We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need to gauge away unobservable invariances in the definition of a distance between a signal and its estimator, and the consequences this implies for the statistical mechanics treatment of such models, taking as a motivating example the extensive rank matrix factorization problem.
Symmetry-Aware Bayesian Optimization via Max Kernels
School of Computer and Communication Sciences, École polytechnique fédérale de Lausanne (EPFL)（计算机与通信科学学院，瑞士联邦理工学院（EPFL））；Institute of Mathematics, École polytechnique fédérale de Lausanne (EPFL)（数学学院，瑞士联邦理工学院（EPFL））
针对贝叶斯优化中利用对称性但 max kernel 非半正定的问题，提出其 PSD 投影核，在不增加计算复杂度的情况下显著降低合成与真实基准上的遗憾。
Modelling time-order effects in haptic perception with a Bayesian dynamical framework
Instituto Balseiro, Centro Atómico Bariloche（巴尔塞罗研究所，巴里洛切原子中心）；Department of Applications of Physics and Biology to Health Sciences, Centro Atómico Bariloche（巴里洛切原子中心应用物理与生物健康科学系）；Department of Translational Research, Centro Atómico Bariloche（巴里洛切原子中心转化研究系）；Institute for Intelligent Interactive Systems, Department of Computer Science, ETH Zürich（苏黎世联邦理工学院计算机学院智能交互系统研究所）
Prediction Markets as Bayesian Inverse Problems: Uncertainty Quantification, Identifiability, and Information Gain from Price-Volume Histories under Latent Types
Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces
St. Petersburg State University（圣彼得堡国立大学）；University of Oxford（牛津大学）；Neapolis University Pafos（帕福斯尼阿波利斯大学）；University of Cambridge（剑桥大学）；Cornell University（康奈尔大学）；ETH Zürich（苏黎世联邦理工学院）
Bayesian Inference of Minimally Complex Models with Interactions of Arbitrary Order
University of Amsterdam（阿姆斯特丹大学）；University of Pennsylvania（宾夕法尼亚大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜勒·萨拉姆国际理论物理中心）
Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact case
St. Petersburg State University and University of Oxford（圣彼得堡国立大学和牛津大学）；St. Petersburg State University and Neapolis University Pafos（圣彼得堡国立大学和纳皮奥斯大学帕福斯）；University of Cambridge and Cornell University（剑桥大学和康奈尔大学）；ETH Zürich（苏黎世联邦理工学院）
Provable and scalable quantum Gaussian processes for quantum learning
Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）；Department of Computer Science（计算机科学系）；Institute of Applied Mathematics, University of British Columbia（不列颠哥伦比亚大学应用数学学院）；Stewart Blusson Quantum Matter Institute（斯图尔特·布卢森量子物质研究所）；Information Sciences, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室信息科学部）；Donostia International Physics Center（多诺西亚国际物理中心）；Department of Applied Physics, Gipuzkoa School of Engineering, University of the Basque Country (UPV/EHU)（巴斯克国家大学（UPV/EHU）吉普兹科亚工程学院应用物理系）；Biophysics, Doctoral School, Universidad Autónoma de Madrid（马德里自治大学生物物理系博士学院）；Department for Quantum Information（量子信息部）；Computation at Kepler (QUICK), Johannes Kepler University（开普勒大学量子信息与计算部（QUICK））；Quantum Science Center, Oak Ridge, TN 37931, USA（橡树岭量子科学中心）
