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The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

Computational Engineering, Finance, and Science · Computer Science 2026-02-05 Mihaela Chiappetta , Massimo Carraturo , Alexander Raßloff , Markus Kästner , Ferdinando Auricchio

Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with…

Machine Learning · Computer Science 2026-05-22 Sofianos Panagiotis Fotias , Vassilis Gaganis

In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and…

Portfolio Management · Quantitative Finance 2019-03-13 Joan Gonzalvez , Edmond Lezmi , Thierry Roncalli , Jiali Xu

Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function,…

Machine Learning · Statistics 2019-04-03 Felix Berkenkamp , Angela P. Schoellig , Andreas Krause

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Computational Physics · Physics 2025-06-09 Christopher DeGrendele , Dongwook Lee

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…

Machine Learning · Computer Science 2026-05-07 Jesse Schneider , William J. Welch

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

Machine Learning · Statistics 2015-11-25 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…

Machine Learning · Statistics 2017-12-01 Sebastian Urban , Marcus Basalla , Patrick van der Smagt

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that…

Machine Learning · Statistics 2026-03-30 Wenwen Li , Daniel Sanz-Alonso , Ruiyi Yang

A body of work has been done to automate machine learning algorithm to highlight the importance of model choice. Automating the process of choosing the best forecasting model and its corresponding parameters can result to improve a wide…

Machine Learning · Computer Science 2021-09-02 Nadhir Hassen , Irina Rish

Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function requires training a…

Machine Learning · Computer Science 2016-11-15 Tarun Kathuria , Amit Deshpande , Pushmeet Kohli

Bayesian optimisation (BO) is a powerful framework for global optimisation of costly functions, using predictions from Gaussian process models (GPs). In this work, we apply BO to functions that exhibit invariance to a known group of…

Machine Learning · Computer Science 2024-10-23 Theodore Brown , Alexandru Cioba , Ilija Bogunovic

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when…

Computational Engineering, Finance, and Science · Computer Science 2025-02-04 Saurabh Deshpande , Hussein Rappel , Mark Hobbs , Stéphane P. A. Bordas , Jakub Lengiewicz

Gaussian process (GP) models have been used in a wide range of battery applications, in which different kernels were manually selected with considerable expertise. However, to capture complex relationships in the ever-growing amount of…

Systems and Control · Electrical Eng. & Systems 2025-05-06 Huang Zhang , Xixi Liu , Faisal Altaf , Torsten Wik

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

Machine Learning · Computer Science 2024-07-18 Hwanwoo Kim , Daniel Sanz-Alonso

While modern machine learning has transformed numerous application domains, its growing computational demands increasingly constrain scalability and efficiency, particularly on embedded and resource-limited platforms. In practice, neural…

Machine Learning · Computer Science 2025-10-30 Bernhard Klein

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In…

Machine Learning · Computer Science 2021-06-30 Shuhan Zhang , Fan Yang , Changhao Yan , Dian Zhou , Xuan Zeng

In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…

Machine Learning · Computer Science 2024-06-05 Jangseop Park , Namwoo Kang

Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand…

Machine Learning · Computer Science 2023-09-15 Michael Y. Li , Erin Grant , Thomas L. Griffiths

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Machine Learning · Statistics 2022-11-07 Vidhi Lalchand , Wessel P. Bruinsma , David R. Burt , Carl E. Rasmussen