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Chaudhary, Neha, and Priti Dimri. "LATENT FINGERPRINT IMAGE ENHANCEMENT BASED ON OPTIMIZED BENT IDENTITY BASED CONVOLUTIONAL NEURAL NETWORK." Indian Journal of Computer Science and Engineering 12, no. 5 (October 20, 2021): 1477–93. http://dx.doi.org/10.21817/indjcse/2021/v12i5/211205124.
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Fingerprints are unique biometric systems (BSs) in which none of the human possesses similar fingerprint structures. It is one of the most significant biometric processes used in the identification of criminals. Latent fingerprints or latents are generated mainly by the finger sweat or oil deposits which is left by the suspects unintentionally. The impressions of latents are blurred or smudgy in nature and not viewed by naked eye. These fingerprints are of low quality, corrupted by noise, degraded by technological factors and exhibit minor details. Latents display consistent structural info when observed as an image. Image Enhancement is necessary in latents, to transform the latent (noisy) image into fine-quality (enhanced) image. In this work, a new image enhancement approach named BI-CNN (Bent Identity-Convolution Neural Network) with Spatial Pyramid Max Pooling (SPMP) model optimized using TSOA (Tunicate Swarm Optimization Algorithm) is presented to produce an enhanced latent at the output. This procedure involves the integration of ROI (Region Of Interest) Estimation, Anisotropic Gaussian Filter (AGF) based Pre-filtering, Fingerprint alignment using Sobel Filter, Intrinsic Feature patch extraction using Optimized BI-CNN, GAT (Graph Attention) network based Similarity Estimation followed by image reconstruction and feedback module. The implementation tool used in this work is PYTHON platform. The proposed optimized BI-CNN framework tested on dual public datasets namely IIITD-latent finger print and IIITD-MOLF have shown enhanced outcomes. Thus, the IIITD -latent fingerprint database obtained 83.33% on Rank-10 accuracy and 39.33% on Rank-25 accuracy.
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Alvarez, M. A., D. Luengo, and N. D. Lawrence. "Linear Latent Force Models Using Gaussian Processes." IEEE Transactions on Pattern Analysis and Machine Intelligence 35, no. 11 (November 2013): 2693–705. http://dx.doi.org/10.1109/tpami.2013.86.
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Oune, Nicholas, and Ramin Bostanabad. "Latent map Gaussian processes for mixed variable metamodeling." Computer Methods in Applied Mechanics and Engineering 387 (December 2021): 114128. http://dx.doi.org/10.1016/j.cma.2021.114128.
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Panos, Aristeidis, Petros Dellaportas, and Michalis K. Titsias. "Large scale multi-label learning using Gaussian processes." Machine Learning 110, no. 5 (April 14, 2021): 965–87. http://dx.doi.org/10.1007/s10994-021-05952-5.
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AbstractWe introduce a Gaussian process latent factor model for multi-label classification that can capture correlations among class labels by using a small set of latent Gaussian process functions. To address computational challenges, when the number of training instances is very large, we introduce several techniques based on variational sparse Gaussian process approximations and stochastic optimization. Specifically, we apply doubly stochastic variational inference that sub-samples data instances and classes which allows us to cope with Big Data. Furthermore, we show it is possible and beneficial to optimize over inducing points, using gradient-based methods, even in very high dimensional input spaces involving up to hundreds of thousands of dimensions. We demonstrate the usefulness of our approach on several real-world large-scale multi-label learning problems.
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Hall, Peter, Hans-Georg Mller, and Fang Yao. "Modelling sparse generalized longitudinal observations with latent Gaussian processes." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70, no. 4 (September 2008): 703–23. http://dx.doi.org/10.1111/j.1467-9868.2008.00656.x.
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Mattos, César Lincoln C., Andreas Damianou, Guilherme A. Barreto, and Neil D. Lawrence. "Latent Autoregressive Gaussian Processes Models for Robust System Identification." IFAC-PapersOnLine 49, no. 7 (2016): 1121–26. http://dx.doi.org/10.1016/j.ifacol.2016.07.353.
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Gammelli, Daniele, Inon Peled, Filipe Rodrigues, Dario Pacino, Haci A. Kurtaran, and Francisco C. Pereira. "Estimating latent demand of shared mobility through censored Gaussian Processes." Transportation Research Part C: Emerging Technologies 120 (November 2020): 102775. http://dx.doi.org/10.1016/j.trc.2020.102775.
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Dew, Ryan, Asim Ansari, and Yang Li. "Modeling Dynamic Heterogeneity Using Gaussian Processes." Journal of Marketing Research 57, no. 1 (October 14, 2019): 55–77. http://dx.doi.org/10.1177/0022243719874047.
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Marketing research relies on individual-level estimates to understand the rich heterogeneity of consumers, firms, and products. While much of the literature focuses on capturing static cross-sectional heterogeneity, little research has been done on modeling dynamic heterogeneity, or the heterogeneous evolution of individual-level model parameters. In this work, the authors propose a novel framework for capturing the dynamics of heterogeneity, using individual-level, latent, Bayesian nonparametric Gaussian processes. Similar to standard heterogeneity specifications, this Gaussian process dynamic heterogeneity (GPDH) specification models individual-level parameters as flexible variations around population-level trends, allowing for sharing of statistical information both across individuals and within individuals over time. This hierarchical structure provides precise individual-level insights regarding parameter dynamics. The authors show that GPDH nests existing heterogeneity specifications and that not flexibly capturing individual-level dynamics may result in biased parameter estimates. Substantively, they apply GPDH to understand preference dynamics and to model the evolution of online reviews. Across both applications, they find robust evidence of dynamic heterogeneity and illustrate GPDH’s rich managerial insights, with implications for targeting, pricing, and market structure analysis.
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Zhang, Dongmei, Yuyang Zhang, Bohou Jiang, Xinwei Jiang, and Zhijiang Kang. "Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching." Energies 13, no. 17 (August 19, 2020): 4290. http://dx.doi.org/10.3390/en13174290.
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Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.
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Lu, Chi-Ken, and Patrick Shafto. "Conditional Deep Gaussian Processes: Multi-Fidelity Kernel Learning." Entropy 23, no. 11 (November 20, 2021): 1545. http://dx.doi.org/10.3390/e23111545.
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Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, it was pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fidelity data. Then the moment matching method is applied to approximate the marginal prior of conditional DGP with a GP. The obtained effective kernels are implicit functions of the lower-fidelity data, manifesting the expressivity contributed by distribution propagation within the hierarchy. The hyperparameters are learned via optimizing the approximate marginal likelihood. Experiments with synthetic and high dimensional data show comparable performance against other multi-fidelity regression methods, variational inference, and multi-output GP. We conclude that, with the low fidelity data and the hierarchical DGP structure, the effective kernel encodes the inductive bias for true function allowing the compositional freedom.
