics, University of Seoul, S. Korea (jj.jeon@uos.ac.kr). This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv available on arxiv

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