On the relationship between online Gaussian process regression and kernel least mean squares algorithms

The interactive development of economic globalization, informatization, marketization, and urbanization has reshaped the urban commercial landscape and society, and poses new requirements for the business environment. New commerce forms that are based on information technology and electronic payment and integrate online and offline forms are growing rapidly in China. However, the relationship between new commerce forms and the business environment has not received sufficient academic attention. Using 29 major cities in China, this paper constructs a new business index system consisting of the following six sub-indexes: the characteristic hotels index, the Starbucks index, the Freshhema index, the concept bookstores index, the smart convenience stores index, and the healthcare and medical examination index. The entropy coupled with the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method was used for quantitative evaluation of urban new business vitality. We found that the Freshhema index and smart convenient store index are the two most important evaluation factors. The relationship between the new business index and the business environment was examined through multiple linear regression (MLR) and Gaussian process regression (GPR) analysis. We found that the MLR is not a valid model, and instead, the nonlinear GPR model has good explanatory power for this relationship. The results show that human capital has a more important effect than the economic development level on business vitality. The rise and development of new commercial forms depend on the innovation and optimization of the business environment.

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The Variational Gaussian Approximation Revisited

Neural Computation ◽

10.1162/neco.2008.08-07-592 ◽

2009 ◽

Vol 21 (3) ◽

pp. 786-792 ◽

Cited By ~ 52

Author(s):

Manfred Opper ◽

Cédric Archambeau

Keyword(s):

Machine Learning ◽

Gaussian Process ◽

Learning Community ◽

Gaussian Approximation ◽

Good Reason ◽

Random Variables ◽

Gaussian Process Regression ◽

Variational Approximation ◽

Posterior Distributions ◽

The Relationship

The variational approximation of posterior distributions by multivariate gaussians has been much less popular in the machine learning community compared to the corresponding approximation by factorizing distributions. This is for a good reason: the gaussian approximation is in general plagued by an [Formula: see text] number of variational parameters to be optimized, N being the number of random variables. In this letter, we discuss the relationship between the Laplace and the variational approximation, and we show that for models with gaussian priors and factorizing likelihoods, the number of variational parameters is actually [Formula: see text]. The approach is applied to gaussian process regression with nongaussian likelihoods.

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Leaf Anthocyanin Content Retrieval with Partial Least Squares and Gaussian Process Regression from Spectral Reflectance Data

Sensors ◽

10.3390/s21093078 ◽

2021 ◽

Vol 21 (9) ◽

pp. 3078

Author(s):

Yingying Li ◽

Jingfeng Huang

Keyword(s):

Gaussian Process ◽

Least Squares ◽

Partial Least Squares ◽

Gaussian Process Regression ◽

Research Field ◽

Anthocyanin Content ◽

Least Squares Regression ◽

Content Retrieval ◽

First Time ◽

The Relationship

Leaf pigment content retrieval is an essential research field in remote sensing. However, retrieval studies on anthocyanins are quite rare compared to those on chlorophylls and carotenoids. Given the critical physiological significance of anthocyanins, this situation should be improved. In this study, using the reflectance, partial least squares regression (PLSR) and Gaussian process regression (GPR) were sought to retrieve the leaf anthocyanin content. To our knowledge, this is the first time that PLSR and GPR have been employed in such studies. The results showed that, based on the logarithmic transformation of the reflectance (log(1/R)) with 564 and 705 nm, the GPR model performed the best (R2/RMSE (nmol/cm2): 0.93/2.18 in the calibration, and 0.93/2.20 in the validation) of all the investigated methods. The PLSR model involved four wavelengths and achieved relatively low accuracy (R2/RMSE (nmol/cm2): 0.87/2.88 in calibration, and 0.88/2.89 in validation). GPR apparently outperformed PLSR. The reason was likely that the non-linear property made GPR more effective than the linear PLSR in characterizing the relationship for the absorbance vs. content of anthocyanins. For GPR, selected wavelengths around the green peak and red edge region (one from each) were promising to build simple and accurate two-wavelength models with R2 > 0.90.

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Using Gaussian Process Regression to Integrate the Transition Structure Factor Curve for the Many-Body Correlation Energy

10.26226/morressier.5fa409874d4e91fe5c54b97a ◽

2020 ◽

Author(s):

Laura Weiler

Keyword(s):

Gaussian Process ◽

Structure Factor ◽

Correlation Energy ◽

Gaussian Process Regression ◽

Many Body ◽

Transition Structure ◽

The Many ◽

Structure Factor Curve ◽

Body Correlation

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Exchange Spin Coupling from Gaussian Process Regression

10.26434/chemrxiv.12589541.v3 ◽

2020 ◽

Author(s):

Marc Philipp Bahlke ◽

Natnael Mogos ◽

Jonny Proppe ◽

Carmen Herrmann

Keyword(s):

Machine Learning ◽

Gaussian Process ◽

Gaussian Process Regression ◽

Molecular Magnets ◽

Molecular Structures ◽

Spin Coupling ◽

Structure Property ◽

Data Set ◽

Uncertainty Estimates

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.

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

10.26434/chemrxiv.6406505.v2 ◽

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>

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