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Hubin, Aliaksandr, Geir O. Storvik, Paul E. Grini, and Melinka A. Butenko. "A Bayesian Binomial Regression Model with Latent Gaussian Processes for Modelling DNA Methylation." Austrian Journal of Statistics 49, no. 4 (April 13, 2020): 46–56. http://dx.doi.org/10.17713/ajs.v49i4.1124.
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Epigenetic observations are represented by the total number of reads from a given pool of cells and the number of methylated reads, making it reasonable to model this data by a binomial distribution. There are numerous factors that can influence the probability of success in a particular region. Moreover, there is a strong spatial (alongside the genome) dependence of these probabilities. We incorporate dependence on the covariates and the spatial dependence of the methylation probability for observations from a pool of cells by means of a binomial regression model with a latent Gaussian field and a logit link function. We apply a Bayesian approach including prior specifications on model configurations. We run a mode jumping Markov chain Monte Carlo algorithm (MJMCMC) across different choices of covariates in order to obtain the joint posterior distribution of parameters and models. This also allows finding the best set of covariates to model methylation probability within the genomic region of interest and individual marginal inclusion probabilities of the covariates.
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Shi, Fan, Bin Li, and Xiangyang Xue. "Raven's Progressive Matrices Completion with Latent Gaussian Process Priors." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 11 (May 18, 2021): 9612–20. http://dx.doi.org/10.1609/aaai.v35i11.17157.
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Abstract reasoning ability is fundamental to human intelligence. It enables humans to uncover relations among abstract concepts and further deduce implicit rules from the relations. As a well-known abstract visual reasoning task, Raven's Progressive Matrices (RPM) are widely used in human IQ tests. Although extensive research has been conducted on RPM solvers with machine intelligence, few studies have considered further advancing the standard answer-selection (classification) problem to a more challenging answer-painting (generating) problem, which can verify whether the model has indeed understood the implicit rules. In this paper we aim to solve the latter one by proposing a deep latent variable model, in which multiple Gaussian processes are employed as priors of latent variables to separately learn underlying abstract concepts from RPMs; thus the proposed model is interpretable in terms of concept-specific latent variables. The latent Gaussian process also provides an effective way of extrapolation for answer painting based on the learned concept-changing rules. We evaluate the proposed model on RPM-like datasets with multiple continuously-changing visual concepts. Experimental results demonstrate that our model requires only few training samples to paint high-quality answers, generate novel RPM panels, and achieve interpretability through concept-specific latent variables.
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Payne, R. D., N. Guha, Y. Ding, and B. K. Mallick. "A conditional density estimation partition model using logistic Gaussian processes." Biometrika 107, no. 1 (December 5, 2019): 173–90. http://dx.doi.org/10.1093/biomet/asz064.
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Summary Conditional density estimation seeks to model the distribution of a response variable conditional on covariates. We propose a Bayesian partition model using logistic Gaussian processes to perform conditional density estimation. The partition takes the form of a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The methodology models data in which the density changes sharply throughout the covariate space, and can be used to determine where important changes in the density occur. The Markov chain Monte Carlo algorithm involves a Laplace approximation on the latent variables of the logistic Gaussian process model which marginalizes the parameters in each partition element, allowing an efficient search of the approximate posterior distribution of the tessellation. The method is consistent when the density is piecewise constant in the covariate space or when the density is Lipschitz continuous with respect to the covariates. In simulation and application to wind turbine data, the model successfully estimates the partition structure and conditional distribution.
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Lu, Chi-Ken, and Patrick Shafto. "Conditional Deep Gaussian Processes: Empirical Bayes Hyperdata Learning." Entropy 23, no. 11 (October 23, 2021): 1387. http://dx.doi.org/10.3390/e23111387.
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It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.
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Krese, Blaž, and Erik Štrumbelj. "A Bayesian approach to time-varying latent strengths in pairwise comparisons." PLOS ONE 16, no. 5 (May 20, 2021): e0251945. http://dx.doi.org/10.1371/journal.pone.0251945.
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The famous Bradley-Terry model for pairwise comparisons is widely used for ranking objects and is often applied to sports data. In this paper we extend the Bradley-Terry model by allowing time-varying latent strengths of compared objects. The time component is modelled with barycentric rational interpolation and Gaussian processes. We also allow for the inclusion of additional information in the form of outcome probabilities. Our models are evaluated and compared on toy data set and real sports data from ATP tennis matches and NBA games. We demonstrated that using Gaussian processes is advantageous compared to barycentric rational interpolation as they are more flexible to model discontinuities and are less sensitive to initial parameters settings. However, all investigated models proved to be robust to over-fitting and perform well with situations of volatile and of constant latent strengths. When using barycentric rational interpolation it has turned out that applying Bayesian approach gives better results than by using MLE. Performance of the models is further improved by incorporating the outcome probabilities.
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Zhang, Wenbo, and Wei Gu. "Parameter Estimation for Several Types of Linear Partial Differential Equations Based on Gaussian Processes." Fractal and Fractional 6, no. 8 (August 8, 2022): 433. http://dx.doi.org/10.3390/fractalfract6080433.
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This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under the idea of data-driven methods, the algorithms based on Gaussian processes are constructed to solve the inverse problem, where we encode the distribution information of the data into the kernels and construct an efficient data learning machine. We then estimate the unknown parameters of the partial differential Equations (PDEs), which include high-order partial differential equations, partial integro-differential equations, fractional partial differential equations and a system of partial differential equations. Finally, several numerical tests are provided. The results of the numerical experiments prove that the data-driven methods based on Gaussian processes not only estimate the parameters of the considered PDEs with high accuracy but also approximate the latent solutions and the inhomogeneous terms of the PDEs simultaneously.
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Serradilla, J., J. Q. Shi, and A. J. Morris. "Fault detection based on Gaussian process latent variable models." Chemometrics and Intelligent Laboratory Systems 109, no. 1 (November 2011): 9–21. http://dx.doi.org/10.1016/j.chemolab.2011.07.003.
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Zhao, Yuan, and Il Memming Park. "Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains." Neural Computation 29, no. 5 (May 2017): 1293–316. http://dx.doi.org/10.1162/neco_a_00953.
