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Deep generative models through the lens of the manifold hypothesis: A survey and new connections
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 …
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 …
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
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 …
generative modeling, that is, generating new data given a covariate (or control variable). To …
Deep Regression for Repeated Measurements
Nonparametric mean function regression with repeated measurements serves as a
cornerstone for many statistical branches, such as longitudinal/panel/functional data …
cornerstone for many statistical branches, such as longitudinal/panel/functional data …
Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
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 …
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 …
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 …
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 …
adversarial networks (GANs). In particular, we first provide both theoretical and practical …