We consider the problem of personalizing audio to maximize user experience. Briefly, we aim to find a filter $h^*$, which applied to any music or speech, will maximize the user's satisfaction. This is a black-box optimization problem since the user's satisfaction function is unknown. Substantive work has been done on this topic where the key idea is to play audio samples to the user, each shaped by a different filter $h_i$, and query the user for their satisfaction scores $f(h_i)$. A family of ``surrogate" functions is then designed to fit these scores and the optimization method gradually refines these functions to arrive at the filter $\hat{h}^*$ that maximizes satisfaction. In certain applications, we observe that a second type of querying is possible where users can tell us the individual elements $h^*[j]$ of the optimal filter $h^*$. Consider an analogy from cooking where the goal is to cook a recipe that maximizes user satisfaction. A user can be asked to score various cooked recipes (e.g., tofu fried rice) or to score individual ingredients (say, salt, sugar, rice, chicken, etc.). Given a budget of $B$ queries, where a query can be of either type, our goal is to find the recipe that will maximize this user's satisfaction. Our proposal builds on Sparse Gaussian Process Regression (GPR) and shows how a hybrid approach can outperform any one type of querying. Our results are validated through simulations and real world experiments, where volunteers gave feedback on music/speech audio and were able to achieve high satisfaction levels. We believe this idea of hybrid querying opens new problems in black-box optimization and solutions can benefit other applications beyond audio personalization.
This paper develops a Bayesian Generalised Pareto Regression (GPR) model to forecast extreme losses in Indian equity markets, with a focus on the Nifty 50 index. Extreme negative returns, though rare, can cause significant financial disruption, and accurate modelling of such events is essential for effective risk management. Traditional Generalised Pareto Distribution (GPD) models often ignore market conditions; in contrast, our framework links the scale parameter to covariates using a log-linear function, allowing tail risk to respond dynamically to market volatility. We examine four prior choices for Bayesian regularisation of regression coefficients: Cauchy, Lasso (Laplace), Ridge (Gaussian), and Zellner's g-prior. Simulation results suggest that the Cauchy prior delivers the best trade-off between predictive accuracy and model simplicity, achieving the lowest RMSE, AIC, and BIC values. Empirically, we apply the model to large negative returns (exceeding 5%) in the Nifty 50 index. Volatility measures from the Nifty 50, S&P 500, and gold are used as covariates to capture both domestic and global risk drivers. Our findings show that tail risk increases significantly with higher market volatility. In particular, both S&P 500 and gold volatilities contribute meaningfully to crash prediction, highlighting global spillover and flight-to-safety effects. The proposed GPR model offers a robust and interpretable approach for tail risk forecasting in emerging markets. It improves upon traditional EVT-based models by incorporating real-time financial indicators, making it useful for practitioners, policymakers, and financial regulators concerned with systemic risk and stress testing.
Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we propose a knowledge score for predictions from Gaussian process regression (GPR) models that quantifies the extent to which observing data have reduced our uncertainty about a prediction. The knowledge score is interpretable and naturally bounded between 0 and 1. We demonstrate in several experiments that the knowledge score can anticipate when predictions from a GPR model are accurate, and that this anticipation improves performance in tasks such as anomaly detection, extrapolation, and missing data imputation. Source code for this project is available online at https://github.com/KurtButler/GP-knowledge.
This study proposes a high-performance dual-parameter full waveform inversion framework (FWI) for ground-penetrating radar (GPR), accelerated through the hybrid compilation of CUDA kernel functions and PyTorch. The method leverages the computational efficiency of GPU programming while preserving the flexibility and usability of Python-based deep learning frameworks. By integrating customized CUDA kernels into PyTorch's automatic differentiation mechanism, the framework enables accurate and efficient inversion of both dielectric permittivity and electrical conductivity. Experimental evaluations on synthetic data and real wavefield data demonstrate that the proposed method achieves dual-parameter FWI for GPR data while maintaining high accuracy. Moreover, the framework is flexible and extensible, supporting optional regularization strategies such as total variation and multi-scale inversion. These features make the proposed approach a practical and scalable framework for rapid GPR-based subsurface imaging in applications including civil engineering, environmental monitoring, and geophysical exploration.
