# Bayesian Optimization over Bounded Domains with the Beta Product Kernel

arXiv: https://arxiv.org/abs/2506.16316 · HTML: https://mlsanity.com/paper/2506.16316/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1706.00090/) (2017)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [Non-Stationary Spectral Kernels](https://mlsanity.com/paper/1705.08736/) (2017)
- [Approximation beats concentration? An approximation view on inference with smooth radial kernels](https://mlsanity.com/paper/1801.03437/) (2018)
- [On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2008.08757/) (2020)
- [Tight Regret Bounds for Bayesian Optimization in One Dimension](https://mlsanity.com/paper/1805.11792/) (2018)
- [Non-Stationary Spatial Modeling](https://mlsanity.com/paper/2212.08043/) (2022)
- [A Corrected Expected Improvement Acquisition Function Under Noisy Observations](https://mlsanity.com/paper/2310.05166/) (2023)

## Built on by (most cited first, 1 of 1)

- [Distributional sentiment modeling and anomaly detection for consumer complaint assessment](https://mlsanity.com/paper/2609.31653/) (2026)

## Abstract (arXiv)

Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the domain of the function, which may limit their applicability in bounded domains. To address the limitation, we introduce the Beta kernel, a non-stationary kernel induced by a product of Beta distribution density functions. Such a formulation allows our kernel to naturally model functions on bounded domains. We present statistical evidence supporting the hypothesis that the kernel exhibits an exponential eigendecay rate, based on empirical analyses of its spectral properties across different settings. Our experimental results demonstrate the robustness of the Beta kernel in modeling functions with optima located near the faces or vertices of the unit hypercube. The experiments show that our kernel consistently outperforms a wide range of kernels, including the well-known Mat'ern and RBF, in different problems, including synthetic function optimization and the compression of vision and language models.