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When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded populations of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent trajectories, particularly from single-trial population recordings, may help us understand the dynamics that drive neural computation. However, due to the biophysical constraints and noise in the spike trains, inferring trajectories from data is a challenging statistical problem in general. Here, we propose a practical and efficient inference method, the variational latent gaussian process (vLGP). The vLGP combines a generative model with a history-dependent point process observation, together with a smoothness prior on the latent trajectories. The vLGP improves on earlier methods for recovering latent trajectories, which assume either observation models inappropriate for point processes or linear dynamics. We compare and validate vLGP on both simulated data sets and population recordings from the primary visual cortex. In the V1 data set, we find that vLGP achieves substantially higher performance than previous methods for predicting omitted spike trains, as well as capturing both the toroidal topology of visual stimuli space and the noise correlation. These results show that vLGP is a robust method with the potential to reveal hidden neural dynamics from large-scale neural recordings.
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Mahdi, Esam, Sana Alshamari, Maryam Khashabi, and Alya Alkorbi. "Hierarchical Bayesian Spatio-Temporal Modeling for PM10 Prediction." Journal of Applied Mathematics 2021 (September 11, 2021): 1–11. http://dx.doi.org/10.1155/2021/8003952.
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Over the past few years, hierarchical Bayesian models have been extensively used for modeling the joint spatial and temporal dependence of big spatio-temporal data which commonly involves a large number of missing observations. This article represented, assessed, and compared some recently proposed Bayesian and non-Bayesian models for predicting the daily average particulate matter with a diameter of less than 10 (PM10) measured in Qatar during the years 2016–2019. The disaggregating technique with a Markov chain Monte Carlo method with Gibbs sampler are used to handle the missing data. Based on the obtained results, we conclude that the Gaussian predictive processes with autoregressive terms of the latent underlying space-time process model is the best, compared with the Bayesian Gaussian processes and non-Bayesian generalized additive models.
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Xu, Jingyun, and Zhiduan Cai. "Gaussian mixture deep dynamic latent variable model with application to soft sensing for multimode industrial processes." Applied Soft Computing 114 (January 2022): 108092. http://dx.doi.org/10.1016/j.asoc.2021.108092.
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Wöber, Wilfried, Lars Mehnen, Manuel Curto, Papius Dias Tibihika, Genanaw Tesfaye, and Harald Meimberg. "Investigating Shape Variation Using Generalized Procrustes Analysis and Machine Learning." Applied Sciences 12, no. 6 (March 20, 2022): 3158. http://dx.doi.org/10.3390/app12063158.
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The biological investigation of a population’s shape diversity using digital images is typically reliant on geometrical morphometrics, which is an approach based on user-defined landmarks. In contrast to this traditional approach, the progress in deep learning has led to numerous applications ranging from specimen identification to object detection. Typically, these models tend to become black boxes, which limits the usage of recent deep learning models for biological applications. However, the progress in explainable artificial intelligence tries to overcome this limitation. This study compares the explanatory power of unsupervised machine learning models to traditional landmark-based approaches for population structure investigation. We apply convolutional autoencoders as well as Gaussian process latent variable models to two Nile tilapia datasets to investigate the latent structure using consensus clustering. The explanatory factors of the machine learning models were extracted and compared to generalized Procrustes analysis. Hypotheses based on the Bayes factor are formulated to test the unambiguity of population diversity unveiled by the machine learning models. The findings show that it is possible to obtain biologically meaningful results relying on unsupervised machine learning. Furthermore we show that the machine learning models unveil latent structures close to the true population clusters. We found that 80% of the true population clusters relying on the convolutional autoencoder are significantly different to the remaining clusters. Similarly, 60% of the true population clusters relying on the Gaussian process latent variable model are significantly different. We conclude that the machine learning models outperform generalized Procrustes analysis, where 16% of the population cluster was found to be significantly different. However, the applied machine learning models still have limited biological explainability. We recommend further in-depth investigations to unveil the explanatory factors in the used model.
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Peng, Kaixiang, Bingzheng Wang, and Jie Dong. "An Efficient Quality-Related Fault Diagnosis Method for Real-Time Multimode Industrial Process." Journal of Control Science and Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/9560206.
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Focusing on quality-related complex industrial process performance monitoring, a novel multimode process monitoring method is proposed in this paper. Firstly, principal component space clustering is implemented under the guidance of quality variables. Through extraction of model tags, clustering information of original training data can be acquired. Secondly, according to multimode characteristics of process data, the monitoring model integrated Gaussian mixture model with total projection to latent structures is effective after building the covariance description form. The multimode total projection to latent structures (MTPLS) model is the foundation of problem solving about quality-related monitoring for multimode processes. Then, a comprehensive statistics index is defined which is based on the posterior probability of the monitored samples belonging to each Gaussian component in the Bayesian theory. After that, a combined index is constructed for process monitoring. Finally, motivated by the application of traditional contribution plot in fault diagnosis, a gradient contribution rate is applied for analyzing the variation of variable contribution rate along samples. Our method can ensure the implementation of online fault monitoring and diagnosis for multimode processes. Performances of the whole proposed scheme are verified in a real industrial, hot strip mill process (HSMP) compared with some existing methods.
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Nightingale, Glenna, Megan Laxton, and Janine B. Illian. "How does the community COVID-19 level of risk impact on that of a care home?" PLOS ONE 16, no. 12 (December 31, 2021): e0260051. http://dx.doi.org/10.1371/journal.pone.0260051.
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Objectives To model the risk of COVID-19 mortality in British care homes conditional on the community level risk. Methods A two stage modeling process (“doubly latent”) which includes a Besag York Mollie model (BYM) and a Log Gaussian Cox Process. The BYM is adopted so as to estimate the community level risks. These are incorporated in the Log Gaussian Cox Process to estimate the impact of these risks on that in care homes. Results For an increase in the risk at the community level, the number of COVID-19 related deaths in the associated care home would be increased by exp (0.833), 2. This is based on a simulated dataset. In the context of COVID-19 related deaths, this study has illustrated the estimation of the risk to care homes in the presence of background community risk. This approach will be useful in facilitating the identification of the most vulnerable care homes and in predicting risk to new care homes. Conclusions The modeling of two latent processes have been shown to be successfully facilitated by the use of the BYM and Log Gaussian Cox Process Models. Community COVID-19 risks impact on that of the care homes embedded in these communities.
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Abdel-Aziz, Hamzah, and Xenofon Koutsoukos. "Online Model Learning of Buildings Using Stochastic Hybrid Systems Based on Gaussian Processes." Journal of Control Science and Engineering 2017 (2017): 1–18. http://dx.doi.org/10.1155/2017/3035892.
