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.
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.
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.
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.
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.
Ground penetrating radar (GPR) based localization has gained significant recognition in robotics due to its ability to detect stable subsurface features, offering advantages in environments where traditional sensors like cameras and LiDAR may struggle. However, existing methods are primarily focused on small-scale place recognition (PR), leaving the challenges of PR in large-scale maps unaddressed. These challenges include the inherent sparsity of underground features and the variability in underground dielectric constants, which complicate robust localization. In this work, we investigate the geometric relationship between GPR echo sequences and underground scenes, leveraging the robustness of directional features to inform our network design. We introduce learnable Gabor filters for the precise extraction of directional responses, coupled with a direction-aware attention mechanism for effective geometric encoding. To further enhance performance, we incorporate a shift-invariant unit and a multi-scale aggregation strategy to better accommodate variations in di-electric constants. Experiments conducted on public datasets demonstrate that our proposed EDENet not only surpasses existing solutions in terms of PR performance but also offers advantages in model size and computational efficiency.
Interference prediction and resource allocation are critical challenges in mission-critical applications where stringent latency and reliability constraints must be met. This paper proposes a novel Gaussian process regression (GPR)-based framework for predictive interference management and resource allocation in future 6G networks. Firstly, the received interference power is modeled as a Gaussian process, enabling both the prediction of future interference values and their corresponding estimation of uncertainty bounds. Differently from conventional machine learning methods that extract patterns from a given set of data without any prior belief, a Gaussian process assigns probability distributions to different functions that possibly represent the data set which can be further updates using Bayes' rule as more data points are observed. For instance, unlike deep neural networks, the GPR model requires only a few sample points to update its prior beliefs in real-time. Furthermore, we propose a proactive resource allocation scheme that dynamically adjusts resources according to predicted interference. The performance of the proposed approach is evaluated against two benchmarks prediction schemes, a moving average-based estimator and the ideal genie-aided estimator. The GPR-based method outperforms the moving average-based estimator and achieves near-optimal performance, closely matching the genie-aided benchmark.
The primary challenge of cross-domain few-shot segmentation (CD-FSS) is the domain disparity between the training and inference phases, which can exist in either the input data or the target classes. Previous models struggle to learn feature representations that generalize to various unknown domains from limited training domain samples. In contrast, the large-scale visual model SAM, pre-trained on tens of millions of images from various domains and classes, possesses excellent generalizability. In this work, we propose a SAM-aware graph prompt reasoning network (GPRN) that fully leverages SAM to guide CD-FSS feature representation learning and improve prediction accuracy. Specifically, we propose a SAM-aware prompt initialization module (SPI) to transform the masks generated by SAM into visual prompts enriched with high-level semantic information. Since SAM tends to divide an object into many sub-regions, this may lead to visual prompts representing the same semantic object having inconsistent or fragmented features. We further propose a graph prompt reasoning (GPR) module that constructs a graph among visual prompts to reason about their interrelationships and enable each visual prompt to aggregate information from similar prompts, thus achieving global semantic consistency. Subsequently, each visual prompt embeds its semantic information into the corresponding mask region to assist in feature representation learning. To refine the segmentation mask during testing, we also design a non-parameter adaptive point selection module (APS) to select representative point prompts from query predictions and feed them back to SAM to refine inaccurate segmentation results. Experiments on four standard CD-FSS datasets demonstrate that our method establishes new state-of-the-art results. Code: https://github.com/CVL-hub/GPRN.
While recent low-light image enhancement (LLIE) methods have made significant advancements, they still face challenges in terms of low visual quality and weak generalization ability when applied to complex scenarios. To address these issues, we propose a semi-supervised method based on latent mean-teacher and Gaussian process, named LMT-GP. We first design a latent mean-teacher framework that integrates both labeled and unlabeled data, as well as their latent vectors, into model training. Meanwhile, we use a mean-teacher-assisted Gaussian process learning strategy to establish a connection between the latent and pseudo-latent vectors obtained from the labeled and unlabeled data. To guide the learning process, we utilize an assisted Gaussian process regression (GPR) loss function. Furthermore, we design a pseudo-label adaptation module (PAM) to ensure the reliability of the network learning. To demonstrate our method's generalization ability and effectiveness, we apply it to multiple LLIE datasets and high-level vision tasks. Experiment results demonstrate that our method achieves high generalization performance and image quality. The code is available at https://github.com/HFUT-CV/LMT-GP.
Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random neural network whose hidden weights and biases are sampled from a probability distribution. Only the final output layer is fit to data. In randomized algorithms like RFR, the hyperparameters that characterize the sampling distribution greatly impact performance, yet are not directly accessible from samples. This makes optimization of hyperparameters via standard (gradient-based) optimization tools inapplicable. Inspired by Bayesian ideas from GPR, this paper introduces a random objective function that is tailored for hyperparameter tuning of vector-valued random features. The objective is minimized with ensemble Kalman inversion (EKI). EKI is a gradient-free particle-based optimizer that is scalable to high-dimensions and robust to randomness in objective functions. A numerical study showcases the new black-box methodology to learn hyperparameter distributions in several problems that are sensitive to the hyperparameter selection: two global sensitivity analyses, integrating a chaotic dynamical system, and solving a Bayesian inverse problem from atmospheric dynamics. The success of the proposed EKI-based algorithm for RFR suggests its potential for automated optimization of hyperparameters arising in other randomized algorithms.
The field of explainable artificial intelligence (XAI) attempts to develop methods that provide insight into how complicated machine learning methods make predictions. Many methods of explanation have focused on the concept of feature attribution, a decomposition of the model's prediction into individual contributions corresponding to each input feature. In this work, we explore the problem of feature attribution in the context of Gaussian process regression (GPR). We take a principled approach to defining attributions under model uncertainty, extending the existing literature. We show that although GPR is a highly flexible and non-parametric approach, we can derive interpretable, closed-form expressions for the feature attributions. When using integrated gradients as an attribution method, we show that the attributions of a GPR model also follow a Gaussian process distribution, which quantifies the uncertainty in attribution arising from uncertainty in the model. We demonstrate, both through theory and experimentation, the versatility and robustness of this approach. We also show that, when applicable, the exact expressions for GPR attributions are both more accurate and less computationally expensive than the approximations currently used in practice. The source code for this project is freely available under MIT license at https://github.com/KurtButler/2024_attributions_paper.
The thesis focuses on developing a data-driven algorithm, based on machine learning, to solve the stochastic alternating current (AC) chance-constrained (CC) Optimal Power Flow (OPF) problem. Although the AC CC-OPF problem has been successful in academic circles, it is highly nonlinear and computationally demanding, which limits its practical impact. The proposed approach aims to address this limitation and demonstrate its empirical efficiency through applications to multiple IEEE test cases. To solve the non-convex and computationally challenging CC AC-OPF problem, the proposed approach relies on a machine learning Gaussian process regression (GPR) model. The full Gaussian process (GP) approach is capable of learning a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The proposed approach uses various approximations for GP-uncertainty propagation. The full GP CC-OPF approach exhibits highly competitive and promising results, outperforming the state-of-the-art sample-based chance constraint approaches. To further improve the robustness and complexity/accuracy trade-off of the full GP CC-OPF, a fast data-driven setup is proposed. This setup relies on the sparse and hybrid Gaussian processes (GP) framework to model the power flow equations with input uncertainty.
Modeling epidemic spread is critical for informing policy decisions aimed at mitigation. Accordingly, in this work we present a new data-driven method based on Gaussian process regression (GPR) to model epidemic spread through the difference on the logarithmic scale of the infected cases. We bound the variance of the predictions made by GPR, which quantifies the impact of epidemic data on the proposed model. Next, we derive a high-probability error bound on the prediction error in terms of the distance between the training points and a testing point, the posterior variance, and the level of change in the spreading process, and we assess how the characteristics of the epidemic spread and infection data influence this error bound. We present examples that use GPR to model and predict epidemic spread by using real-world infection data gathered in the UK during the COVID-19 epidemic. These examples illustrate that, under typical conditions, the prediction for the next twenty days has 94.29% of the noisy data located within the 95% confidence interval, validating these predictions. We further compare the modeling and prediction results with other methods, such as polynomial regression, k-nearest neighbors (KNN) regression, and neural networks, to demonstrate the benefits of leveraging GPR in disease spread modeling.
Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph machine learning, with polynomial filters applied for graph convolutions, where all nodes share the identical filter weights to mine their local contexts. Despite the success, existing spectral GNNs usually fail to deal with complex networks (e.g., WWW) due to such homogeneous spectral filtering setting that ignores the regional heterogeneity as typically seen in real-world networks. To tackle this issue, we propose a novel diverse spectral filtering (DSF) framework, which automatically learns node-specific filter weights to exploit the varying local structure properly. Particularly, the diverse filter weights consist of two components -- A global one shared among all nodes, and a local one that varies along network edges to reflect node difference arising from distinct graph parts -- to balance between local and global information. As such, not only can the global graph characteristics be captured, but also the diverse local patterns can be mined with awareness of different node positions. Interestingly, we formulate a novel optimization problem to assist in learning diverse filters, which also enables us to enhance any spectral GNNs with our DSF framework. We showcase the proposed framework on three state-of-the-arts including GPR-GNN, BernNet, and JacobiConv. Extensive experiments over 10 benchmark datasets demonstrate that our framework can consistently boost model performance by up to 4.92% in node classification tasks, producing diverse filters with enhanced interpretability. Code is available at \url{https://github.com/jingweio/DSF}.
