scholarly journals Development of a non-parametric Gaussian process model in the three-dimensional equilibrium reconstruction code V3FIT

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Eric C. Howell ◽  
J. D. Hanson
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Gaussian Process Regression ◽  
Equilibrium Reconstruction ◽  
Equilibrium Profiles ◽  
Mean Function ◽  
Best Fit ◽  
Non Parametric

A non-parametric Gaussian process regression model is developed in the three-dimensional equilibrium reconstruction code V3FIT. A Gaussian process is a normal distribution of functions that is uniquely defined by specifying a mean function and covariance kernel function. Gaussian process regression assumes that an unknown profile belongs to a particular Gaussian process and uses Bayesian analysis to select the function the give the best fit to measured data. The implementation in V3FIT uses a hybrid representation where Gaussian processes are used to infer some of the equilibrium profiles and standard parametric techniques are used to infer the remaining profiles. The implementation of the Gaussian process is tested using both synthetic data and experimental data from multiple machines.

SAMPL6 Challenge Results from pKa Predictions Based on a General Gaussian Process Model

2018 ◽  
Author(s):  
Caitlin C. Bannan ◽  
David Mobley ◽  
A. Geoff Skillman
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Molecular Graph ◽  
Gaussian Process Regression ◽  
Ionization State ◽  
Training Set ◽  
Physiochemical Properties ◽  
Quantile Plots ◽  
Physical And Chemical ◽  
Good Agreement

<div>A variety of fields would benefit from accurate pK<sub>a</sub> predictions, especially drug design due to the affect a change in ionization state can have on a molecules physiochemical properties.</div><div>Participants in the recent SAMPL6 blind challenge were asked to submit predictions for microscopic and macroscopic pK<sub>a</sub>s of 24 drug like small molecules.</div><div>We recently built a general model for predicting pK<sub>a</sub>s using a Gaussian process regression trained using physical and chemical features of each ionizable group.</div><div>Our pipeline takes a molecular graph and uses the OpenEye Toolkits to calculate features describing the removal of a proton.</div><div>These features are fed into a Scikit-learn Gaussian process to predict microscopic pK<sub>a</sub>s which are then used to analytically determine macroscopic pK<sub>a</sub>s.</div><div>Our Gaussian process is trained on a set of 2,700 macroscopic pK<sub>a</sub>s from monoprotic and select diprotic molecules.</div><div>Here, we share our results for microscopic and macroscopic predictions in the SAMPL6 challenge.</div><div>Overall, we ranked in the middle of the pack compared to other participants, but our fairly good agreement with experiment is still promising considering the challenge molecules are chemically diverse and often polyprotic while our training set is predominately monoprotic.</div><div>Of particular importance to us when building this model was to include an uncertainty estimate based on the chemistry of the molecule that would reflect the likely accuracy of our prediction. </div><div>Our model reports large uncertainties for the molecules that appear to have chemistry outside our domain of applicability, along with good agreement in quantile-quantile plots, indicating it can predict its own accuracy.</div><div>The challenge highlighted a variety of means to improve our model, including adding more polyprotic molecules to our training set and more carefully considering what functional groups we do or do not identify as ionizable. </div>

scholarly journals Gaussian Process Autoregression for Joint Angle Prediction Based on sEMG Signals

2021 ◽  
Vol 9 ◽  
Author(s):  
Jie Liang ◽  
Zhengyi Shi ◽  
Feifei Zhu ◽  
Wenxin Chen ◽  
Xin Chen ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Probabilistic Model ◽  
Autoregressive Model ◽  
Process Model ◽  
Joint Angle ◽  
Gaussian Process Model ◽  
The Mean ◽  
Test Scenarios ◽  
Semg Signals ◽  
Non Parametric

There is uncertainty in the neuromusculoskeletal system, and deterministic models cannot describe this significant presence of uncertainty, affecting the accuracy of model predictions. In this paper, a knee joint angle prediction model based on surface electromyography (sEMG) signals is proposed. To address the instability of EMG signals and the uncertainty of the neuromusculoskeletal system, a non-parametric probabilistic model is developed using a Gaussian process model combined with the physiological properties of muscle activation. Since the neuromusculoskeletal system is a dynamic system, the Gaussian process model is further combined with a non-linear autoregressive with eXogenous inputs (NARX) model to create a Gaussian process autoregression model. In this paper, the normalized root mean square error (NRMSE) and the correlation coefficient (CC) are compared between the joint angle prediction results of the Gaussian process autoregressive model prediction and the actual joint angle under three test scenarios: speed-dependent, multi-speed and speed-independent. The mean of NRMSE and the mean of CC for all test scenarios in the healthy subjects dataset and the hemiplegic patients dataset outperform the results of the Gaussian process model, with significant differences (p &lt; 0.05 and p &lt; 0.05, p &lt; 0.05 and p &lt; 0.05). From the perspective of uncertainty, a non-parametric probabilistic model for joint angle prediction is established by using Gaussian process autoregressive model to achieve accurate prediction of human movement.

