Free energy surface reconstruction from umbrella samples using Gaussian process regression

We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost reduction to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant additional computation. A software implementation is made available on www.libatoms.org.

Free energy surface reconstruction from umbrella samples using Gaussian process regression II: Multiple collective variables

We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive allows the concurrent use of histograms and free energy gradients and can easily be extended to include further data. In Part I we review the necessary theory and test the method for one collective variable. We demonstrate improved performance with respect to the weighted histogram analysis method and obtain meaningful error bars without any significant additional computation. In Part II we consider the case of multiple collective variables and compare to a reconstruction using least squares fitting of radial basis functions. We find substantial improvements in the regimes of spatially sparse data or short sampling trajectories. A software implementation is made available on www.libatoms.org.

Automatic construction and natural-language description of nonparametric regression models

Copyright © 2014, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of statistical models to discover a good explanation of a data set, and then produces a detailed report with figures and natural- language text. Our approach treats unknown regression functions non- parametrically using Gaussian processes, which has two important consequences. First, Gaussian processes can model functions in terms of high-level properties (e.g. smoothness, trends, periodicity, changepoints). Taken together with the compositional structure of our language of models this allows us to automatically describe functions in simple terms. Second, the use of flexible nonparametric models and a rich language for composing them in an open-ended manner also results in state- of-the-art extrapolation performance evaluated over 13 real time series data sets from various domains.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

The mean value concept in mono-linear regression of multi-variables and its application to trace studies in geosciences

IEECAS SKLLQG

CO2 Flux Estimation by Different Regression Methods from an Alpine Meadow on the Qinghai-Tibetan Plateau

National Key Research and Development Program [2010CB833500]; National Natural Science Foundation of China [30590381]; Chinese Academy of Sciences [KZCX2-YW-432]

Semisupervised Dimensionality Reduction and Classification Through Virtual Label Regression

Semisupervised dimensionality reduction has been attracting much attention as it not only utilizes both labeled and unlabeled data simultaneously, but also works well in the situation of out-of-sample. This paper proposes an effective approach of semisupervised dimensionality reduction through label propagation and label regression. Different from previous efforts, the new approach propagates the label information from labeled to unlabeled data with a well-designed mechanism of random walks, in which outliers are effectively detected and the obtained virtual labels of unlabeled data can be well encoded in a weighted regression model. These virtual labels are thereafter regressed with a linear model to calculate the projection matrix for dimensionality reduction. By this means, when the manifold or the clustering assumption of data is satisfied, the labels of labeled data can be correctly propagated to the unlabeled data; and thus, the proposed approach utilizes the labeled and the unlabeled data more effectively than previous work. Experimental results are carried out upon several databases, and the advantage of the new approach is well demonstrated.

Selection for variables in quantitative structure-activity/property relationship studies - Comparison between methods of orthogonal descriptors and leaps-and-bounds regression analysis

In this paper, the comparison of orthogonal descriptors and Leaps-and-Bounds regression analysis is performed. The results obtained by using orthogonal descriptors are better than that obtained by using Leaps-and-Bounds regression for the data set of nitrobenzenes used in this study. Leaps-and-Bounds regression can be used effectively for selection of variables in quantitative structure-activity/property relationship(QSAR/QSPR) studies. Consequently, orthogonalisation of descriptors is also a good method for variable selection for studies on QSAR/QSPR.

Studies on the method of leaps and bounds regression

In this paper, we introduce the method of leaps and bounds regression which can be used to select variables quickly and obtain the best regression models. These models contain one variable, two variables, three variables and so on. The results obtained by using leaps and bounds regression were compared with those achieved by using stepwise regression to lead to the conclusion that leaps and bounds regression is an effective method.

Prediction of molar absorptivities of color reagents during their color reactions with cerium using multiple regression analysis and neural network

A quantitative structure-property study has been made on the relationship between molar absorptivities (epsilon) of asymmetrical phosphone bisazo derivatives of chromotropic acid and their color reactions with cerium by multiple regression analysis and neural network. The new topological indices A(x1) - A(x3) suggested in our laboratory and molecular connectivity indices of 43 compounds have been calculated. The results obtained from the two methods are compared. The neural network model is superior to the regression analysis technique and gave a prediction which was sufficiently accurate to estimate the molar absorptivities of color reagents during their color reactions with cerium.

Study on Phenol Compounds Using Multiple Regression and Neural Network Methods

In this paper, the molecular connectivity indices and the electronic charge parameters of forty-eight phenol compounds nave been calculated. and applied for studying the relationship between partition coefficients and structure of phenol compounds. The results demonstrate that the properties of compounds can be described better with selective parameters, and the results obtained by neural network are superior to that by multiplle regression.

Quantitative structure-property relationships for colour reagents and their colour reactions with ytterbium using regression analysis and computational neural networks

In this paper, the new topological indices A(x1)-A(x3) suggested in our laboratory and molecular connectivity indices have been applied to multivariate analysis in structure-property studies. The topological indices of twenty asymmetrical phosphono bisazo derivatives of chromotropic acid have been calculated. The structure-property relationships between colour reagents and their colour reactions with ytterbium have been studied by A(x1)-A(x3) indices and molecular connectivity indices with satisfactory results. Multiple regression analysis and neural networks were employed simultaneously in this study.

QUANTITATIVE STRUCTURE-ACTIVITY-RELATIONSHIPS FOR TOXICITY OF PHENOLS USING REGRESSION-ANALYSIS AND COMPUTATIONAL NEURAL NETWORKS

Quantitative structure-toxicity models were developed that directly link the molecular structures of a et of 50 alkYlated and/or halogenated phenols with their polar narcosis toxicity, expressed as the negative logarithm of the IGC50 (50% growth inhibitor

品牌表现评价反应时与关注特性的关系

The decision making of customers has been a great concern in the field of customer research. Although China has entered the era of brand consumption and development, due to the different understanding of the regarded attributes between companies and customers, the phenomenon of “The awarded products don’t sell well, but the products which sell well can’t get the award.” appears. At the same time there is little research on the relationship between the brand and the customers has been conducted in China now. Traditional research on customer psychology employ questionnaires, depth interview and group discussions as the major methods. In cognitive psychology, the limitation of explicit memory has been revealed by implicit memory; moreover, unconscious cognition and implicit memory can also influence customers' remark of the brand. Therefore, the traditional methods are not accurate enough. Reaction time is an effective way to reveal testing equality, and it can also reveal implicit cognition. Based on the researches intends to investigate the validity of attention attributes in the method of reaction time by questionnaires and time reaction testing of 360 customers in 3 cities, which may, probably, overcomes the limitation of the traditional research methods. The 352 valid samples were analyzed by SPSS. The results showed there was no distinct corresponding relationship between the product attributes and reaction time. The different key attributes from questionnaire importance rating and the shortest reaction time standards were used to regressively analyze the results of customers’ overall rating (such as overall satisfaction,objective quality, recommend intention).The results indicated that the coefficiency of regression of the special attributes chosen from reaction time to overall rating was distinct, while the coefficiency of the special attributes chosen from importance rating to overall rating was not. The main conclusions are: 1. Regarded attributes can be obtained by the reaction time of brand performance rating. 2. Regarded attributes obtained by the reaction time of brand performance rating are more accurate than those by importance rating questionnaires. 3. The brand’s core attributes should includes regarded attributes during the decision making process.