GAIN: Missing Data Imputation using Generative Adversarial Nets

Jinsung YoonJames JordonMihaela van der Schaar

article2018ICML1,456 citations

Presents Generative Adversarial Imputation Nets (GAIN), a framework that adapts GANs with a hint-conditioned discriminator to accurately model the underlying data distribution and outperform standard missing data imputation methods.

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Missing data is a common challenge across healthcare, finance, and industrial analytics, occurring whenever measurements are lost, omitted, or too costly or risky to collect. Conventional imputation techniques often fail to capture complex distributions or require complete datasets during training, which is unrealistic for many real-world environments.

The article introduces and evaluates Generative Adversarial Imputation Nets (GAIN), a machine learning framework designed to infer missing values accurately even when only incomplete datasets are available for training.

The proposed method adapts generative adversarial frameworks by having a generator fill in missing values while a discriminator determines which individual components within a record are real and which are generated. To ensure the system learns the true underlying data distribution, the architecture introduces a hint mechanism that provides partial information about missingness to the discriminator. The authors evaluated the approach using five benchmark datasets spanning medical, language, and financial domains, assessing reconstruction error, downstream predictive accuracy, and parameter bias under varying missingness rates.

The evaluation produced four primary findings. First, GAIN consistently outperformed leading imputation baselines across all benchmark datasets, reducing imputation root mean square error by approximately 10% to 28% compared to standard alternatives. Second, ablation analysis confirmed that the adversarial architecture and the hint mechanism provide distinct performance boosts, yielding roughly 15% and 10% improvements respectively over simpler auto-encoder designs. Third, the framework remained robust under high data loss, demonstrating superior predictive performance over benchmark methods as missing data rates approached 80% to 90%. Fourth, the model preserved feature-label relationships more accurately than existing methods, achieving an 8.9% to 79.2% reduction in downstream parameter bias.

These results indicate that adopting this framework can enhance downstream decision-making and operational reliability by significantly reducing errors caused by incomplete data. The ability to train directly on incomplete records reduces data preparation costs and avoids discarding valuable partial information in data-constrained domains.

Organizations handling incomplete tabular datasets should consider integrating this framework into their data-processing pipelines, especially where high missingness degrades downstream model performance. Future work recommended by the source includes expanding evaluations into active sensing, recommender systems, and image error concealment.

Confidence in these findings is supported by rigorous cross-validated benchmarking across multiple domains. However, the theoretical guarantees presented are primarily established under the assumption that data is missing completely at random, meaning operational teams should exercise appropriate caution and validate results when working with non-random missingness patterns.

The Alan Turing Institute University of California, Los Angeles University of Oxford gan generative adversarial networks Generative Adversarial Imputation Nets missing data imputation standard GAN

arXiv: 1806.02920

Paper: Generative Adversarial Networks, Ian J. Goodfellow et al. (2014). It introduces the core Generative Adversarial Networks (GAN) framework of competing generator and discriminator networks that GAIN directly adapts for missing data imputation.
Paper: Conditional Generative Adversarial Nets, Mehdi Mirza et al. (2014). It formalizes conditioning in adversarial nets, providing the foundational mechanism GAIN relies upon to generate missing components conditioned on observed data and hint vectors.
Paper: Globally and locally consistent image completion, SATOSHI IIZUKA et al. (2017). It establishes the paradigm of using adversarial training for data completion and inpainting across arbitrary missing regions.
Paper: Generative Adversarial Networks: An Overview, Antonia Creswell et al. (2017). It provides a foundational overview of GAN training principles and architectures necessary for understanding adversarial generative modeling.

