An estimating equations approach to fitting latent exposure models with longitudinal health outcomes

The analysis of data arising from environmental health studies which collect a large number of measures of exposure can benefit from using latent variable models to summarize exposure information. However, difficulties with estimation of model parameters may arise since existing fitting procedures for linear latent variable models require correctly specified residual variance structures for unbiased estimation of regression parameters quantifying the association between (latent) exposure and health outcomes. We propose an estimating equations approach for latent exposure models with longitudinal health outcomes which is robust to misspecification of the outcome variance. We show that compared to maximum likelihood, the loss of efficiency of the proposed method is relatively small when the model is correctly specified. The proposed equations formalize the ad-hoc regression on factor scores procedure, and generalize regression calibration. We propose two weighting schemes for the equations, and compare their efficiency. We apply this method to a study of the effects of in-utero lead exposure on child development.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS226 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials

Neural message passing on molecular graphs is one of the most promising methods for predicting formation energy and other properties of molecules and materials. In this work we extend the neural message passing model with an edge update network which allows the information exchanged between atoms to depend on the hidden state of the receiving atom. We benchmark the proposed model on three publicly available datasets (QM9, The Materials Project and OQMD) and show that the proposed model yields superior prediction of formation energies and other properties on all three datasets in comparison with the best published results. Furthermore we investigate different methods for constructing the graph used to represent crystalline structures and we find that using a graph based on K-nearest neighbors achieves better prediction accuracy than using maximum distance cutoff or the Voronoi tessellation graph

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Materials property prediction using symmetry-labeled graphs as atomic-position independent descriptors

Computational materials screening studies require fast calculation of the properties of thousands of materials. The calculations are often performed with Density Functional Theory (DFT), but the necessary computer time sets limitations for the investigated material space. Therefore, the development of machine learning models for prediction of DFT calculated properties are currently of interest. A particular challenge for \emph{new} materials is that the atomic positions are generally not known. We present a machine learning model for the prediction of DFT-calculated formation energies based on Voronoi quotient graphs and local symmetry classification without the need for detailed information about atomic positions. The model is implemented as a message passing neural network and tested on the Open Quantum Materials Database (OQMD) and the Materials Project database. The test mean absolute error is 20 meV on the OQMD database and 40 meV on Materials Project Database. The possibilities for prediction in a realistic computational screening setting is investigated on a dataset of 5976 ABSe$_3$ selenides with very limited overlap with the OQMD training set. Pretraining on OQMD and subsequent training on 100 selenides result in a mean absolute error below 0.1 eV for the formation energy of the selenides.Comment: 14 pages including references and 13 figure