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Dynamical models are essential for model-based control methodologies which allow smart buildings to operate autonomously in an energy and cost efficient manner. However, buildings have complex thermal dynamics which are affected externally by the environment and internally by thermal loads such as equipment and occupancy. Moreover, the physical parameters of buildings may change over time as the buildings age or due to changes in the buildings’ configuration or structure. In this paper, we introduce an online model learning methodology to identify a nonparametric dynamical model for buildings when the thermal load is latent (i.e., the thermal load cannot be measured). The proposed model is based on stochastic hybrid systems, where the discrete state describes the level of the thermal load and the continuous dynamics represented by Gaussian processes describe the thermal dynamics of the air temperature. We demonstrate the evaluation of the proposed model using two-zone and five-zone buildings. The data for both experiments are generated using the EnergyPlus software. Experimental results show that the proposed model estimates the thermal load level correctly and predicts the thermal behavior with good performance.
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Lončarević, Zvezdan, Rok Pahič, Aleš Ude, and Andrej Gams. "Generalization-Based Acquisition of Training Data for Motor Primitive Learning by Neural Networks." Applied Sciences 11, no. 3 (January 23, 2021): 1013. http://dx.doi.org/10.3390/app11031013.
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Autonomous robot learning in unstructured environments often faces the problem that the dimensionality of the search space is too large for practical applications. Dimensionality reduction techniques have been developed to address this problem and describe motor skills in low-dimensional latent spaces. Most of these techniques require the availability of a sufficiently large database of example task executions to compute the latent space. However, the generation of many example task executions on a real robot is tedious, and prone to errors and equipment failures. The main result of this paper is a new approach for efficient database gathering by performing a small number of task executions with a real robot and applying statistical generalization, e.g., Gaussian process regression, to generate more data. We have shown in our experiments that the data generated this way can be used for dimensionality reduction with autoencoder neural networks. The resulting latent spaces can be exploited to implement robot learning more efficiently. The proposed approach has been evaluated on the problem of robotic throwing at a target. Simulation and real-world results with a humanoid robot TALOS are provided. They confirm the effectiveness of generalization-based database acquisition and the efficiency of learning in a low-dimensional latent space.
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Liang, Junjie, Yanting Wu, Dongkuan Xu, and Vasant G. Honavar. "Longitudinal Deep Kernel Gaussian Process Regression." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8556–64. http://dx.doi.org/10.1609/aaai.v35i10.17038.
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Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, \ie irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They rely on ad hoc heuristics or expensive trial and error to choose the effective kernels, and (ii) They fail to handle multilevel correlation structure in the data. We introduce Longitudinal deep kernel Gaussian process regression (L-DKGPR) to overcome these limitations by fully automating the discovery of complex multilevel correlation structure from longitudinal data. Specifically, L-DKGPR eliminates the need for ad hoc heuristics or trial and error using a novel adaptation of deep kernel learning that combines the expressive power of deep neural networks with the flexibility of non-parametric kernel methods. L-DKGPR effectively learns the multilevel correlation with a novel additive kernel that simultaneously accommodates both time-varying and the time-invariant effects. We derive an efficient algorithm to train L-DKGPR using latent space inducing points and variational inference. Results of extensive experiments on several benchmark data sets demonstrate that L-DKGPR significantly outperforms the state-of-the-art longitudinal data analysis (LDA) methods.
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Battaglin, Paulo David, and Gilmar Barreto. "Kalman Filtering Solution Converges on a Personal Computer." Journal of Circuits, Systems and Computers 26, no. 01 (October 4, 2016): 1750005. http://dx.doi.org/10.1142/s0218126617500050.
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Instantaneous observability is used to watch a system output with very fast signals as well as it is a system property that enables to estimate system internal states. This property depends on the pair of discrete matrices [Formula: see text] and it considers that the system state equations are known. The problem is that the system states are inside and they are not always accessible directly. A process, which is a time-varying running program in four parts composes the system under investigation here. It is shown it is possible to apply Kalman filtering on a digital personal computer’s system with particularly the four parts like the ones under investigation. A computing process is performed during a period of time called latency. The calculation of latency considers it as a random variable with Gaussian distribution. The potential application of the results attained is the forecasting of data traffic-jam on a digital personal computer, which has very fast signals inside. In a broader perspective, this method to calculate latency can be applied on other digital personal computer processes such as processes on random access memory. It is also possible to apply this method on local area networks and mainframes.
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Zhao, Qibin, Liqing Zhang, and Andrzej Cichocki. "A Tensor-Variate Gaussian Process for Classification of Multidimensional Structured Data." Proceedings of the AAAI Conference on Artificial Intelligence 27, no. 1 (June 30, 2013): 1041–47. http://dx.doi.org/10.1609/aaai.v27i1.8568.
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As tensors provide a natural and efficient representation of multidimensional structured data, in this paper, we consider probabilistic multinomial probit classification for tensor-variate inputs with Gaussian processes (GP) priors placed over the latent function. In order to take into account the underlying multimodes structure information within the model, we propose a framework of probabilistic product kernels for tensorial data based on a generative model assumption. More specifically, it can be interpreted as mapping tensors to probability density function space and measuring similarity by an information divergence. Since tensor kernels enable us to model input tensor observations, the proposed tensor-variate GP is considered as both a generative and discriminative model. Furthermore, a fully variational Bayesian treatment for multiclass GP classification with multinomial probit likelihood is employed to estimate the hyperparameters and infer the predictive distributions. Simulation results on both synthetic data and a real world application of human action recognition in videos demonstrate the effectiveness and advantages of the proposed approach for classification of multiway tensor data, especially in the case that the underlying structure information among multimodes is discriminative for the classification task.
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Lu, Rong, Jennifer L. Miskimins, and Mikhail Zhizhin. "Learning from Nighttime Observations of Gas Flaring in North Dakota for Better Decision and Policy Making." Remote Sensing 13, no. 5 (March 3, 2021): 941. http://dx.doi.org/10.3390/rs13050941.