Paper: Modeling Tabular data using Conditional GAN, Lei Xu et al. (2019). It advances generative adversarial modeling for mixed continuous and discrete tabular distributions, building on the tabular data generation challenges explored in GAIN.
Paper: Time-series Generative Adversarial Networks, Jinsung Yoon et al. (2019). It extends adversarial generative principles from static tabular data vectors to complex sequential and time-series domains.
Paper: Free-Form Image Inpainting With Gated Convolution, Jiahui Yu et al. (2018). It builds upon adversarial data completion methods by introducing learnable gated convolutions for free-form inpainting.
Paper: Image Inpainting for Irregular Holes Using Partial Convolutions, Guilin Liu et al. (2018). It continues research into missing data completion by using partial convolutions with automatic mask updates to handle irregular missing patterns.

Cover for GAIN: Missing Data Imputation using Generative Adversarial Nets

Abstract

We propose a novel method for imputing missing data by adapting the well-known Generative Adversarial Nets (GAN) framework. Accordingly, we call our method Generative Adversarial Imputation Nets (GAIN). The generator (G) observes some components of a real data vector, imputes the missing components conditioned on what is actually observed, and outputs a completed vector. The discriminator (D) then takes a completed vector and attempts to determine which components were actually observed and which were imputed. To ensure that D forces G to learn the desired distribution, we provide D with some additional information in the form of a hint vector. The hint reveals to D partial information about the missingness of the original sample, which is used by D to focus its attention on the imputation quality of particular components. This hint ensures that G does in fact learn to generate according to the true data distribution. We tested our method on various datasets and found that GAIN significantly outperforms state-of-the-art imputation methods.

Topics

gan generative adversarial networks

Keywords

Generative Adversarial Imputation Nets missing data imputation standard GAN multiple imputation multivariate imputation post-imputation prediction matrix completion

1 Introduction
2 Problem Formulation
2.1 Imputation
3 Generative Adversarial Imputation Nets
3.1 Generator
3.2 Discriminator
3.3 Hint
3.4 Objective
4 Theoretical Analysis
5 GAIN Algorithm
6 Experiments
6.1 Source of gain
6.2 Quantitative analysis of GAIN
6.3 GAIN in different settings
6.4 Prediction Performance
6.5 Congeniality of GAIN
7 Conclusion
References

Knowls

Knowl 1 — Generative Adversarial Imputation Nets Architecture
model/method
Generative Adversarial Imputation Nets (GAIN) adapts the generative adversarial framework to impute missing values in data vectors conditioned on observed entries.

Let $\mathcal{X} = \mathcal{X}_1 \times \dots \times \mathcal{X}_d$ be a $d$ -dimensional feature space. A complete data vector is represented by a random variable $X = (X_1, \dots, X_d) \in \mathcal{X}$ , and a mask vector is represented by $M = (M_1, \dots, M_d) \in \{0, 1\}^d$ , where $M_i = 1$ indicates that $X_i$ is observed and $M_i = 0$ indicates that $X_i$ is missing. The partially observed data vector is defined as $\tilde{X} = (\tilde{X}_1, \dots, \tilde{X}_d) \in \tilde{\mathcal{X}} = \tilde{\mathcal{X}}_1 \times \dots \times \tilde{\mathcal{X}}_d$ , where $\tilde{\mathcal{X}}_i = \mathcal{X}_i \cup \{*\}$ and:

$\tilde{X}_i = \begin{cases} X_i, & \text{if } M_i = 1 \\ *, & \text{otherwise} \end{cases}$