The application of 3D ground-penetrating radar (3D-GPR) for subgrade distress detection has gained widespread popularity. To enhance the efficiency and accuracy of detection, pioneering studies have attempted to adopt automatic detection techniques, particularly deep learning. However, existing works typically rely on traditional 1D A-scan, 2D B-scan or 3D C-scan data of the GPR, resulting in either insufficient spatial information or high computational complexity. To address these challenges, we introduce a novel methodology for the subgrade distress detection task by leveraging the multi-view information from 3D-GPR data. Moreover, we construct a real multi-view image dataset derived from the original 3D-GPR data for the detection task, which provides richer spatial information compared to A-scan and B-scan data, while reducing computational complexity compared to C-scan data. Subsequently, we develop a novel \textbf{M}ulti-\textbf{V}iew \textbf{V}usion and \textbf{D}istillation framework, \textbf{GPR-MVFD}, specifically designed to optimally utilize the multi-view GPR dataset. This framework ingeniously incorporates multi-view distillation and attention-based fusion to facilitate significant feature extraction for subgrade distresses. In addition, a self-adaptive learning mechanism is adopted to stabilize the model training and prevent performance degeneration in each branch. Extensive experiments conducted on this new GPR benchmark demonstrate the effectiveness and efficiency of our proposed framework. Our framework outperforms not only the existing GPR baselines, but also the state-of-the-art methods in the fields of multi-view learning, multi-modal learning, and knowledge distillation. We will release the constructed multi-view GPR dataset with expert-annotated labels and the source codes of the proposed framework.
Numerical simulations of high energy-density experiments require equation of state (EOS) models that relate a material's thermodynamic state variables -- specifically pressure, volume/density, energy, and temperature. EOS models are typically constructed using a semi-empirical parametric methodology, which assumes a physics-informed functional form with many tunable parameters calibrated using experimental/simulation data. Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in the EOS predictions. Model uncertainty is challenging for UQ studies since it requires exploring the space of all possible physically consistent functional forms. Thus, it is often neglected in favor of parametric uncertainty, which is easier to quantify without violating thermodynamic laws. This work presents a data-driven machine learning approach to constructing EOS models that naturally captures model uncertainty while satisfying the necessary thermodynamic consistency and stability constraints. We propose a novel framework based on physics-informed Gaussian process regression (GPR) that automatically captures total uncertainty in the EOS and can be jointly trained on both simulation and experimental data sources. A GPR model for the shock Hugoniot is derived and its uncertainties are quantified using the proposed framework. We apply the proposed model to learn the EOS for the diamond solid state of carbon, using both density functional theory data and experimental shock Hugoniot data to train the model and show that the prediction uncertainty reduces by considering the thermodynamic constraints.
How humans understand and recognize the actions of others is a complex neuroscientific problem that involves a combination of cognitive mechanisms and neural networks. Research has shown that humans have brain areas that recognize actions that process top-down attentional information, such as the temporoparietal association area. Also, humans have brain regions dedicated to understanding the minds of others and analyzing their intentions, such as the medial prefrontal cortex of the temporal lobe. Skeleton-based action recognition creates mappings for the complex connections between the human skeleton movement patterns and behaviors. Although existing studies encoded meaningful node relationships and synthesized action representations for classification with good results, few of them considered incorporating a priori knowledge to aid potential representation learning for better performance. LA-GCN proposes a graph convolution network using large-scale language models (LLM) knowledge assistance. First, the LLM knowledge is mapped into a priori global relationship (GPR) topology and a priori category relationship (CPR) topology between nodes. The GPR guides the generation of new "bone" representations, aiming to emphasize essential node information from the data level. The CPR mapping simulates category prior knowledge in human brain regions, encoded by the PC-AC module and used to add additional supervision-forcing the model to learn class-distinguishable features. In addition, to improve information transfer efficiency in topology modeling, we propose multi-hop attention graph convolution. It aggregates each node's k-order neighbor simultaneously to speed up model convergence. LA-GCN reaches state-of-the-art on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets.
The reconstruction of the 3D permittivity map from ground-penetrating radar (GPR) data is of great importance for mapping subsurface environments and inspecting underground structural integrity. Traditional iterative 3D reconstruction algorithms suffer from strong non-linearity, ill-posedness, and high computational cost. To tackle these issues, a 3D deep learning scheme, called 3DInvNet, is proposed to reconstruct 3D permittivity maps from GPR C-scans. The proposed scheme leverages a prior 3D convolutional neural network with a feature attention mechanism to suppress the noise in the C-scans due to subsurface heterogeneous soil environments. Then a 3D U-shaped encoder-decoder network with multi-scale feature aggregation modules is designed to establish the optimal inverse mapping from the denoised C-scans to 3D permittivity maps. Furthermore, a three-step separate learning strategy is employed to pre-train and fine-tune the networks. The proposed scheme is applied to numerical simulation as well as real measurement data. The quantitative and qualitative results show the network capability, generalizability, and robustness in denoising GPR C-scans and reconstructing 3D permittivity maps of subsurface objects.