Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inference

We use the Iocco et al. (2015) compilation of 2,780 circular velocity measurements to analyze the Milky Way rotation curve. We find that the error bars for individual measurements are non-gaussian, and hence instead derive median statistics binned central circular velocity values and error bars from these data. We use these median statistics central values and error bars to fit the data to simple, few parameter, rotation curve functions. These simple functions are unable to adequately capture the significant small scale spatial structure in these data and so provide poor fits. We introduce and use the Gaussian Processes (GP) method to capture this small scale structure and use it to derive Milky Way rotation curves from the binned median statistics circular velocity data. The GP method rotation curves have significant small-scale spatial structure superimposed on a broad rise to galactocentric radius $R\approx7$ kpc and a decline at larger $R$. We use the GP method median statistics rotation curve to measure the Oort $A$ and $B$ constants and other characteristic rotation curve quantities. We study correlations in the residual circular velocities (relative to the GP method rotation curve). Along with other evidence for azimuthal asymmetry of the Milky Way circular rotation velocity field, we find that larger residual circular velocities seem to favor parts of spiral arms.

The ability to predict wind speeds is very important for the security and stability of wind farms and power system operations. Wind speeds typically vary slowly over time, which makes them difficult to forecast. In this study, a hybrid nonlinear estimation approach combining Gaussian process (GP) and unscented Kalman filter (UKF) is proposed to predict dynamic changes of wind speed and improve forecasting accuracy. The proposed approach can provide both point and interval predictions for wind speed. Firstly, the GP method is established as the nonlinear transition function of a state space model, and the covariance obtained from the GP predictive model is used as the process noise. Secondly, UKF is used to solve the state space model and update the initial prediction of short-term wind speed. The proposed hybrid approach can adjust dynamically in conjunction with the distribution changes. In order to evaluate the performance of the proposed hybrid approach, the persistence model, GP model, autoregressive (AR) model, and AR integrated with Kalman filter (KF) model are used to predict the results for comparison. Taking two wind farms in China and the National Renewable Energy Laboratory (NREL) database as the experimental data, the results show that the proposed hybrid approach is suitable for wind speed predictions, and that it can increase forecasting accuracy.

A major challenge in the development of peptide-based vaccines is finding the right immunogenic element, with efficient and long-lasting immunization effects, from large potential targets encoded by pathogen genomes. Computer models are convenient tools for scanning pathogen genomes to preselect candidate immunogenic peptides for experimental validation. Current methods predict many false positives resulting from a low prevalence of true positives. We develop a test reject method based on the prediction uncertainty estimates determined by Gaussian process regression. This method filters false positives among predicted epitopes from a pathogen genome. The performance of stand-alone Gaussian process regression is compared to other state-of-the-art methods using cross validation on 11 benchmark data sets. The results show that the Gaussian process method has the same accuracy as the top performing algorithms. The combination of Gaussian process regression with the proposed test reject method is used to detect true epitopes from the Vaccinia virus genome. The test rejection increases the prediction accuracy by reducing the number of false positives without sacrificing the method's sensitivity. We show that the Gaussian process in combination with test rejection is an effective method for prediction of T-cell epitopes in large and diverse pathogen genomes, where false positives are of concern.

An important feature of Bayesian statistics is the opportunity to do sequential inference: the posterior distribution obtained after seeing a dataset can be used as prior for a second inference. However, when Monte Carlo sampling methods are used for inference, we only have a set of samples from the posterior distribution. To do sequential inference, we then either have to evaluate the second posterior at only these locations and reweight the samples accordingly, or we can estimate a functional description of the posterior probability distribution from the samples and use that as prior for the second inference. Here, we investigated to what extent we can obtain an accurate joint posterior from two datasets if the inference is done sequentially rather than jointly, under the condition that each inference step is done using Monte Carlo sampling. To test this, we evaluated the accuracy of kernel density estimates, Gaussian mixtures, mixtures of factor analyzers, vine copulas and Gaussian processes in approximating posterior distributions, and then tested whether these approximations can be used in sequential inference. In low dimensionality, Gaussian processes are more accurate, whereas in higher dimensionality Gaussian mixtures, mixtures of factor analyzers or vine copulas perform better. In our test cases of sequential inference, using posterior approximations gives more accurate results than direct sample reweighting, but joint inference is still preferable over sequential inference whenever possible. Since the performance is case-specific, we provide an R package mvdens with a unified interface for the density approximation methods.