GAIN consists of two neural networks:
1. Generator ( $G$ ): Takes as input the observed vector $\tilde{X}$ (with unobserved entries replaced by fixed values), the mask vector $M$ , and a masked noise vector $(1 - M) \odot Z$ , where $Z = (Z_1, \dots, Z_d) \in [0, 1]^d$ is independent random noise and $\odot$ denotes element-wise multiplication. The generator outputs a full imputation vector $\bar{X} = G(\tilde{X}, M, (1 - M) \odot Z) \in \mathcal{X}$ . The completed data vector $\hat{X} \in \mathcal{X}$ is then constructed by replacing only the unobserved entries with the generator's outputs:
$\hat{X} = M \odot \tilde{X} + (1 - M) \odot \bar{X}$
1. Discriminator ( $D$ ): Unlike standard GAN discriminators that predict whether an entire sample is real or fake, the GAIN discriminator $D: \mathcal{X} \times \mathcal{H} \to [0, 1]^d$ assesses component-wise authenticity. Given the completed vector $\hat{X}$ and a hint vector $H \in \mathcal{H}$ , the $i$ -th output $D(\hat{X}, H)_i$ predicts the probability that the $i$ -th component of $\hat{X}$ was genuinely observed ( $M_i = 1$ ) rather than imputed ( $M_i = 0$ ).
Knowl 2 — GAIN Hint Mechanism
model/method
The hint mechanism in GAIN provides the discriminator with partial information about the original mask vector $M \in \{0, 1\}^d$ , ensuring that the adversarial training process forces the generator to replicate the true underlying data distribution rather than arbitrary candidate distributions.

A random variable $B = (B_1, \dots, B_d) \in \{0, 1\}^d$ is generated by sampling an index $k \in \{1, \dots, d\}$ uniformly at random and defining:

$B_j = \begin{cases} 1, & \text{if } j \neq k \\ 0, & \text{if } j = k \end{cases}$

The hint vector $H \in \mathcal{H} = \{0, 0.5, 1\}^d$ is then defined conditioned on $M$ and $B$ as:

$H = B \odot M + 0.5(1 - B)$

where $\odot$ denotes element-wise multiplication. For each feature index $j \neq k$ , $H_j = M_j$ , explicitly revealing whether feature $j$ was observed or imputed. For index $k$ , $H_k = 0.5$ , providing no direct disclosure of $M_k$ . For the optimal discriminator $D^*$ , $D^*(x, h)_i = h_i$ when $h_i \in \{0, 1\}$ , so adversarial gradients only evaluate the ambiguous component where $h_i = 0.5$ ( $b_i = 0$ ).
Knowl 3 — Theoretical Convergence to the True Conditional Distribution under MCAR
theoretical result
Let data vector $X \in \mathcal{X}$ and mask vector $M \in \{0, 1\}^d$ satisfy the Missing Completely at Random (MCAR) assumption, such that $M$ is statistically independent of $X$ . Let $\hat{X} = M \odot \tilde{X} + (1 - M) \odot G(\tilde{X}, M, (1 - M) \odot Z)$ , let hint vector $H = B \odot M + 0.5(1 - B)$ with $B_j = 1$ for $j \neq k$ and $B_k = 0$ for uniformly sampled $k \in \{1, \dots, d\}$ , and let $\hat{p}$ denote the joint density of $(\hat{X}, M, H)$ .
1. Optimal Discriminator: For any fixed generator $G$ , the optimal discriminator $D^*$ satisfies:
$D^*(x, h)_i = p_m(M_i = 1 \mid X = x, H = h)$
1. Global Minimum of the Generator Criterion: Substituting $D^*$ into the minimax objective yields the generator criterion $C(G) = \mathbb{E}_{\hat{X}, M, H} \left[ \sum_{i: M_i=1} \log p_m(M_i = 1 \mid \hat{X}, H) + \sum_{i: M_i=0} \log p_m(M_i = 0 \mid \hat{X}, H) \right]$ . A global minimum of $C(G)$ is achieved if and only if:
$\hat{p}(x \mid h, M_i = t) = \hat{p}(x \mid h)$

for all $i \in \{1, \dots, d\}$ , $x \in \mathcal{X}$ , $t \in \{0, 1\}$ , and $h \in \mathcal{H}$ with $p_h(h \mid M_i = t) > 0$ .
1. Distribution Recovery: Under the specified hint mechanism $H = B \odot M + 0.5(1 - B)$ , the solution to the global minimum condition is unique and satisfies:
$\hat{p}(x \mid m_1) = \hat{p}(x \mid m_2) = \hat{p}(x \mid \mathbf{1}) = P(X)$