One of the key challenges that Reinforcement Learning (RL) faces is its limited capability to adapt to a change of data distribution caused by uncertainties. This challenge arises especially in RL systems using deep neural networks as decision makers or policies, which are prone to overfitting after prolonged training on fixed environments. To address this challenge, this paper proposes Gaussian Process Diffusion Policy (GPDP), a new algorithm that integrates diffusion models and Gaussian Process Regression (GPR) to represent the policy. GPR guides diffusion models to generate actions that maximize learned Q-function, resembling the policy improvement in RL. Furthermore, the kernel-based nature of GPR enhances the policy's exploration efficiency under distribution shifts at test time, increasing the chance of discovering new behaviors and mitigating overfitting. Simulation results on the Walker2d benchmark show that our approach outperforms state-of-the-art algorithms under distribution shift condition by achieving around 67.74% to 123.18% improvement in the RL's objective function while maintaining comparable performance under normal conditions.
Ground Penetrating Radar (GPR) is a widely used Non-Destructive Testing (NDT) technique for subsurface exploration, particularly in infrastructure inspection and maintenance. However, conventional interpretation methods are often limited by noise sensitivity and a lack of structural awareness. This study presents a novel framework that enhances the detection of underground utilities, especially pipelines, by integrating shape-aware topological features derived from B-scan GPR images using Topological Data Analysis (TDA), with the spatial detection capabilities of the YOLOv5 deep neural network (DNN). We propose a novel shape-aware topological representation that amplifies structural features in the input data, thereby improving the model's responsiveness to the geometrical features of buried objects. To address the scarcity of annotated real-world data, we employ a Sim2Real strategy that generates diverse and realistic synthetic datasets, effectively bridging the gap between simulated and real-world domains. Experimental results demonstrate significant improvements in mean Average Precision (mAP), validating the robustness and efficacy of our approach. This approach underscores the potential of TDA-enhanced learning in achieving reliable, real-time subsurface object detection, with broad applications in urban planning, safety inspection, and infrastructure management.
We introduce a fast and flexible Machine Learning (ML) framework for pricing derivative products whose valuation depends on volatility surfaces. By parameterizing volatility surfaces with the 5-parameter stochastic volatility inspired (SVI) model augmented by a one-factor term structure adjustment, we first generate numerous volatility surfaces over realistic ranges for these parameters. From these synthetic market scenarios, we then compute high-accuracy valuations using conventional methodologies for two representative products: the fair strike of a variance swap and the price and Greeks of an American put. We then train the Gaussian Process Regressor (GPR) to learn the nonlinear mapping from the input risk factors, which are the volatility surface parameters, strike and interest rate, to the valuation outputs. Once trained, We use the GPR to perform out-of-sample valuations and compare the results against valuations using conventional methodologies. Our ML model achieves very accurate results of $0.5\%$ relative error for the fair strike of variance swap and $1.7\% \sim 3.5\%$ relative error for American put prices and first-order Greeks. More importantly, after training, the model computes valuations almost instantly, yielding a three to four orders of magnitude speedup over Crank-Nicolson finite-difference method for American puts, enabling real-time risk analytics, dynamic hedging and large-scale scenario analysis. Our approach is general and can be extended to other path-dependent derivative products with early-exercise features, paving the way for hybrid quantitative engines for modern financial systems.
This work proposes an empirical air to ground (A2G) propagation model specifically designed for cellular connected unmanned aerial vehicles (UAVs). An in depth aerial drive test was carried out within an operating Long Term Evolution (LTE) network, gathering thorough measurements of key network parameters. Rigid preprocessing and statistical analysis of these data produced a strong foundation for training a new triple layer machine learning (ML) model. The proposed ML framework employs a systematic hierarchical approach. Accordingly, the first two layers, Stepwise Linear Regression (STW) and Ensemble of Bagged Trees (EBT) generate predictions independently, meanwhile, the third layer, Gaussian Process Regression (GPR), explicitly acts as an aggregation layer, refining these predictions to accurately estimate Key Performance Indicators (KPIs) such as Reference Signal Received Power (RSRP), Reference Signal Received Quality (RSRQ), Received Signal Strength (RSSI), and Path Loss (PL). Compared to traditional single layer ML or computationally intensive ray tracing approaches, the proposed triple layer ML framework significantly improves predictive accuracy and robustness, achieving around 99 percent accuracy in training and above 90 percent in testing while utilizing a minimal but effective feature set log transformed 3D and 2D propagation distances, azimuth, and elevation angles. This streamlined feature selection substantially reduces computing complexity, thus enhancing scalability across various operating environments. The proposed frameworks practicality and efficacy for real world deployment in UAV integrated cellular networks are further demonstrated by comparative analyses, which underscore its substantial improvement.
