Statistical Inference, Generative Modeling & Applications
통계추론 및 생성모형 연구실 | Department of Mathematical Sciences, UNIST

I am Young-geun Kim, a tenure-track Assistant Professor in the Department of Mathematical Sciences at UNIST. Before joining UNIST, I was the Hannan Endowed Visiting Assistant Professor in the Department of Statistics and Probability at Michigan State University (2024-2026) and a Postdoctoral Researcher in the Departments of Biostatistics and Psychiatry at Columbia University (2021-2024). I received my Ph.D. in Statistics from Seoul National University (2021).

What is Statistical Generative Modeling?

High-dimensional data, across videos, languages, and biomedical records, can be governed by low-dimensional hidden factors (representations). SIGMA Lab combines Statistical Inference and Generative Modeling with Applications via deep learning to understand complex data with mathematical guarantees.

Our Mission: We build theoretically grounded Generative AI. We welcome students interested in either math/statistics theory or biomedical & video data!

(a) Statistical Inference: Learning pθ*(x) via statistical distance D(pθ, pdata)

(b) Representation Learning: Extracting interpretable latent dynamics from mHealth data

Research Fields

1. Theory: Probabilistic Modeling & Statistical Distances

Keywords: Deep Generative Models · Statistical Distance · Identifiability

We design latent variable models and optimal distance metrics with provable mathematical guarantees:

p_θ(x) = ∫_Z p_θ(x | z) p(z) dz,    θ^* = arg min_θ D(p_θ, p_data)

• Statistical Distances: Conditional Wasserstein generators capturing high-dimensional data geometry without mode collapse.
• Identifiable Generative Models: Mathematical conditions ensuring unique recovery of true hidden factors (z), even under missing data.

(a) Latent Variable Model: Latent (Z1, Z2) generates (X1, X2, X3)

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(b) Realization of (a): 2D (Z1, Z2) (left) & 3D (X1, X2, X3) (right)

Key Related Research

• Kim, Y.-G., Lee, K., and Paik, M.C. (2023). Conditional Wasserstein generator. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI). [Paper] [Code]
• Kim, Y.-G., Liu, Y., and Wei, X. (2023). Covariate-informed representation learning to prevent posterior collapse of iVAE. AISTATS. [Paper] [Code]
• Kim, Y.-G., Kwon, Y., Chang, H., and Paik, M.C. (2020). Lipschitz continuous autoencoders in application to anomaly detection. AISTATS. [Paper] [Code]

2. Convergence: Medical Neuroimaging & Video AI

Keywords: Multi-modal Data · Neuroimaging · Video · Healthcare

Generative models deepen our understanding of data mechanisms, e.g., by disentangling shared (j) and modality-specific (i_m) factors given covariates c:

p_θ(x_1:M | c) = ∫_{J × I1 × ⋯ × IM} (∏_m=1^M p_θm(x_m | j, i_m)) p_θ(j, i_1:M | c) dj di_1:M

• Brain Imaging (MRI): Discovering autism and OCD biomarkers from incomplete multi-site cohorts (ABCD, ENIGMA) under block-missingness.
• Video & Image Synthesis: Predicting future frames and multi-view images via conditional Wasserstein and geodesic models.
• Digital Health & RL: Modeling mobile mood dynamics (EMA) and optimizing personalized clinical treatments via reinforcement learning.

Incomplete Multi-modal Data: Site-specific block-missingness

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Covariate-Informed Disentanglement: Separating shared & subset-specific factors

Key Related Research

• Kim, Y.-G. et al. (2024). Explaining deep learning-based representations of resting state functional connectivity data: focusing on interpreting nonlinear patterns in autism spectrum disorder. Frontiers in Psychiatry.
• Kim, S., Kim, Y.-G., and Wang, Y. (2024). Temporal generative models for learning heterogeneous group dynamics of ecological momentary data. Biometrics. [Paper]
• Kim, Y.-G., Hu, M.-C., Nunes, E.V., Luo, S.X., and Liu, Y. (2025). Optimizing contingency management with reinforcement learning. IEEE ICHI (Long Presentation).

Related Courses & Open Materials

• MTH345: Deep Generative Models: A Statistical Perspective (UNIST) [Course Material & Pilot Lecture Videos]
• MTH344: Mathematical Statistics (UNIST) [Course Material]
• STT997: Advanced Topics in Statistics (MSU) [Course Material]
• Related UNIST Courses: MTH342 (Probability), AI518 (Deep Generative Models)

Recent News

• [Fall 2026] Presenting invited talks on Multi-Modal Representation Learning with Partially Pairwise Observations at CFE-CMStatistics 2026 (Berlin, Germany) and the KMS Fall Conference (Gwangju).
• [09-01-2026] Launched a newly developed undergraduate course at UNIST: MTH345: Deep Generative Models: A Statistical Perspective.
• [Summer 2026] Presented invited talks at ICSA-China 2026 (Shenzhen, China) and the KSS Summer Conference (Gyeongju).
• [03-12-2026] Our proposal for new course development (Deep Generative Models: A Statistical Perspective) has been accepted by UNIST (KRW 20,000,000, 04/2026-07/2026, Role: Principal Developer).
• [02-01-2026] Joined the Department of Mathematical Sciences at UNIST as a tenure-track Assistant Professor.
• [08-06-2025] Our grant proposal (Statistical Understanding of Adversarial Training in Neural Networks, USD 180,000, 08/2025-07/2028) has been funded by the U.S. National Science Foundation (NSF DMS) (Role: Co-PI & Int’l Consultant; PI: Dr. Yue Xing, MSU).
• [03-27-2025] Paper accepted at MIDL 2025: A Novel GNN Framework Integrating Neuroimaging and Behavioral Information to Understand Adolescent Psychiatric Disorders.
• [03-12-2025] Paper accepted at IEEE ICHI 2025 (selected as a long presentation): Optimizing Contingency Management with Reinforcement Learning.