for all $m_1, m_2 \in \{0, 1\}^d$ . Consequently, the distribution of completed samples $\hat{X}$ coincides exactly with the true underlying data distribution $P(X)$ . If $H$ is independent of $M$ , the solution is non-unique and distribution recovery is not guaranteed.
Knowl 4 — GAIN Loss Functions and Objectives
equation
The discriminator and generator in GAIN are trained using modified cross-entropy losses conditioned on the hint-mask $B \in \{0, 1\}^d$ , complemented by a reconstruction loss on observed components for the generator.

Let $m \in \{0, 1\}^d$ be the true mask, $\hat{m} = D(\hat{x}, h) \in [0, 1]^d$ be the discriminator's output, and $b \in \{0, 1\}^d$ indicate revealed hint entries. The discriminator loss $\mathcal{L}_D: \{0, 1\}^d \times [0, 1]^d \times \{0, 1\}^d \to \mathbb{R}$ evaluates only the unrevealed component ( $b_i = 0$ ):

$\mathcal{L}_D(m, \hat{m}, b) = \sum_{i: b_i = 0} \left[ m_i \log(\hat{m}_i) + (1 - m_i) \log(1 - \hat{m}_i) \right]$

The generator's adversarial loss $\mathcal{L}_G: \{0, 1\}^d \times [0, 1]^d \times \{0, 1\}^d \to \mathbb{R}$ encourages the generator to fool the discriminator on imputed entries ( $m_i = 0$ ) where $b_i = 0$ :

$\mathcal{L}_G(m, \hat{m}, b) = -\sum_{i: b_i = 0} (1 - m_i) \log(\hat{m}_i)$

The reconstruction loss $\mathcal{L}_M: \mathbb{R}^d \times \mathbb{R}^d \to \mathbb{R}$ measures the discrepancy between the observed features $x$ and generator outputs $\bar{x}$ on observed entries ( $m_i = 1$ ):

$\mathcal{L}_M(x, \bar{x}) = \sum_{i=1}^d m_i L_M(x_i, \bar{x}_i), \quad \text{where } L_M(x_i, \bar{x}_i) = \begin{cases} (\bar{x}_i - x_i)^2, & \text{if } x_i \text{ is continuous} \\ -x_i \log(\bar{x}_i), & \text{if } x_i \text{ is binary} \end{cases}$

The generator is trained to minimize the combined objective with hyperparameter $\alpha > 0$ :

$\min_G \mathcal{L}_G(m, D(\hat{x}, h), b) + \alpha \mathcal{L}_M(\tilde{x}, \bar{x})$
Knowl 5 — Generative Adversarial Imputation Net Training Algorithm
algorithm
GAIN alternates between updating the discriminator $D$ and updating the generator $G$ using stochastic gradient descent on mini-batches of incomplete data samples.
Input: Dataset D = {(x_tilde^(j), m^(j))}_{j=1}^N, batch sizes k_D, k_G, hyperparameter alpha
Output: Trained generator G and discriminator D
while training loss has not converged do
    // (1) Discriminator optimization
    Draw k_D samples {(x_tilde^(j), m^(j))}_{j=1}^(k_D) from D
    Draw k_D independent noise vectors {z^(j)}_{j=1}^(k_D) from Z ~ [0, 1]^d
    Draw k_D random hint masks {b^(j)}_{j=1}^(k_D) from B in {0, 1}^d
    for j = 1 to k_D do
        x_bar^(j) = G(x_tilde^(j), m^(j), (1 - m^(j)) * z^(j))
        x_hat^(j) = m^(j) * x_tilde^(j) + (1 - m^(j)) * x_bar^(j)
        h^(j) = b^(j) * m^(j) + 0.5 * (1 - b^(j))
    Update D using stochastic gradient descent on:
        grad_D -sum_{j=1}^(k_D) L_D(m^(j), D(x_hat^(j), h^(j)), b^(j))
    // (2) Generator optimization
    Draw k_G samples {(x_tilde^(j), m^(j))}_{j=1}^(k_G) from D
    Draw k_G independent noise vectors {z^(j)}_{j=1}^(k_G) from Z ~ [0, 1]^d
    Draw k_G random hint masks {b^(j)}_{j=1}^(k_G) from B in {0, 1}^d
    for j = 1 to k_G do
        x_bar^(j) = G(x_tilde^(j), m^(j), (1 - m^(j)) * z^(j))
        x_hat^(j) = m^(j) * x_tilde^(j) + (1 - m^(j)) * x_bar^(j)
        h^(j) = b^(j) * m^(j) + 0.5 * (1 - b^(j))
    Update G using stochastic gradient descent on:
        grad_G sum_{j=1}^(k_G) [ L_G(m^(j), D(x_hat^(j), h^(j)), b^(j)) + alpha * L_M(x_tilde^(j), x_bar^(j)) ]
end while