Adaptive sampling based on Gaussian process regression (GPR) has already been applied with considerable success to generate boundary test scenarios for multi-UAV systems (MUS). One of the key techniques in such researches is leveraging the accurate prediction of the MUS performance through GPR in different test scenarios. Due to the potential correlations among the multiple MUS performance metrics, current researches commonly utilize a multi-output GPR (MOGPR) to model the multiple performance metrics simultaneously. This approach can achieve a more accurate prediction, rather than modeling each metric individually. However, MOGPR still suffers from negative transfer. When the feature of one output variable is incorrectly learned by another, the models training process will be negatively affected, leading to a decline in prediction performance. To solve this problem, this paper proposes a novel adaptive regularization approach into the conventional MOGPR training process. Unlike existing regularization approaches for mitigating negative transfer in MOGPR, our method penalizes the inconsistencies among output-specific characteristic parameters using adaptively adjustable regularization weights. This mechanism helps each set of output parameters avoid local optima. Consequently, it yields simultaneous improvements in predictive accuracy across all outputs. Finally, we validate our approach on a numerical case and on a boundary test scenario generation case for a MUS multi-objectives search task.
This paper investigates the application of machine learning regression algorithms Kernel Ridge Regression (KRR), Huber Regressor (HR), and Gaussian Process Regression (GPR) for predicting sound power levels of gensets, offering significant value for marketing and sales teams during the early bidding process. When engine sizes and genset enclosure dimensions are tentative, and measured noise data is unavailable, these algorithms enable reliable noise level estimation for unbuilt gensets. The study utilizes high fidelity datasets from over 100 experiments conducted at Cummins Acoustics Technology Center (ATC) in a hemi-anechoic chamber, adhering to ISO 3744 standards. By using readily available information from the bidding and initial design stages, KRR predicts sound power with an average accuracy of within 5 dBA. While HR and GPR show slightly higher prediction errors, all models effectively capture the overall noise trends across various genset configurations. These findings present a promising method for early-stage noise estimation in genset design.
The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally activated events within the harmonic approximation of transition state theory. When combined directly with electronic structure calculations, the number of energy and atomic force evaluations needed for convergence is a primary issue. Here, we describe an efficient implementation of Gaussian process regression (GPR) acceleration of the minimum mode following method where a dimer is used to estimate the lowest eigenmode of the Hessian. A surrogate energy surface is constructed and updated after each electronic structure calculation. The method is applied to a test set of 500 molecular reactions previously generated by Hermez and coworkers [J. Chem. Theory Comput. 18, 6974 (2022)]. An order of magnitude reduction in the number of electronic structure calculations needed to reach the saddle point configurations is obtained by using the GPR compared to the dimer method. Despite the wide range in stiffness of the molecular degrees of freedom, the calculations are carried out using Cartesian coordinates and are found to require similar number of electronic structure calculations as an elaborate internal coordinate method implemented in the Sella software package. The present implementation of the GPR surrogate model in C++ is efficient enough for the wall time of the saddle point searches to be reduced in 3 out of 4 cases even though the calculations are carried out at a low Hartree-Fock level.
The composite current source (CCS) model has been adopted as an advanced timing model that represents the current behavior of cells for improved accuracy and better capability than traditional non-linear delay models (NLDM) to model complex dynamic effects and interactions under advanced process nodes. However, the high accuracy requirement, large amount of data and extensive simulation cost pose severe challenges to CCS characterization. To address these challenges, we introduce a novel Gaussian Process Regression(GPR) model with active learning(AL) to establish the characterization framework efficiently and accurately. Our approach significantly outperforms conventional commercial tools as well as learning based approaches by achieving an average absolute error of 2.05 ps and a relative error of 2.27% for current waveform of 57 cells under 9 process, voltage, temperature (PVT) corners with TSMC 22nm process. Additionally, our model drastically reduces the runtime to 27% and the storage by up to 19.5x compared with that required by commercial tools.