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In today’s oil industry, companies frequently flare the produced natural gas from oil wells. The flaring activities are extensive in some regions including North Dakota. Besides company-reported data, which are compiled by the North Dakota Industrial Commission, flaring statistics such as count and volume can be estimated via Visible Infrared Imaging Radiometer Suite nighttime observations. Following data gathering and preprocessing, Bayesian machine learning implemented with Markov chain Monte Carlo methods is performed to tackle two tasks: flaring time series analysis and distribution approximation. They help further understanding of the flaring profiles and reporting qualities, which are important for decision/policy making. First, although fraught with measurement and estimation errors, the time series provide insights into flaring approaches and characteristics. Gaussian processes are successful in inferring the latent flaring trends. Second, distribution approximation is achieved by unsupervised learning. The negative binomial and Gaussian mixture models are utilized to describe the distributions of field flare count and volume, respectively. Finally, a nearest-neighbor-based approach for company level flared volume allocation is developed. Potential discrepancies are spotted between the company reported and the remotely sensed flaring profiles.
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Xie, Luodi, Huimin Huang, and Qing Du. "A Co-Embedding Model with Variational Auto-Encoder for Knowledge Graphs." Applied Sciences 12, no. 2 (January 12, 2022): 715. http://dx.doi.org/10.3390/app12020715.
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Knowledge graph (KG) embedding has been widely studied to obtain low-dimensional representations for entities and relations. It serves as the basis for downstream tasks, such as KG completion and relation extraction. Traditional KG embedding techniques usually represent entities/relations as vectors or tensors, mapping them in different semantic spaces and ignoring the uncertainties. The affinities between entities and relations are ambiguous when they are not embedded in the same latent spaces. In this paper, we incorporate a co-embedding model for KG embedding, which learns low-dimensional representations of both entities and relations in the same semantic space. To address the issue of neglecting uncertainty for KG components, we propose a variational auto-encoder that represents KG components as Gaussian distributions. In addition, compared with previous methods, our method has the advantages of high quality and interpretability. Our experimental results on several benchmark datasets demonstrate our model’s superiority over the state-of-the-art baselines.
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Zhang, Yan, Huaiping Jin, Haipeng Liu, Biao Yang, and Shoulong Dong. "Deep Semi-Supervised Just-in-Time Learning Based Soft Sensor for Mooney Viscosity Estimation in Industrial Rubber Mixing Process." Polymers 14, no. 5 (March 3, 2022): 1018. http://dx.doi.org/10.3390/polym14051018.
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Soft sensor technology has become an effective tool to enable real-time estimations of key quality variables in industrial rubber-mixing processes, which facilitates efficient monitoring and a control of rubber manufacturing. However, it remains a challenging issue to develop high-performance soft sensors due to improper feature selection/extraction and insufficiency of labeled data. Thus, a deep semi-supervised just-in-time learning-based Gaussian process regression (DSSJITGPR) is developed for Mooney viscosity estimation. It integrates just-in-time learning, semi-supervised learning, and deep learning into a unified modeling framework. In the offline stage, the latent feature information behind the historical process data is extracted through a stacked autoencoder. Then, an evolutionary pseudo-labeling estimation approach is applied to extend the labeled modeling database, where high-confidence pseudo-labeled data are obtained by solving an explicit pseudo-labeling optimization problem. In the online stage, when the query sample arrives, a semi-supervised JITGPR model is built from the enlarged modeling database to achieve Mooney viscosity estimation. Compared with traditional Mooney-viscosity soft sensor methods, DSSJITGPR shows significant advantages in extracting latent features and handling label scarcity, thus delivering superior prediction performance. The effectiveness and superiority of DSSJITGPR has been verified through the Mooney viscosity prediction results from an industrial rubber-mixing process.
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Chen, Dongming, Mingshuo Nie, Hupo Zhang, Zhen Wang, and Dongqi Wang. "Network Embedding Algorithm Taking in Variational Graph AutoEncoder." Mathematics 10, no. 3 (February 2, 2022): 485. http://dx.doi.org/10.3390/math10030485.
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Complex networks with node attribute information are employed to represent complex relationships between objects. Research of attributed network embedding fuses the topology and the node attribute information of the attributed network in the common latent representation space, to encode the high-dimensional sparse network information to the low-dimensional dense vector representation, effectively improving the performance of the network analysis tasks. The current research on attributed network embedding is presently facing problems of high-dimensional sparsity of attribute eigenmatrix and underutilization of attribute information. In this paper, we propose a network embedding algorithm taking in a variational graph autoencoder (NEAT-VGA). This algorithm first pre-processes the attribute features, i.e., the attribute feature learning of the network nodes. Then, the feature learning matrix and the adjacency matrix of the network are fed into the variational graph autoencoder algorithm to obtain the Gaussian distribution of the potential vectors, which more easily generate high-quality node embedding representation vectors. Then, the embedding of the nodes obtained by sampling this Gaussian distribution is reconstructed with structural and attribute losses. The loss function is minimized by iterative training until the low-dimension vector representation, containing network structure information and attribute information of nodes, can be better obtained, and the performance of the algorithm is evaluated by link prediction experimental results.
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Istodor, Alin Viorel, Laura-Cristina Rusu, Gratiela Georgiana Noja, Alexandra Roi, Ciprian Roi, Emanuel Bratu, Georgiana Moise, Maria Puiu, Simona Sorina Farcas, and Nicoleta Ioana Andreescu. "An Observational Study on Cephalometric Characteristics and Patterns Associated with the Prader–Willi Syndrome: A Structural Equation Modelling and Network Approach." Applied Sciences 11, no. 7 (April 2, 2021): 3177. http://dx.doi.org/10.3390/app11073177.
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Examining specific patterns of major cranio-facial alterations through cephalometric measurements in order to improve the Prader–Willi (PWS) syndrome diagnostic poses a major challenge of identifying interlinkages between numerous credentials. These interactions can be captured through probabilistic models of conditional independence between heterogeneous variables. Our research included 18 subjects (aged 4 to 28 years) genetically diagnosed with Prader–Willi syndrome and a healthy control group (matched age and sex). A morphometric and cephalometric analysis was performed upon all the subjects in order to obtain the needed specific data. We have, therefore, firstly deployed several integrated Gaussian graphical models (GGMs) to capture the positive and negative partial correlations and the intensity of the connections between numerous credentials configured to determine specific cranio-facial characteristics of patients with PWS compared to others without this genetic disorder (case-control analysis). Afterwards, we applied structural equation modelling (SEM) with latent class analysis to assess the impact of these coordinates on the prevalence of the Prader–Willi diagnostic. We found that there are latent interactions of features affected by external variables, and the interlinkages are strapping particularly between cranial base (with an important role in craniofacial disharmonies) and facial heights, as important characteristic patterns in determining the Prader–Willi diagnostic, while the overall patterns are significantly different in PWS and the control group. These results impact the field by providing an enhanced comprehensive perspective on cephalometric characteristics and specific patterns associated with Prader–Willi syndrome that can be used as benchmarks in determining the diagnostic of this rare genetic disorder. Furthermore, the two innovative exploratory research tools applied in this paper are very useful to the craniofacial field to infer the connections/dependencies between variables (particularly biological variables and genes) on cephalometric characteristics and specific patterns associated with Prader–Willi syndrome.