scholarly journals Vision-Based Satellite Recognition and Pose Estimation Using Gaussian Process Regression

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Haopeng Zhang ◽  
Cong Zhang ◽  
Zhiguo Jiang ◽  
Yuan Yao ◽  
Gang Meng
Keyword(s):  
Gaussian Process ◽  
Pose Estimation ◽  
Gaussian Process Regression ◽  
Regression Function ◽  
Mean Value ◽  
Training Data ◽  
Simulated Image ◽  
Lighting Conditions ◽  
Mean Function ◽  
Imaging Sensors

In this paper, we address the problem of vision-based satellite recognition and pose estimation, which is to recognize the satellite from multiviews and estimate the relative poses using imaging sensors. We propose a vision-based method to solve these two problems using Gaussian process regression (GPR). Assuming that the regression function mapping from the image (or feature) of the target satellite to its category or pose follows a Gaussian process (GP) properly parameterized by a mean function and a covariance function, the predictive equations can be easily obtained by a maximum-likelihood approach when training data are given. These explicit formulations can not only offer the category or estimated pose by the mean value of the predicted output but also give its uncertainty by the variance which makes the predicted result convincing and applicable in practice. Besides, we also introduce a manifold constraint to the output of the GPR model to improve its performance for satellite pose estimation. Extensive experiments are performed on two simulated image datasets containing satellite images of 1D and 2D pose variations, as well as different noises and lighting conditions. Experimental results validate the effectiveness and robustness of our approach.

scholarly journals An Efficient Radio Map Updating Algorithm based on K-Means and Gaussian Process Regression

2018 ◽  
Vol 71 (5) ◽  
pp. 1055-1068 ◽  
Author(s):  
Jianli Zhao ◽  
Xiang Gao ◽  
Xin Wang ◽  
Chunxiu Li ◽  
Min Song ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Gaussian Process ◽  
Predictive Model ◽  
Gaussian Process Regression ◽  
Environment Changes ◽  
Model Based ◽  
Map Updating ◽  
Mean Function ◽  
Radio Map ◽  
Indoor Localisation

Fingerprint-based indoor localisation suffers from influences such as fingerprint pre-collection, environment changes and expending a lot of manpower and time to update the radio map. To solve the problem, we propose an efficient radio map updating algorithm based on K-Means and Gaussian Process Regression (KMGPR). The algorithm builds a Gaussian Process Regression (GPR) predictive model based on a Gaussian mean function and realises the update of the radio map using K-Means. We have conducted experiments to evaluate the performance of the proposed algorithm and results show that GPR using the Gaussian mean function improves localisation accuracy by about 13·76% compared with other functions and KMGPR can reduce the computational complexity by about 7% to 20% with no obvious effects on accuracy.

scholarly journals Variational Inference for Sparse Gaussian Process Modulated Hawkes Process

2020 ◽  
Vol 34 (04) ◽  
pp. 6803-6810
Author(s):  
Rui Zhang ◽  
Christian Walder ◽  
Marian-Andrei Rizoiu
Keyword(s):  
Model Selection ◽  
Gaussian Process ◽  
Linear Time ◽  
Expectation Maximization Algorithm ◽  
Synthetic Data ◽  
Variational Inference ◽  
Hawkes Process ◽  
Prediction Confidence ◽  
Inference Schema ◽  
Non Parametric

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the non-parametric Bayesian HP has been proposed. However, the inference of such models suffers from unscalability or slow convergence. In this paper, we aim to solve both problems. Specifically, first, we propose a new non-parametric Bayesian HP in which the triggering kernel is modeled as a squared sparse Gaussian process. Then, we propose a novel variational inference schema for model optimization. We employ the branching structure of the HP so that maximization of evidence lower bound (ELBO) is tractable by the expectation-maximization algorithm. We propose a tighter ELBO which improves the fitting performance. Further, we accelerate the novel variational inference schema to linear time complexity by leveraging the stationarity of the triggering kernel. Different from prior acceleration methods, ours enjoys higher efficiency. Finally, we exploit synthetic data and two large social media datasets to evaluate our method. We show that our approach outperforms state-of-the-art non-parametric frequentist and Bayesian methods. We validate the efficiency of our accelerated variational inference schema and practical utility of our tighter ELBO for model selection. We observe that the tighter ELBO exceeds the common one in model selection.