Knowl 6 — Imputation Error Across Benchmark Datasets

data/table

The imputation performance of GAIN was evaluated against five baseline methods (MICE, MissForest, Matrix completion, Auto-encoder, and Expectation-Maximization) across five UCI Machine Learning Repository datasets (Breast, Spam, Letter, Credit, and News) under a 20% Missing Completely at Random (MCAR) protocol. Experiments were conducted with 10 repetitions of 5-fold cross-validation, measuring Root Mean Squared Error (RMSE).

Algorithm	Breast	Spam	Letter	Credit	News
GAIN	.0546 $\pm$ .0006	.0513 $\pm$ .0016	.1198 $\pm$ .0005	.1858 $\pm$ .0010	.1441 $\pm$ .0007
MICE	.0646 $\pm$ .0028	.0699 $\pm$ .0010	.1537 $\pm$ .0006	.2585 $\pm$ .0011	.1763 $\pm$ .0007
MissForest	.0608 $\pm$ .0013	.0553 $\pm$ .0013	.1605 $\pm$ .0004	.1976 $\pm$ .0015	.1623 $\pm$ .0120
Matrix	.0946 $\pm$ .0020	.0542 $\pm$ .0006	.1442 $\pm$ .0006	.2602 $\pm$ .0073	.2282 $\pm$ .0005
Auto-encoder	.0697 $\pm$ .0018	.0670 $\pm$ .0030	.1351 $\pm$ .0009	.2388 $\pm$ .0005	.1667 $\pm$ .0014
EM	.0634 $\pm$ .0021	.0712 $\pm$ .0012	.1563 $\pm$ .0012	.2604 $\pm$ .0015	.1912 $\pm$ .0011

GAIN achieved the lowest RMSE across all five benchmark datasets, outperforming both discriminative (MICE, MissForest, Matrix completion) and generative (Auto-encoder, EM) benchmarks.

Knowl 7 — Ablation Study of GAIN Architectural Components

data/table

An ablation study evaluated the relative contribution of each architectural component in GAIN: the adversarial generator loss $\mathcal{L}_G$ , the reconstruction loss on observed features $\mathcal{L}_M$ , and the discriminator hint mechanism $H$ . Performance is measured in terms of mean $\pm$ standard deviation of RMSE and percentage performance gain relative to ablated versions under 20% MCAR missingness across five UCI datasets.