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Lenkoski, Alex, and Fredrik L. Aanes. "Sovereign Risk Indices and Bayesian Theory Averaging." Econometrics 8, no. 2 (May 29, 2020): 22. http://dx.doi.org/10.3390/econometrics8020022.
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In economic applications, model averaging has found principal use in examining the validity of various theories related to observed heterogeneity in outcomes such as growth, development, and trade. Though often easy to articulate, these theories are imperfectly captured quantitatively. A number of different proxies are often collected for a given theory and the uneven nature of this collection requires care when employing model averaging. Furthermore, if valid, these theories ought to be relevant outside of any single narrowly focused outcome equation. We propose a methodology which treats theories as represented by latent indices, these latent processes controlled by model averaging on the proxy level. To achieve generalizability of the theory index our framework assumes a collection of outcome equations. We accommodate a flexible set of generalized additive models, enabling non-Gaussian outcomes to be included. Furthermore, selection of relevant theories also occurs on the outcome level, allowing for theories to be differentially valid. Our focus is on creating a set of theory-based indices directed at understanding a country’s potential risk of macroeconomic collapse. These Sovereign Risk Indices are calibrated across a set of different “collapse” criteria, including default on sovereign debt, heightened potential for high unemployment or inflation and dramatic swings in foreign exchange values. The goal of this exercise is to render a portable set of country/year theory indices which can find more general use in the research community.
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Yamagishi, Noriko, Stephen J. Anderson, and Mitsuo Kawato. "The observant mind: self-awareness of attentional status." Proceedings of the Royal Society B: Biological Sciences 277, no. 1699 (June 9, 2010): 3421–26. http://dx.doi.org/10.1098/rspb.2010.0891.
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Visual perception is dependent not only on low-level sensory input but also on high-level cognitive factors such as attention. In this paper, we sought to determine whether attentional processes can be internally monitored for the purpose of enhancing behavioural performance. To do so, we developed a novel paradigm involving an orientation discrimination task in which observers had the freedom to delay target presentation—by any amount required—until they judged their attentional focus to be complete. Our results show that discrimination performance is significantly improved when individuals self-monitor their level of visual attention and respond only when they perceive it to be maximal. Although target delay times varied widely from trial-to-trial (range 860 ms–12.84 s), we show that their distribution is Gaussian when plotted on a reciprocal latency scale. We further show that the neural basis of the delay times for judging attentional status is well explained by a linear rise-to-threshold model. We conclude that attentional mechanisms can be self-monitored for the purpose of enhancing human decision-making processes, and that the neural basis of such processes can be understood in terms of a simple, yet broadly applicable, linear rise-to-threshold model.
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Foon, See Lee, Nazira Anisa Rahim, Ahmad Zainal, and Zhang Jie. "Selective combination in multiple neural networks prediction using independent component regression approach." Chemical Engineering Research Bulletin 19 (September 10, 2017): 12. http://dx.doi.org/10.3329/cerb.v19i0.33772.
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<p>Biological processes are highly nonlinear in nature and difficult to represent accurately by simple mathematical models. However, this problem can be solved by using neural network. Neural network is a prominent modeling tool especially when it comes to intricate process such as biological process. In this paper, a multiple single hidden layer with ten hidden neurons Feedforward Artificial Neural Network (FANN) was used to model the complex and dynamic relationships between the input (dilution rate, D) and outputs (conversion, y and dimensionless temperature value, θ) for the reactive biological process. Levenberg-Marquardt Backpropagation training method was used. The multiple neural networks predicted outputs were then combined through three different methods which area simple averaging, Principal Component Regression (PCR) and Independent Component Regression (ICR). Multiple neural networks which were created by the bootstrap approach help improved single neural network performance as well as the model robustness for nonlinear process modeling. Comparison was made between the three methods. The result showed that ICR is slightly superior between the three methods especially in noise level 1,2 and 3, however ICR slightly suffer in noise level 4 and 5. This is due to the independent component regression used the latent factors and non-Gaussian distribution of y and θ values for the combination.</p><p>Chemical Engineering Research Bulletin 19(2017) 12-19</p>
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Wang, Chuanmeizhi, Bijan Pesaran, and Maryam M. Shanechi. "Modeling multiscale causal interactions between spiking and field potential signals during behavior." Journal of Neural Engineering 19, no. 2 (March 7, 2022): 026001. http://dx.doi.org/10.1088/1741-2552/ac4e1c.
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Abstract Objective. Brain recordings exhibit dynamics at multiple spatiotemporal scales, which are measured with spike trains and larger-scale field potential signals. To study neural processes, it is important to identify and model causal interactions not only at a single scale of activity, but also across multiple scales, i.e. between spike trains and field potential signals. Standard causality measures are not directly applicable here because spike trains are binary-valued but field potentials are continuous-valued. It is thus important to develop computational tools to recover multiscale neural causality during behavior, assess their performance on neural datasets, and study whether modeling multiscale causalities can improve the prediction of neural signals beyond what is possible with single-scale causality. Approach. We design a multiscale model-based Granger-like causality method based on directed information and evaluate its success both in realistic biophysical spike-field simulations and in motor cortical datasets from two non-human primates (NHP) performing a motor behavior. To compute multiscale causality, we learn point-process generalized linear models that predict the spike events at a given time based on the history of both spike trains and field potential signals. We also learn linear Gaussian models that predict the field potential signals at a given time based on their own history as well as either the history of binary spike events or that of latent firing rates. Main results. We find that our method reveals the true multiscale causality network structure in biophysical simulations despite the presence of model mismatch. Further, models with the identified multiscale causalities in the NHP neural datasets lead to better prediction of both spike trains and field potential signals compared to just modeling single-scale causalities. Finally, we find that latent firing rates are better predictors of field potential signals compared with the binary spike events in the NHP datasets. Significance. This multiscale causality method can reveal the directed functional interactions across spatiotemporal scales of brain activity to inform basic science investigations and neurotechnologies.
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Fific, Mario. "Dynamics of serial position change in probe-recognition task." Psihologija 35, no. 3-4 (2002): 261–85. http://dx.doi.org/10.2298/psi0203261f.
