Deep generative models through the lens of the manifold hypothesis: A survey and new connections

G Loaiza-Ganem, BL Ross, R Hosseinzadeh… - arxiv preprint arxiv …, 2024 - arxiv.org
In recent years there has been increased interest in understanding the interplay between
deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses …

Understanding scaling laws with statistical and approximation theory for transformer neural networks on intrinsically low-dimensional data

A Havrilla, W Liao - arxiv preprint arxiv:2411.06646, 2024 - arxiv.org
When training deep neural networks, a model's generalization error is often observed to
follow a power scaling law dependent both on the model size and the data size. Perhaps the …

Conditional Diffusion Models are Minimax-Optimal and Manifold-Adaptive for Conditional Distribution Estimation

R Tang, L Lin, Y Yang - arxiv preprint arxiv:2409.20124, 2024 - arxiv.org
We consider a class of conditional forward-backward diffusion models for conditional
generative modeling, that is, generating new data given a covariate (or control variable). To …

Deep Regression for Repeated Measurements

S Yan, F Yao, H Zhou - Journal of the American Statistical …, 2025 - Taylor & Francis
Nonparametric mean function regression with repeated measurements serves as a
cornerstone for many statistical branches, such as longitudinal/panel/functional data …

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

H Liu, Z Zhang, W Liao, H Schaeffer - arxiv preprint arxiv:2410.00357, 2024 - arxiv.org
Neural scaling laws play a pivotal role in the performance of deep neural networks and have
been observed in a wide range of tasks. However, a complete theoretical framework for …

A statistical analysis of Wasserstein autoencoders for intrinsically low-dimensional data

S Chakraborty, PL Bartlett - arxiv preprint arxiv:2402.15710, 2024 - arxiv.org
Variational Autoencoders (VAEs) have gained significant popularity among researchers as a
powerful tool for understanding unknown distributions based on limited samples. This …

Deep Generative Demand Learning for Newsvendor and Pricing

S Gong, H Liu, X Zhang - arxiv preprint arxiv:2411.08631, 2024 - arxiv.org
We consider data-driven inventory and pricing decisions in the feature-based newsvendor
problem, where demand is influenced by both price and contextual features and is modeled …

Generative adversarial learning with optimal input dimension and its adaptive generator architecture

Z Tan, L Zhou, H Lin - arxiv preprint arxiv:2405.03723, 2024 - arxiv.org
We investigate the impact of the input dimension on the generalization error in generative
adversarial networks (GANs). In particular, we first provide both theoretical and practical …