Algorithm	Breast	Spam	Letter	Credit	News
GAIN	.0546 $\pm$ .0006	.0513 $\pm$ .0016	.1198 $\pm$ .0005	.1858 $\pm$ .0010	.1441 $\pm$ .0007
GAIN w/o $\mathcal{L}_G$	.0701 $\pm$ .0021	.0676 $\pm$ .0029	.1344 $\pm$ .0012	.2436 $\pm$ .0012	.1612 $\pm$ .0024
	(22.1%)	(24.1%)	(10.9%)	(23.7%)	(10.6%)
GAIN w/o $\mathcal{L}_M$	.0767 $\pm$ .0015	.0672 $\pm$ .0036	.1586 $\pm$ .0024	.2533 $\pm$ .0048	.2522 $\pm$ .0042
	(28.9%)	(23.7%)	(24.4%)	(26.7%)	(42.9%)
GAIN w/o Hint	.0639 $\pm$ .0018	.0582 $\pm$ .0008	.1249 $\pm$ .0011	.2173 $\pm$ .0052	.1521 $\pm$ .0008
	(14.6%)	(11.9%)	(4.1%)	(14.5%)	(5.3%)
GAIN w/o Hint $\mathcal{L}_M$	.0782 $\pm$ .0016	.0700 $\pm$ .0064	.1671 $\pm$ .0052	.2789 $\pm$ .0071	.2527 $\pm$ .0052
	(30.1%)	(26.7%)	(28.3%)	(33.4%)	(43.0%)

The full GAIN framework improves RMSE by approximately 15% over the standard auto-encoder baseline (GAIN w/o $\mathcal{L}_G$ ), and incorporating the hint mechanism provides an additional improvement of approximately 10% over the unhinted model.

Knowl 8 — Post-Imputation Downstream Classification Performance

data/table

The utility of imputed datasets was evaluated by training a standard downstream classifier (logistic regression) on data completed by each imputation method under 20% MCAR missingness. Performance was assessed using the Area Under the Receiver Operating Characteristic Curve (AUROC) across four binary classification UCI datasets over 10 independent experiments with 5-fold cross-validation.

Algorithm	Breast	Spam	Credit	News
GAIN	.9930 $\pm$ .0073	.9529 $\pm$ .0023	.7527 $\pm$ .0031	.9711 $\pm$ .0027
MICE	.9914 $\pm$ .0034	.9495 $\pm$ .0031	.7427 $\pm$ .0026	.9451 $\pm$ .0037
MissForest	.9860 $\pm$ .0112	.9520 $\pm$ .0061	.7498 $\pm$ .0047	.9597 $\pm$ .0043
Matrix	.9897 $\pm$ .0042	.8639 $\pm$ .0055	.7059 $\pm$ .0150	.8578 $\pm$ .0125
Auto-encoder	.9916 $\pm$ .0059	.9403 $\pm$ .0051	.7485 $\pm$ .0031	.9321 $\pm$ .0058
EM	.9899 $\pm$ .0147	.9217 $\pm$ .0093	.7390 $\pm$ .0079	.8987 $\pm$ .0157

GAIN consistently achieves the highest post-imputation AUROC across all tested datasets. While downstream prediction differences are modest when 80% of data is observed, the superior imputation quality provides a consistent positive margin over all baseline methods.

Knowl 9 — Congeniality of Imputation Models

data/table

Congeniality evaluates how faithfully an imputation model preserves the true underlying feature-label relationship. It is measured by calculating the discrepancy between logistic regression parameters $w$ fit on the complete Credit dataset and parameters $\hat{w}$ fit on the Credit dataset after introducing missing values and imputing them. Discrepancies are measured by mean bias $(\|w - \hat{w}\|_1)$ and mean square error $(\|w - \hat{w}\|_2)$ .

Algorithm	Mean Bias $(\\|w - \hat{w}\\|_1)$	MSE $(\\|w - \hat{w}\\|_2)$
GAIN	0.3163 $\pm$ 0.0887	0.5078 $\pm$ 0.1137
MICE	0.8315 $\pm$ 0.2293	0.9467 $\pm$ 0.2083
MissForest	0.6730 $\pm$ 0.1937	0.7081 $\pm$ 0.1625
Matrix completion	1.5321 $\pm$ 0.0017	1.6660 $\pm$ 0.0015
Auto-encoder	0.3500 $\pm$ 0.1503	0.5608 $\pm$ 0.1697
EM	0.8418 $\pm$ 0.2675	0.9369 $\pm$ 0.2296

GAIN achieves lower mean bias and mean square error in estimated downstream model parameters than all benchmark imputation algorithms, demonstrating performance improvements between 8.9% and 79.2% in preserving the true feature-label relationships.