Location data are among the most widely used context data in context-aware and ubiquitous computing applications. Many systems with distinct deployment costs and positioning accuracies have been developed over the past decade for indoor positioning. The most useful method is focused on the received signal strength and provides a set of signal transmission access points. However, compiling a manual measuring Received Signal Strength (RSS) fingerprint database involves high costs and thus is impractical in an online prediction environment. The system used in this study relied on the Gaussian process method, which is a nonparametric model that can be characterized completely by using the mean function and the covariance matrix. In addition, the Naive Bayes method was used to verify and simplify the computation of precise predictions. The authors conducted several experiments on simulated and real environments at Tianjin University. The experiments examined distinct data size, different kernels, and accuracy. The results showed that the proposed method not only can retain positioning accuracy but also can save computation time in location predictions.

Optimization and comparison of models for core temperature prediction of mother rabbits using infrared thermography

This paper focuses on water demand forecasting for predictive control of Drinking Water Networks (DWN) in the short term by using Gaussian Process (GP). For the predictive control strategy, system states in a finite horizon are generated by a DWN model and demands are regarded as system disturbances. The goal is to provide a demand estimation within a given confidence interval. For the sake of obtaining a desired forecasting performance, the forecasting process is carried out in two parts: the expected part is forecasted by Double-Seasonal Holt-Winters (DSHW) method and the stochastic part is forecasted by GP method. The mean value of water demand is firstly estimated by DSHW while GP provides estimations within a confidence interval. GP is applied with random inputs to propagate uncertainty at each step. Results of the application of the proposed approach to a real case study based on the Barcelona DWN have shown that the general goal has been successfully reached.

<p>Proteins are the major nitrogen-containing biochemical constituents of plants. Since nitrogen (N) cannot be measured directly using remote sensing data, leaf protein content constitutes a valid proxy for this main limiting plant nutrient. In the past, mainly linear parametric algorithms, such as vegetation indices, have been employed to retrieve this non-state variable from optical reflectance data. Moreover, most studies solely relied on the relationship of chlorophyll content with nitrogen. In contrast, our study presents a hybrid model inversion scheme of a physically-based approach via protein retrieval combined with advanced machine learning regression. The leaf optical properties PROSPECT-PRO model, including the newly calibrated specific absorption coefficients (SAC) of proteins, was coupled with the canopy reflectance model 4SAIL to PROSAIL-PRO. A generic synthetic database of model input parameters with corresponding reflectance was simulated and used for training two different machine learning regression methods: a standard homoscedastic Gaussian Process (GP) and a variational heteroscedastic GP regression that accounts for signal-to-noise correlations. Both GP methods have the interesting feature of providing confidence intervals for the estimates. As part of multiple field campaigns, carried out in the scientific preparation framework of the Environmental Mapping and Analysis Program (EnMAP), spectra of maize and winter wheat were acquired to simulate EnMAP data and plant-organ-specific nitrogen measurements were destructively collected for validation. Both GP models yielded excellent performance in learning the nonlinear relationship between specific protein absorption bands and area-based above-ground N. They also performed similar or even outperformed other nonlinear nonparametric approaches. Physical validation of the estimates against in situ nitrogen measurements from leaves plus stalks yielded a root mean square error (RMSE) of 2.5 g/m². The variational heteroscedastic GP provided a more differentiated pattern of uncertainty with tighter confidence intervals within low-value regimes compared to the standard GP. The inclusion of fruit nitrogen content for validation deteriorated the results of all models, which can be explained by the inability of radiation in the optical domain to penetrate the thick tissues of maize cobs and wheat ears. Following some further validation exercises, we aim to implement GP-based algorithms for global agricultural monitoring of above-ground N derived from future satellite imaging spectroscopy data.</p>

