Jong‐June Jeon

Seunghwan An, Kyungwoo Song, Jong-June Jeon

We present a new supervised learning technique for the Variational AutoEncoder (VAE) that allows it to learn a causally disentangled representation and generate causally disentangled outcomes simultaneously. We call this approach Causally Disentangled Generation (CDG). CDG is a generative model that accurately decodes an output based on a causally disentangled representation. Our research demonstrates that adding supervised regularization to the encoder alone is insufficient for achieving a generative model with CDG, even for a simple task. Therefore, we explore the necessary and sufficient conditions for achieving CDG within a specific model. Additionally, we introduce a universal metric for evaluating the causal disentanglement of a generative model. Empirical results from both image and tabular datasets support our findings.

Seunghwan An, Jong-June Jeon

The Gaussianity assumption has been consistently criticized as a main limitation of the Variational Autoencoder (VAE) despite its efficiency in computational modeling. In this paper, we propose a new approach that expands the model capacity (i.e., expressive power of distributional family) without sacrificing the computational advantages of the VAE framework. Our VAE model's decoder is composed of an infinite mixture of asymmetric Laplace distribution, which possesses general distribution fitting capabilities for continuous variables. Our model is represented by a special form of a nonparametric M-estimator for estimating general quantile functions, and we theoretically establish the relevance between the proposed model and quantile estimation. We apply the proposed model to synthetic data generation, and particularly, our model demonstrates superiority in easily adjusting the level of data privacy.

Sungchul Hong, Yunjin Choi, Jong-June Jeon

Accurate forecasting of river water levels is vital for effectively managing traffic flow and mitigating the risks associated with natural disasters. This task presents challenges due to the intricate factors influencing the flow of a river. Recent advances in machine learning have introduced numerous effective forecasting methods. However, these methods lack interpretability due to their complex structure, resulting in limited reliability. Addressing this issue, this study proposes a deep learning model that quantifies interpretability, with an emphasis on water level forecasting. This model focuses on generating quantitative interpretability measurements, which align with the common knowledge embedded in the input data. This is facilitated by the utilization of a transformer architecture that is purposefully designed with masking, incorporating a multi-layer network that captures spatiotemporal causation. We perform a comparative analysis on the Han River dataset obtained from Seoul, South Korea, from 2016 to 2021. The results illustrate that our approach offers enhanced interpretability consistent with common knowledge, outperforming competing methods and also enhances robustness against distribution shift.

Sungchul Hong, Jong-June Jeon

The optimal allocation of assets has been widely discussed with the theoretical analysis of risk measures, and pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model. The $α$-risk plays a crucial role in deriving a broad class of pessimistic optimal portfolios. However, estimating an optimal portfolio assessed by a pessimistic risk is still challenging due to the absence of a computationally tractable model. In this study, we propose an integral of $α$-risk called the \textit{uniform pessimistic risk} and the computational algorithm to obtain an optimal portfolio based on the risk. Further, we investigate the theoretical properties of the proposed risk in view of three different approaches: multiple quantile regression, the proper scoring rule, and distributionally robust optimization. Real data analysis of three stock datasets (S\&P500, CSI500, KOSPI200) demonstrates the usefulness of the proposed risk and portfolio model.

Seunghwan An, Jong-June Jeon

The assumption of conditional independence among observed variables, primarily used in the Variational Autoencoder (VAE) decoder modeling, has limitations when dealing with high-dimensional datasets or complex correlation structures among observed variables. To address this issue, we introduced the Cramer-Wold distance regularization, which can be computed in a closed-form, to facilitate joint distributional learning for high-dimensional datasets. Additionally, we introduced a two-step learning method to enable flexible prior modeling and improve the alignment between the aggregated posterior and the prior distribution. Furthermore, we provide theoretical distinctions from existing methods within this category. To evaluate the synthetic data generation performance of our proposed approach, we conducted experiments on high-dimensional datasets with multiple categorical variables. Given that many readily available datasets and data science applications involve such datasets, our experiments demonstrate the effectiveness of our proposed methodology.

Seunghwan An, Sungchul Hong, Jong-June Jeon

In the process of training a generative model, it becomes essential to measure the discrepancy between two high-dimensional probability distributions: the generative distribution and the ground-truth distribution of the observed dataset. Recently, there has been growing interest in an approach that involves slicing high-dimensional distributions, with the Cramer-Wold distance emerging as a promising method. However, we have identified that the Cramer-Wold distance primarily focuses on joint distributional learning, whereas understanding marginal distributional patterns is crucial for effective synthetic data generation. In this paper, we introduce a novel measure of dissimilarity, the mixture Cramer-Wold distance. This measure enables us to capture both marginal and joint distributional information simultaneously, as it incorporates a mixture measure with point masses on standard basis vectors. Building upon the mixture Cramer-Wold distance, we propose a new generative model called CWDAE (Cramer-Wold Distributional AutoEncoder), which shows remarkable performance in generating synthetic data when applied to real tabular datasets. Furthermore, our model offers the flexibility to adjust the level of data privacy with ease.

SeungHwan An, Hosik Choi, Jong-June Jeon

We propose a new semi-supervised learning method of Variational AutoEncoder (VAE) which yields a customized and explainable latent space by EXplainable encoder Network (EXoN). Customization means a manual design of latent space layout for specific labeled data. To improve the performance of our VAE in a classification task without the loss of performance as a generative model, we employ a new semi-supervised classification method called SCI (Soft-label Consistency Interpolation). The classification loss and the Kullback-Leibler divergence play a crucial role in constructing explainable latent space. The variability of generated samples from our proposed model depends on a specific subspace, called activated latent subspace. Our numerical results with MNIST and CIFAR-10 datasets show that EXoN produces an explainable latent space and reduces the cost of investigating representation patterns on the latent space.

Jong-June Jeon, Yongdai Kim, Sungho Won et al.

Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional computational time, which becomes severe in high-dimensional cases. As such, we propose an efficient solution path algorithm for a $l_1$ regularized regression with compositional data. The algorithm is then extended to a classification model with compositional predictors. We also compare its computational speed with that of previously developed algorithms and apply the proposed algorithm to analyze human gut microbiome data.