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Relationship between practice and serial position effects was investigated, in order to obtain more evidence for underlying short-term memory processes. The investigated relationship is termed the dynamics of serial position change. To address this issue, the present study investigated mean latency, errors, and performed Ex-Gaussian convolution analysis. In six-block trials the probe-recognition task was used in the so-called fast experimental procedure. The serial position effect was significant in all six blocks. Both primacy and recency effects were detected, with primacy located in the first two blocks, producing a non-linear serial position effect. Although the serial position function became linear from the third block on, the convolution analysis revealed a non-linear change of the normal distribution parameter, suggesting special status of the last two serial positions. Further, separation of convolution parameters for serial position and practice was observed, suggesting different underlying mechanisms. In order to account for these findings, a strategy shift mechanism is suggested, rather then a mechanism based on changing the manner of memory scanning. Its influence is primarily located at the very beginning of the experimental session. The pattern of results of errors regarding the dynamics of serial position change closely paralleled those on reaction times. Several models of short-term memory were evaluated in order to account for these findings.
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Aitken, F., F. M. J. Mccluskey, and A. Denat. "An energy model for artificially generated bubbles in liquids." Journal of Fluid Mechanics 327 (November 25, 1996): 373–92. http://dx.doi.org/10.1017/s0022112096008580.
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A mathematical analysis is carried out to model the series of processes following the occurrence of an electron avalanche in a liquid right through to the emission of a pressure transient and the formation of a bubble. The initial energy distribution is chosen to be Gaussian and it is assumed that the electrical energy injected into the system is transformed into thermal and mechanical components. From the mechanical point of view, an outgoing spherical pressure transient is formed at the edge of the plasma region, and at a later time a bubble is also formed. Theoretically, the pressure transient accounts for about 15% of the total injected energy, while it is necessary to revert to experimental results to fix the energy associated with the bubble (about 2%). A minimum such value can, however, be estimated. The maximum pressure amplitude is calculated. Concerning the thermal component of the energy, some is absorbed as internal energy by the liquid, while the remainder is stocked as latent heat of vaporization. The maximum temperature difference is derived as are the different energies as functions of the total injected energy. The advantage of this type of model is that the gas/vapour temperature in the bubble can continue to rise after the phase change takes place. The maximum bubble size following a given energy injection is calculated assuming an adiabatic expansion process. A mathematical expression for the liquid flow induced by the outgoing pressure transient is also found. Comparison between experimental and theoretical results is particularly good.
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Vasilyev, V. I., M. V. Vasilyeva, S. P. Stepanov, N. I. Sidnyaev, O. I. Matveeva, and A. N. Tseeva. "Numerical Solution of the Two-Phase Stefan Problem in the Enthalpy Formulation with Smoothing the Coefficients." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (97) (August 2021): 4–23. http://dx.doi.org/10.18698/1812-3368-2021-4-4-23.
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To simulate heat transfer processes with phase transitions, the classical enthalpy model of Stefan is used, accompanied by phase transformations of the medium with absorption and release of latent heat of a change in the state of aggregation. The paper introduces a solution to the two-phase Stefan problem for a one-dimensional quasilinear second-order parabolic equation with discontinuous coefficients. A method for smearing the Dirac delta function using the smoothing of discontinuous coefficients by smooth functions is proposed. The method is based on the use of the integral of errors and the Gaussian normal distribution with an automated selection of the value of the interval of their smoothing by the desired function (temperature). The discontinuous coefficients are replaced by bounded smooth temperature functions. For the numerical solution, the finite difference method and the finite element method with an automated selection of the smearing and smoothing parameters for the coefficients at each time layer are used. The results of numerical calculations are compared with the solution of Stefan’s two-phase self-similar problem --- with a mathematical model of the formation of the ice cover of the reservoir. Numerical simulation of the thawing effect of installing additional piles on the existing pile field is carried out. The temperature on the day surface of the base of the structure is set with account for the amplitude of air temperature fluctuations, taken from the data of the Yakutsk meteorological station. The study presents the results of numerical calculations for concrete piles installed in the summer in large-diameter drilled wells using cement-sand mortars with a temperature of 25 °С. The distributions of soil temperature are obtained for different points in time
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Eweis-Labolle, Jonathan, Nicholas Oune, and Ramin Bostanabad. "Data Fusion with Latent Map Gaussian Processes." Journal of Mechanical Design, May 9, 2022, 1–41. http://dx.doi.org/10.1115/1.4054520.
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Abstract Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, flexibility to jointly fuse any number of data sources, and ability to visualize correlations between data sources. This visualization allows the user to detect model form errors or determine the optimum strategy for high-fidelity emulation by fitting LMGP only to the subset of the data sources that are well-correlated. We also develop a new kernel function that enables LMGPs to not only build a probabilistic multi-fidelity surrogate but also estimate calibration parameters with high accuracy and consistency. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to existing technologies. We demonstrate the benefits of LMGP-based data fusion by comparing its performance against competing methods on a wide range of examples.
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Kleiber, William, Richard W. Katz, and Balaji Rajagopalan. "Daily spatiotemporal precipitation simulation using latent and transformed Gaussian processes." Water Resources Research 48, no. 1 (January 2012). http://dx.doi.org/10.1029/2011wr011105.
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Wang, Liwei, Suraj Yerramilli, Akshay Iyer, Daniel Apley, Ping Zhu, and Wei Chen. "Scalable Gaussian Processes for Data-Driven Design Using Big Data With Categorical Factors." Journal of Mechanical Design 144, no. 2 (September 15, 2021). http://dx.doi.org/10.1115/1.4052221.
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Abstract Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big data sets, categorical inputs, and multiple responses, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent-variable Gaussian process (LVGP) model where categorical factors are mapped into a continuous latent space to enable GP modeling of mixed-variable data sets. By extending variational inference to LVGP models, the large training data set is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multiple responses that might have distinct behaviors. Comparative studies demonstrate that the proposed method scales well for large data sets with over 104 data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent space is obtained to draw insights into the effect of categorical factors, such as those associated with “building blocks” of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials.
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Coveney, Sam, Caroline H. Roney, Cesare Corrado, Richard D. Wilkinson, Jeremy E. Oakley, Steven A. Niederer, and Richard H. Clayton. "Calibrating cardiac electrophysiology models using latent Gaussian processes on atrial manifolds." Scientific Reports 12, no. 1 (October 4, 2022). http://dx.doi.org/10.1038/s41598-022-20745-z.