This study applies the Gaussian Analytical Hierarchy Process (Gaussian AHP) to landslide susceptibility mapping and demonstrates its superior methodological rigor and predictive performance relative to the traditional AHP method. Susceptibility maps produced by Gaussian AHP allocated 26.31% of the study area to the very high susceptibility class, outperforming the traditional AHP’s estimated share (23.52%), and achieved a more balanced distribution across all five classes. Validation against a high resolution inventory of 97,742 landslide samples collected during the February 2023 São Sebastião event—divided into 70% training and 30% validation subsets—yielded improved metrics: ROC area under the curve of 0.6360 versus 0.6220; overall accuracy of 0.6364 versus 0.6229, balanced accuracy of 0.6356 versus 0.6221; and sensitivity of 0.3585 versus 0.3116, for the Gaussian and traditional AHP methods respectively. An uncertainty analysis quantified a 56.16% disagreement between the two methods, revealing that Gaussian AHP reduced classification ambiguity in critical classes. A complementary density-based assessment, comparing observed landslide crown points and scar polygons against susceptibility class areas, showed that Gaussian AHP produced a gradual, coherent increase in normalized landslide density from very low to very high susceptibility, whereas traditional AHP displayed sharp breaks in intermediate classes. These findings confirm that Gaussian AHP enhances objectivity, spatial coherence, and operational reliability, better aligning high density landslide clusters with the highest susceptibility zones. By leveraging statistical weighting, Gaussian AHP streamlines data preprocessing and reduces the need for expert calibration, making it well suited for assessments in data rich environments. The statistical weighting procedure facilitates the integration of diverse geospatial datasets and supports robust, reproducible multicriteria decision analysis. Its integration with accurate machine learning-derived land use/land cover data and refined climate data is recommended to further improve predictive accuracy and support proactive landslide risk management strategies. The proposed approach can additionally meet operational purposes, provided that near real-time climate data, updated geospatial databases, and massive computing resources are available.

In nonparametric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates under Gaussian process priors shows that it is possible to achieve optimal or near-optimal posterior contraction rates if the smoothness of the Gaussian process matches that of the target function. Among those priors, Gaussian process with a parametric Matérn covariance function is particularly notable in that its degree of smoothness can be determined by a dedicated smoothness parameter. Ma and Bhadra (2023) recently introduced a new family of covariance functions called the Confluent Hypergeometric (CH) class that simultaneously possess two parameters: one controls the tail index of the polynomially decaying covariance function, and the other parameter controls the degree of mean-squared smoothness analogous to the Matérn class. In this paper, we show that with proper choice of rescaling parameters in the Matérn and CH covariance functions, it is possible to obtain the minimax optimal posterior contraction rate for η-regular functions for nonparametric regression model with fixed design. Unlike the previous results for unrescaled cases, the smoothness parameter of the covariance function need not equal η for achieving the optimal minimax rate, for either rescaled Matérn or rescaled CH covariances, illustrating a key benefit of rescaling. We also consider a fully Bayesian treatment of the rescaling parameters and show the resulting posterior distributions still contract at the minimax-optimal rate. The resultant hierarchical Bayesian procedure is fully adaptive to the unknown true smoothness. The theoretical properties of the rescaled and hierarchical Matérn and CH classes are further verified via extensive simulations and an illustration on a geospatial data set is presented.

We propose a supervised machine learning (ML) approach based on Gaussian process (GP) regression to position users in a distributed massive multiple-input multiple-output (DM-MIMO) system from their uplink received signal strength (RSS). The proposed approach serves as a proof-of-concept that we can localize users by training an ML model with noise-free RSS and using the trained model to estimate the test user locations from their noisy RSS. We consider two GP methods for localization, namely, the conventional GP (CGP) and the numerical approximation GP (NaGP). We find that the CGP provides unrealistically small $2\sigma $ error-bars on the location estimates. Therefore, we derive the true predictive distribution and employ NaGP to obtain realistic $2\sigma $ error-bars on the location estimates. Next, we derive a Bayesian Cramer–Rao lower bound (BCRLB) on the root-mean-squared-error (RMSE) performance of the two GP methods. Numerical studies reveal that: 1) the NaGP indeed provides realistic $2\sigma $ error-bars on the estimated locations; 2) both the CGP and NaGP achieve RMSEs that are close to the BCRLBs; 3) the presence of correlated shadowing improves the RMSE performance; and 4) extrapolation to the zero input noise scenario can significantly improve the RMSE achieved by the NaGP.

Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data, existing methods typically rely on a stationary GP assumption for approximation, and can thus perform poorly when the underlying response surface is nonstationary, that is, it has some regions of rapid change and other regions with little change. Such non-stationarity is, however, ubiquitous in real-world problems, including our motivating application for surrogate modeling of computer experiments. We propose a new Product of Sparse GP (ProSpar-GP) method for scalable GP modeling with massive nonstationary data. The ProSpar-GP makes use of a carefully-constructed product-of-experts formulation of sparse GP experts, where different experts are placed within local regions of non-stationarity. These GP experts are fit via a novel variational inference approach, which capitalizes on mini-batching and GPU acceleration for efficient optimization of inducing points and length-scale parameters for each expert. We further show that the ProSpar-GP is Kolmogorov-consistent, in that its generative distribution defines a valid stochastic process over the prediction space; such a property provides essential stability for variational inference, particularly in the presence of non-stationarity. We then demonstrate the improved performance of the ProSpar-GP over the state-of-the-art, in a suite of numerical experiments and an application for surrogate modeling of a satellite drag simulator. Supplemental materials for this article are available online.

This paper aims to directly denoise option price while adhering to the no–arbitrageconditions. To achieve our goal, we propose the Gaussian Process (GP) method thatentails training the GP on noisy data of option prices as a linear function of the pairof maturity and strike. Utilizing the GP approach not only allows for removing noiseson the option price surface by verifying the no–arbitrage conditions but also is a proba-bilistic approach that allows quantifying the uncertainty on the quantity of interest byconstructing confidence bands around the estimate. The GP further permits forecastingout-of-the-sample prices without needing to compute the risk-neutral density of the op-tion price surface. To investigate the efficiency of GP in removing the noise from optionprices, we tested it on a simulated dataset. The overall MSE between the computedBlack–Scholes prices and the GP denoised is 0.10, and between the Black–Scholes pricesand the noisy prices is 2.21 - a 95.33% noise removal. The curves of the graphs for thedenoised prices are all convex and non–increasing in strikes, upholding the no–arbitrageconditions. To our best knowledge, the challenge of directly denoising option prices hasled to little interest in this area, and our work is the first to undertake this task

Modeling of human motor intention plays an essential role in predictively controlling a robotic system in human-robot interaction tasks. In most machine learning techniques, human motor behavior is modeled as a generic stochastic process. However, the integration of a priori knowledge about underlying system structures can provide insights on otherwise unobservable intrinsic states that yield the superior prediction performance and increased generalization capabilities. We present a novel method for modeling human motor behavior that explicitly includes a neuroscientifically supported model of human motor control, in which the dynamics of the human arm are modeled by a mechanical impedance that tracks a latent desired trajectory. We adopt a Bayesian setting by defining Gaussian process (GP) priors for the impedance elements and the latent desired trajectory. This enables exploitation of a priori human arm impedance knowledge for regression of interaction forces through inference of a latent desired human trajectory. The method is validated using simulated data, with particular focus on effects of GP prior parameterization and intention estimation capabilities. The superior prediction performance is shown with respect to a naive GP prior. Anexperiment with human participants evaluates generalization capabilities and effects of training data sparsity. We derive the correlations of an impedance-based GP model of human motor behavior that exploits a priori knowledge. The model effectively predicts interaction forces by inferring a latent desired human trajectory in previously observed as well as unobserved regions of the input space.

Due to the high specific stiffness and strength, composite shells have been widely used in fuel tanks of launch vehicles. The buckling analysis of composite shells with cutouts based on the finite element (FE) method is too time-consuming. From the point-of-view of model size reduction, a novel Proper Orthogonal Decomposition (POD)-based buckling method is proposed in this paper, which can significantly increase the computational efficiency of buckling analysis. In order to improve the efficiency and effectiveness of prediction and optimization of composite shells with multiple cutouts, the POD method is integrated into an optimization framework that uses Gaussian process (GP) machine learning method. First, the training set used for the machine learning training is generated efficiently by means of the POD method. Then, the obtained set is trained and tested based on the Gaussian process method. The inputs are ply angles of the composite shell and the output is the buckling load of the composite shell containing cutouts. In order to maximize the buckling load of the composite shell against cutouts, the Genetic Algorithm is combined with the trained Gaussian process method to search for the optimal ply angles. Finally, an illustrative example is carried out to demonstrate the effectiveness of the proposed prediction and optimization framework.