Knowl 10 — Empirical Robustness to Missing Rates, Sample Size, and Dimensionality
empirical result
Empirical sensitivity evaluations on the Credit dataset demonstrate the robustness of GAIN across varying data characteristics compared to its closest competitors, MissForest and Auto-encoder:
1. Missing Rate Scaling: As the proportion of missing data increases from 10% to 80% (and up to 90% for post-imputation AUROC), GAIN maintains lower RMSE and higher AUROC across the entire range. The AUROC performance advantage of GAIN over MissForest and Auto-encoder widens significantly at higher missing rates (e.g., 60%--90%), because high missingness makes downstream predictions increasingly reliant on the generative quality of the imputed features.
2. Sample Size Scaling: As sample size increases from $0.5 \times 10^4$ to $4.0 \times 10^4$ , the RMSE of GAIN decreases rapidly, and the performance margin over MissForest and Auto-encoder widens due to GAIN's capacity to optimize its neural network parameters with larger training sample sizes.
3. Feature Dimensionality: GAIN maintains stable imputation RMSE across feature dimensions ranging from 5 to 25. In contrast, discriminative models such as MissForest suffer substantial degradation in RMSE when the number of available feature dimensions is small.

Coverage note — Omitted qualitative image error concealment figures on MNIST mentioned in Section 7 as preliminary material relegated to the supplementary materials.

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Citation

MLA

Yoon, J., et al. “GAIN: Missing Data Imputation Using Generative Adversarial Nets”. arXiv, 2018, http://arxiv.org/abs/1806.02920v1.

APA

Yoon, J., Jordon, J., & Schaar, M. van . der . (2018). GAIN: Missing Data Imputation using Generative Adversarial Nets. arXiv. http://arxiv.org/abs/1806.02920v1

Chicago

Yoon, J., J. Jordon, and M. van . der . Schaar. 2018. “GAIN: Missing Data Imputation Using Generative Adversarial Nets”. arXiv. http://arxiv.org/abs/1806.02920v1.

Harvard

Yoon, J., Jordon, J. and Schaar, M. van . der . (2018) “GAIN: Missing Data Imputation using Generative Adversarial Nets”, arXiv [Preprint]. Available at: http://arxiv.org/abs/1806.02920v1.

Vancouver

1. Yoon J, Jordon J, Schaar M van der (2018) GAIN: Missing Data Imputation using Generative Adversarial Nets. arXiv

BibTeX

@article{yoon2018gain,
  title = {GAIN: Missing Data Imputation using Generative Adversarial Nets},
  author = {Yoon, Jinsung and Jordon, James and Schaar, Mihaela van der},
  year = {2018},
  journal = {arXiv},
  url = {http://arxiv.org/abs/1806.02920v1},
  eprint = {1806.02920}
}

Metadata:arXiv

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GAIN: Missing Data Imputation using Generative Adversarial Nets

Abstract

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Table of Contents

Knowls

Knowl 1 — Generative Adversarial Imputation Nets Architecture

Knowl 2 — GAIN Hint Mechanism

Knowl 3 — Theoretical Convergence to the True Conditional Distribution under MCAR

Knowl 4 — GAIN Loss Functions and Objectives

Knowl 5 — Generative Adversarial Imputation Net Training Algorithm

Knowl 6 — Imputation Error Across Benchmark Datasets

Knowl 7 — Ablation Study of GAIN Architectural Components

Knowl 8 — Post-Imputation Downstream Classification Performance

Knowl 9 — Congeniality of Imputation Models

Knowl 10 — Empirical Robustness to Missing Rates, Sample Size, and Dimensionality

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