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is large or when the underlying function contains multi-scale features that are difficult to represent by a stationary kernel. To address the former, training of GPs with large-scale data is often performed through inducing point approximations (also known as sparse GP regression (GPR)), where the size of the covariance matrices in GPR is reduced considerably through a greedy search on the data set. To aid the latter, deep GPs have gained traction as hierarchical models that resolve multi-scale features by combining multiple GPs. Posterior inference in deep GPs requires a sampling or, more usual, a variational approximation. Variational approximations lead to large-scale stochastic, non-convex optimisation problems and the resulting approximation tends to represent uncertainty incorrectly. In this work, we combine variational learning with MCMC to develop a particle-based expectation-maximisation method to simultaneously find inducing points within the large-scale data (variationally) and accurately train the GPs (sampling-based). The result is a highly efficient and accurate methodology for deep GP training on large-scale data. We test our method on standard benchmark problems.
Urban roads and infrastructure, vital to city operations, face growing threats from subsurface anomalies like cracks and cavities. Ground Penetrating Radar (GPR) effectively visualizes underground conditions employing electromagnetic (EM) waves; however, accurate anomaly detection via GPR remains challenging due to limited labeled data, varying subsurface conditions, and indistinct target boundaries. Although visually image-like, GPR data fundamentally represent EM waves, with variations within and between waves critical for identifying anomalies. Addressing these, we propose the Reservoir-enhanced Segment Anything Model (Res-SAM), an innovative framework exploiting both visual discernibility and wave-changing properties of GPR data. Res-SAM initially identifies apparent candidate anomaly regions given minimal prompts, and further refines them by analyzing anomaly-induced changing information within and between EM waves in local GPR data, enabling precise and complete anomaly region extraction and category determination. Real-world experiments demonstrate that Res-SAM achieves high detection accuracy (>85%) and outperforms state-of-the-art. Notably, Res-SAM requires only minimal accessible non-target data, avoids intensive training, and incorporates simple human interaction to enhance reliability. Our research provides a scalable, resource-efficient solution for rapid subsurface anomaly detection across diverse environments, improving urban safety monitoring while reducing manual effort and computational cost.
Obtaining accurate transition state (TS) energies is a bottleneck in computational screening of complex materials and reaction networks due to the high cost of TS search methods and first-principles methods such as density functional theory (DFT). Here we propose a machine learning (ML) model for predicting TS energies based on Gaussian process regression with the Wasserstein Weisfeiler-Lehman graph kernel (WWL-GPR). Applying the model to predict adsorption and TS energies for the reverse water-gas shift (RWGS) reaction on single-atom alloy (SAA) catalysts, we show that it can significantly improve the accuracy compared to traditional approaches based on scaling relations or ML models without a graph representation. Further benefitting from the low cost of model training, we train an ensemble of WWL-GPR models to obtain uncertainties through subsampling of the training data and show how these uncertainties propagate to turnover frequency (TOF) predictions through the construction of an ensemble of microkinetic models. Comparing the errors in model-based vs DFT-based TOF predictions, we show that the WWL-GPR model reduces errors by almost an order of magnitude compared to scaling relations. This demonstrates the critical impact of accurate energy predictions on catalytic activity estimation. Finally, we apply our model to screen new materials, identifying promising catalysts for RWGS. This work highlights the power of combining advanced ML techniques with DFT and microkinetic modeling for screening catalysts for complex reactions like RWGS, providing a robust framework for future catalyst design.
Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability density functions (pdfs) but require accurate prior models and many likelihood evaluations. Dimensionality-reduction methods, such as principal component analysis (PCA), can help define the prior and train surrogate models that efficiently approximate costly forward solvers. However, for problems like full waveform inversion, the complex input/output relations often cannot be captured well by surrogate models trained only on prior samples, leading to biased results. Including samples from high-posterior-probability regions can improve accuracy, but these regions are hard to identify in advance. We propose an iterative method that progressively refines the surrogate model. Starting with low-frequency data, we train an initial surrogate and perform an MCMC inversion. The resulting posterior samples are then used to retrain the surrogate, allowing us to expand the frequency bandwidth in the next inversion step. Repeating this process reduces model errors and improves the surrogate's accuracy over the relevant input domain. Ultimately, we obtain a highly accurate surrogate across the full bandwidth, enabling a final MCMC inversion. Numerical results from 2D synthetic crosshole Ground Penetrating Radar (GPR) examples show that our method outperforms ray-based approaches and those relying solely on prior sampling. The overall computational cost is reduced by about two orders of magnitude compared to full finite-difference time-domain modeling.
