arXiv Statistics ML
Optimal Allocation of Embedding Dimensions under Finite-Sample Constraints
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Concentration bounds on response-based vector embeddings of black-box generative models
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A Multi-stage Constrained Optimization Framework for Data-driven Problems
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Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
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Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization
The paper investigates nonlinear dimensionality reduction for Bayesian optimisation (BO) by transforming high‑dimensional black‑box optimisation problems into a sequence of low‑dimensional latent‑space BO (LSBO) tasks. It extends earlier linear embedding approaches by using variational autoencoders (VAEs), deep metric loss, and adaptive retraining to better capture nonlinear structure, and couples LSBO with sequential domain reduction (SDR‑LSBO) to progressively narrow search domains. Experiments on GPU‑accelerated BoTorch with Matérn‑5/2 Gaussian‑process surrogates show that VAE‑based LSBO outperforms adaptive linear embeddings, and the authors provide a theoretical analysis of latent‑space error versus representation gap under PAC‑Bayes conditions.