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AbstractModels of electrical excitation and recovery in the heart have become increasingly detailed, but have yet to be used routinely in the clinical setting to guide personalized intervention in patients. One of the main challenges is calibrating models from the limited measurements that can be made in a patient during a standard clinical procedure. In this work, we propose a novel framework for the probabilistic calibration of electrophysiology parameters on the left atrium of the heart using local measurements of cardiac excitability. Parameter fields are represented as Gaussian processes on manifolds and are linked to measurements via surrogate functions that map from local parameter values to measurements. The posterior distribution of parameter fields is then obtained. We show that our method can recover parameter fields used to generate localised synthetic measurements of effective refractory period. Our methodology is applicable to other measurement types collected with clinical protocols, and more generally for calibration where model parameters vary over a manifold.
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Gu, Mengyang, and Hanmo Li. "Gaussian Orthogonal Latent Factor Processes for Large Incomplete Matrices of Correlated Data." Bayesian Analysis -1, no. -1 (January 1, 2022). http://dx.doi.org/10.1214/21-ba1295.
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Li, Yikuan, Shishir Rao, Abdelaali Hassaine, Rema Ramakrishnan, Dexter Canoy, Gholamreza Salimi-Khorshidi, Mohammad Mamouei, Thomas Lukasiewicz, and Kazem Rahimi. "Deep Bayesian Gaussian processes for uncertainty estimation in electronic health records." Scientific Reports 11, no. 1 (October 19, 2021). http://dx.doi.org/10.1038/s41598-021-00144-6.
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AbstractOne major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the main two scalable uncertainty estimation methods. However, deep Bayesian neural networks suffer from lack of expressiveness, and more expressive models such as deep kernel learning, which is an extension of sparse Gaussian process, captures only the uncertainty from the higher-level latent space. Therefore, the deep learning model under it lacks interpretability and ignores uncertainty from the raw data. In this paper, we merge features of the deep Bayesian learning framework with deep kernel learning to leverage the strengths of both methods for a more comprehensive uncertainty estimation. Through a series of experiments on predicting the first incidence of heart failure, diabetes and depression applied to large-scale electronic medical records, we demonstrate that our method is better at capturing uncertainty than both Gaussian processes and deep Bayesian neural networks in terms of indicating data insufficiency and identifying misclassifications, with a comparable generalization performance. Furthermore, by assessing the accuracy and area under the receiver operating characteristic curve over the predictive probability, we show that our method is less susceptible to making overconfident predictions, especially for the minority class in imbalanced datasets. Finally, we demonstrate how uncertainty information derived by the model can inform risk factor analysis towards model interpretability.
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Deng, Shiguang, Carlos Mora, Diran Apelian, and Ramin Bostanabad. "Data-Driven Calibration of Multi-Fidelity Multiscale Fracture Models via Latent Map Gaussian Process." Journal of Mechanical Design, October 12, 2022, 1–15. http://dx.doi.org/10.1115/1.4055951.
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Abstract Fracture modeling of metallic alloys with microscopic pores relies on multiscale damage simulations which typically ignore the manufacturing-induced spatial variabilities in porosity. This simplification is made because of the prohibitive computational expenses of explicitly modeling spatially varying microstructures in a macroscopic part. To address this challenge and open the doors for fracture-aware design of multiscale materials, we propose a data-driven framework that integrates a mechanistic reduced-order model (ROM) with a calibration scheme based on random processes. Our ROM drastically accelerates direct numerical simulations (DNS) by using a stabilized damage algorithm and systematically reducing the degrees of freedom via clustering. Since clustering affects local strain fields and hence the fracture response, we calibrate the ROM by constructing a multi-fidelity random process based on latent map Gaussian processes (LMGPs). In particular, we use LMGPs to calibrate the damage parameters of an ROM as a function of microstructure and clustering (i.e., fidelity) level such that the ROM faithfully surrogates DNS. We demonstrate the application of our framework in predicting the damage behavior of a multiscale metallic component with spatially varying porosity. Our results indicate that microstructural porosity can significantly affect the performance of macro components and hence must be considered in the design process.
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Semenova, Elizaveta, Yidan Xu, Adam Howes, Theo Rashid, Samir Bhatt, Swapnil Mishra, and Seth Flaxman. "PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation." Journal of The Royal Society Interface 19, no. 191 (June 2022). http://dx.doi.org/10.1098/rsif.2022.0094.
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Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context, they are used to encode correlation structures over space and can generalize well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two-stage approach on Bayesian, small-area estimation tasks.
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Botsas, Themistoklis, Indranil Pan, Lachlan R. Mason, and Omar K. Matar. "Multiphase flow applications of nonintrusive reduced-order models with Gaussian process emulation." Data-Centric Engineering 3 (2022). http://dx.doi.org/10.1017/dce.2022.19.
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Abstract Reduced-order models (ROMs) are computationally inexpensive simplifications of high-fidelity complex ones. Such models can be found in computational fluid dynamics where they can be used to predict the characteristics of multiphase flows. In previous work, we presented a ROM analysis framework that coupled compression techniques, such as autoencoders, with Gaussian process regression in the latent space. This pairing has significant advantages over the standard encoding–decoding routine, such as the ability to interpolate or extrapolate in the initial conditions’ space, which can provide predictions even when simulation data are not available. In this work, we focus on this major advantage and show its effectiveness by performing the pipeline on three multiphase flow applications. We also extend the methodology by using deep Gaussian processes as the interpolation algorithm and compare the performance of our two variations, as well as another variation from the literature that uses long short-term memory networks, for the interpolation.
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Gu, Mengyang, Xubo Liu, Xinyi Fang, and Sui Tang. "Scalable Marginalization of Correlated Latent Variables with Applications to Learning Particle Interaction Kernels." New England Journal of Statistics in Data Science, 2022, 1–15. http://dx.doi.org/10.51387/22-nejsds13.
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Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data, such as spatio-temporal or functional observations. We first introduce Gaussian processes (GPs) for modeling correlated data and highlight the computational challenge, where the computational complexity increases cubically fast along with the number of observations. We then review the connection between the state space model and GPs with Matérn covariance for temporal inputs. The Kalman filter and Rauch-Tung-Striebel smoother were introduced as a scalable marginalization technique for computing the likelihood and making predictions of GPs without approximation. We introduce recent efforts on extending the scalable marginalization idea to the linear model of coregionalization for multivariate correlated output and spatio-temporal observations. In the final part of this work, we introduce a novel marginalization technique to estimate interaction kernels and forecast particle trajectories. The computational progress lies in the sparse representation of the inverse covariance matrix of the latent variables, then applying conjugate gradient for improving predictive accuracy with large data sets. The computational advances achieved in this work outline a wide range of applications in molecular dynamic simulation, cellular migration, and agent-based models.