Reproducibility and reliability remain pressing challenges for generative AI systems whose behavior can drift with each model update or prompt revision. We introduce GPR-bench, a lightweight, extensible benchmark that operationalizes regression testing for general purpose use cases. GPR-bench couples an open, bilingual (English and Japanese) dataset covering eight task categories (e.g., text generation, code generation, and information retrieval) and 10 scenarios in each task categories (80 total test cases for each language) with an automated evaluation pipeline that employs "LLM-as-a-Judge" scoring of correctness and conciseness. Experiments across three recent model versions - gpt-4o-mini, o3-mini, and o4-mini - and two prompt configurations (default versus concise-writing instruction) reveal heterogeneous quality. Our results show that newer models generally improve correctness, but the differences are modest and not statistically significant, suggesting that GPR-bench may not be sufficiently challenging to differentiate between recent model versions. In contrast, the concise-writing instruction significantly enhances conciseness (+12.37 pp, Mann-Whitney U test: p < 0.001, effect size r = 0.2995) with minimal degradations on accuracy (-1.7 pp), demonstrating the effectiveness of prompt engineering. Released under the MIT License, GPR- bench lowers the barrier to initiating reproducibility monitoring and provides a foundation for community-driven extensions, while also raising important considerations about benchmark design for rapidly evolving language models.
The Koopman Operator Theory opens the door for application of rich linear systems theory for computationally efficient modeling and optimal control of nonlinear systems by providing a globally linear representation for complex nonlinear systems. However, methodologies for Koopman Operator discovery struggle with the dependency on the set of selected observable functions and meaningful uncertainty quantification. The primary objective of this work is to leverage Gaussian process regression (GPR) to develop a probabilistic Koopman linear model while removing the need for heuristic observable specification. In this work, we present inverted Gaussian process optimization based Koopman Operator learning (iGPK), an automatic differentiation-based approach to simultaneously learn the observable-operator combination. We show that the proposed iGPK method is robust to observation noise in the training data, while also providing good uncertainty quantification, such that the predicted distribution consistently encapsulates the ground truth, even for noisy training data.
We investigate the extreme return connectedness between the food, fossil energy, and clean energy markets using the quantile connectedness approach, which combines the traditional spillover index with quantile regression. Our results show that return connectedness at the tails (57.91% for the right tail and 61.47% for the left tail) is significantly higher than at the median (23.02%). Further-more, dynamic analysis reveals that connectedness fluctuates over time, with notable increases during extreme events. Among these markets, fossil energy market consistently acts as the net receiver, while clean energy market primarily serves as the net transmitter. Additionally, we use linear and nonlinear ARDL models to examine the role of external uncertainties on return connectedness. We find that climate policy uncertainty (CPU), geopolitical risk (GPR), and the COVID-19pandemic significantly impact median connectedness, while economic policy uncertainty (EPU),GPR, and trade policy uncertainty (TPU) are crucial drivers of extreme connectedness. Our findings provide valuable insights for investors and policymakers on risk spillover effects between food and energy markets under both normal and extreme market conditions.
In this work, we propose the use of Ground Penetrating Radar (GPR) for rover localization on Mars. Precise pose estimation is an important task for mobile robots exploring planetary surfaces, as they operate in GPS-denied environments. Although visual odometry provides accurate localization, it is computationally expensive and can fail in dim or high-contrast lighting. Wheel encoders can also provide odometry estimation, but are prone to slipping on the sandy terrain encountered on Mars. Although traditionally a scientific surveying sensor, GPR has been used on Earth for terrain classification and localization through subsurface feature matching. The Perseverance rover and the upcoming ExoMars rover have GPR sensors already equipped to aid in the search of water and mineral resources. We propose to leverage GPR to aid in Mars rover localization. Specifically, we develop a novel GPR-based deep learning model that predicts 1D relative pose translation. We fuse our GPR pose prediction method with inertial and wheel encoder data in a filtering framework to output rover localization. We perform experiments in a Mars analog environment and demonstrate that our GPR-based displacement predictions both outperform wheel encoders and improve multi-modal filtering estimates in high-slip environments. Lastly, we present the first dataset aimed at GPR-based localization in Mars analog environments, which will be made publicly available upon publication.