scholarly journals Similarities and differences in spatial and non-spatial cognitive maps

2020 ◽  
Author(s):  
Charley M. Wu ◽  
Eric Schulz ◽  
Mona M. Garvert ◽  
Björn Meder ◽  
Nicolas W. Schuck
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Gaussian Process Regression ◽  
Cognitive Maps ◽  
Spatial Task ◽  
Cognitive Map ◽  
Learning Curves ◽  
Conceptual Domain ◽  
Subject Design ◽  
Spatial Domains

AbstractLearning and generalization in spatial domains is often thought to rely on a “cognitive map”, representing relationships between spatial locations. Recent research suggests that this same neural machinery is also recruited for reasoning about more abstract, conceptual forms of knowledge. Yet, to what extent do spatial and conceptual reasoning share common computational principles, and what are the implications for behavior? Using a within-subject design we studied how participants used spatial or conceptual distances to generalize and search for correlated rewards in successive multi-armed bandit tasks. Participant behavior indicated sensitivity to both spatial and conceptual distance, and was best captured using a Bayesian model of generalization that formalized distance-dependent generalization and uncertainty-guided exploration as a Gaussian Process regression with a radial basis function kernel. The same Gaussian Process model best captured human search decisions and judgments in both domains, and could simulate realistic learning curves, where we found equivalent levels of generalization in spatial and conceptual tasks. At the same time, we also find characteristic differences between domains. Relative to the spatial domain, participants showed reduced levels of uncertainty-directed exploration and increased levels of random exploration in the conceptual domain. Participants also displayed a one-directional transfer effect, where experience in the spatial task boosted performance in the conceptual task, but not vice versa. While confidence judgments indicated that participants were sensitive to the uncertainty of their knowledge in both tasks, they did not or could not leverage their estimates of uncertainty to guide exploration in the conceptual task. These results support the notion that value-guided learning and generalization recruit cognitive-map dependent computational mechanisms in spatial and conceptual domains. Yet both behavioral and model-based analyses suggest domain specific differences in how these representations map onto actions.Author summaryThere is a resurgence of interest in “cognitive maps” based on recent evidence that the hippocampal-entorhinal system encodes both spatial and non-spatial relational information, with far-reaching implications for human behavior. Yet little is known about the commonalities and differences in the computational principles underlying human learning and decision making in spatial and non-spatial domains. We use a within-subject design to examine how humans search for either spatially or conceptually correlated rewards. Using a Bayesian learning model, we find evidence for the same computational mechanisms of generalization across domains. While participants were sensitive to expected rewards and uncertainty in both tasks, how they leveraged this knowledge to guide exploration was different: participants displayed less uncertainty-directed and more random exploration in the conceptual domain. Moreover, experience with the spatial task improved conceptual performance, but not vice versa. These results provide important insights about the degree of overlap between spatial and conceptual cognition.

scholarly journals SAMPL6 Challenge Results from pKa Predictions Based on a General Gaussian Process Model

2018 ◽  
Author(s):  
Caitlin C. Bannan ◽  
David L. Mobley ◽  
Geoff Skillman
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Molecular Graph ◽  
Gaussian Process Regression ◽  
Ionization State ◽  
Training Set ◽  
Physiochemical Properties ◽  
Quantile Plots ◽  
Physical And Chemical ◽  
Good Agreement

<div>A variety of fields would benefit from accurate pK<sub>a</sub> predictions, especially drug design due to the affect a change in ionization state can have on a molecules physiochemical properties.</div><div>Participants in the recent SAMPL6 blind challenge were asked to submit predictions for microscopic and macroscopic pK<sub>a</sub>s of 24 drug like small molecules.</div><div>We recently built a general model for predicting pK<sub>a</sub>s using a Gaussian process regression trained using physical and chemical features of each ionizable group.</div><div>Our pipeline takes a molecular graph and uses the OpenEye Toolkits to calculate features describing the removal of a proton.</div><div>These features are fed into a Scikit-learn Gaussian process to predict microscopic pK<sub>a</sub>s which are then used to analytically determine macroscopic pK<sub>a</sub>s.</div><div>Our Gaussian process is trained on a set of 2,700 macroscopic pK<sub>a</sub>s from monoprotic and select diprotic molecules.</div><div>Here, we share our results for microscopic and macroscopic predictions in the SAMPL6 challenge.</div><div>Overall, we ranked in the middle of the pack compared to other participants, but our fairly good agreement with experiment is still promising considering the challenge molecules are chemically diverse and often polyprotic while our training set is predominately monoprotic.</div><div>Of particular importance to us when building this model was to include an uncertainty estimate based on the chemistry of the molecule that would reflect the likely accuracy of our prediction. </div><div>Our model reports large uncertainties for the molecules that appear to have chemistry outside our domain of applicability, along with good agreement in quantile-quantile plots, indicating it can predict its own accuracy.</div><div>The challenge highlighted a variety of means to improve our model, including adding more polyprotic molecules to our training set and more carefully considering what functional groups we do or do not identify as ionizable. </div>

scholarly journals Minimum Mode Saddle Point Searches Using Gaussian Process Regression with Inverse-Distance Covariance Function

2019 ◽  
Author(s):  
Olli-Pekka Koistinen ◽  
Vilhjálmur Ásgeirsson ◽  
Aki Vehtari ◽  
Hannes Jónsson
Keyword(s):  
Saddle Point ◽  
Gaussian Process ◽  
Process Model ◽  
Energy Surface ◽  
Saddle Points ◽  
Gaussian Process Regression ◽  
Dissociative Adsorption ◽  
Initial Guess ◽  
Initial State ◽  
Model Based

The minimum mode following method can be used to find saddle points on an energy surface by following a direction guided by the lowest curvature mode. Such calculations are often started close to a minimum on the energy surface to find out which transitions can occur from an initial state of the system, but it is also common to start from the vicinity of a first order saddle point making use of an initial guess based on intuition or more approximate calculations. In systems where accurate evaluations of the energy and its gradient are computationally intensive, it is important to exploit the information of the previous evaluations to enhance the performance. Here, we show that the number of evaluations required for convergence to the saddle point can be significantly reduced by making use of an approximate energy surface obtained by a Gaussian process model based on inverse inter-atomic distances, evaluating accurate energy and gradient at the saddle point of the approximate surface and then correcting the model based on the new information. The performance of the method is tested with start points chosen randomly in the vicinity of saddle points for dissociative adsorption of an H2 molecule on the Cu(110) Surface and three gas phase chemical reactions.<br>

scholarly journals Improving the mean and uncertainty of ultraviolet multi-filter rotating shadowband radiometer in situ calibration factors: utilizing Gaussian process regression with a new method to estimate dynamic input uncertainty

2019 ◽  
Vol 12 (2) ◽  
pp. 935-953 ◽  
Author(s):  
Maosi Chen ◽  
Zhibin Sun ◽  
John M. Davis ◽  
Yan-An Liu ◽  
Chelsea A. Corr ◽  
...  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Average Method ◽  
Moving Average ◽  
Gaussian Process Regression ◽  
Input Uncertainty ◽  
In Situ Calibration ◽  
The Mean ◽  
Mean Function

Abstract. To recover the actual responsivity for the Ultraviolet Multi-Filter Rotating Shadowband Radiometer (UV-MFRSR), the complex (e.g., unstable, noisy, and with gaps) time series of its in situ calibration factors (V0) need to be smoothed. Many smoothing techniques require accurate input uncertainty of the time series. A new method is proposed to estimate the dynamic input uncertainty by examining overall variation and subgroup means within a moving time window. Using this calculated dynamic input uncertainty within Gaussian process (GP) regression provides the mean and uncertainty functions of the time series. This proposed GP solution was first applied to a synthetic signal and showed significantly smaller RMSEs than a Gaussian process regression performed with constant values of input uncertainty and the mean function. GP was then applied to three UV-MFRSR V0 time series at three ground sites. The method appropriately accounted for variation in slopes, noises, and gaps at all sites. The validation results at the three test sites (i.e., HI02 at Mauna Loa, Hawaii; IL02 at Bondville, Illinois; and OK02 at Billings, Oklahoma) demonstrated that the agreement among aerosol optical depths (AODs) at the 368 nm channel calculated using V0 determined by the GP mean function and the equivalent AERONET AODs were consistently better than those calculated using V0 from standard techniques (e.g., moving average). For example, the average AOD biases of the GP method (0.0036 and 0.0032) are much lower than those of the moving average method (0.0119 and 0.0119) at IL02 and OK02, respectively. The GP method's absolute differences between UV-MFRSR and AERONET AOD values are approximately 4.5 %, 21.6 %, and 16.0 % lower than those of the moving average method at HI02, IL02, and OK02, respectively. The improved accuracy of in situ UVMRP V0 values suggests the GP solution is a robust technique for accurate analysis of complex time series and may be applicable to other fields.

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