Finite-Dimensional Gaussian Approximation with Linear Inequality Constraints

López-Lopera, Andrés F.; Bachoc, François; Durrande, Nicolas; Roustant, Olivier

doi:10.1137/17m1153157

Cited by 60 publications

(106 citation statements)

References 28 publications

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“…Other possible potential future work is to derive the GP-Protein framework with multiple mRNA profiles (driving-forces) and multiple gap proteins (outputs). Finally, one may consider accounting for positiveness constraints into the GP framework using finite-dimensional Gaussian approximations (see, e.g., Maatouk and Bay, 2017;López-Lopera et al, 2018).…”

Section: Resultsmentioning

confidence: 99%

Physically-Inspired Gaussian Process Models for Post-Transcriptional Regulation in Drosophila

López-Lopera

Durrande²,

Álvarez

2021

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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The regulatory process of Drosophila is thoroughly studied for understanding a great variety of biological principles. While pattern-forming gene networks are analysed in the transcription step, post-transcriptional events (e.g. translation, protein processing) play an important role in establishing protein expression patterns and levels. Since the post-transcriptional regulation of Drosophila depends on spatiotemporal interactions between mRNAs and gap proteins, proper physically-inspired stochastic models are required to study the link between both quantities. Previous research attempts have shown that using Gaussian processes (GPs) and differential equations lead to promising predictions when analysing regulatory networks. Here we aim at further investigating two types of physically-inspired GP models based on a reaction-diffusion equation where the main difference lies in where the prior is placed. While one of them has been studied previously using protein data only, the other is novel and yields a simple approach requiring only the differentiation of kernel functions. In contrast to other stochastic frameworks, discretising the spatial space is not required here. Both GP models are tested under different conditions depending on the availability of gap gene mRNA expression data. Finally, their performances are assessed on a high-resolution dataset describing the blastoderm stage of the early embryo of Drosophila melanogaster

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Section: Resultsmentioning

confidence: 99%

Physically-Inspired Gaussian Process Models for Post-Transcriptional Regulation in Drosophila

López-Lopera

Durrande²,

Álvarez

2021

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…To do so, tensorized finite dimensional projection spaces could be considered (see e.g., [42] or [43]). If the functional inputs are functions from T ⊂ R d → R, then for tensorized projection spaces, the projection dimension is of the form p (1) × ... × p (1) , where p (1) , .…”

Section: Scope Of the Methodologymentioning

confidence: 99%

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Betancourt

Bachoc

Klein

et al. 2020

Reliability Engineering & System Safety

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et al.. Gaussian process metamodeling of functional-input code for coastal flood hazard assessment. Reliability Engineering and System Safety, Elsevier, 2020, 198, Abstract This paper investigates the construction of a metamodel for coastal flooding early warning at the peninsula of Gâvres, France. The code under study is an hydrodynamic model which receives time-varying maritime conditions as inputs. We concentrate on Gaussian pocess metamodels to emulate the behavior of the code. To model the inputs we make a projection of them onto a space of lower dimension. This setting gives rise to a model selection methodology which we use to calibrate four characteristics of our functional-input metamodel: (i) the family of basis functions to project the inputs; (ii) the projection dimension; (iii) the distance to measure similarity between functional input points; and (iv) the set of functional predictors to keep active. The proposed methodology seeks to optimize these parameters for metamodel predictability, at an affordable computational cost. A comparison to a dimensionality reduction approach based on the projection error of the input functions only showed that the latter may lead to unnecessarily large projection dimensions. We also assessed the adaptability of our methodology to changes in the number of training and validation points. The methodology proved its robustness by finding the optimal solution for most of the instances, while being computationally efficient.

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“…. , i n ), or by a more advanced rejection method called Rejection Sampling from the Mode (RSM) [19], or by more involved Markov Chain Monte Carlo (MCMC) methods [4,33,23]; see also their presentations in [18].…”

Section: Sample Zmentioning

confidence: 99%

“…of Z n . The density in (4) is arguably more complicated than a truncated Gaussian density function, for which many implemented algorithms are available, as discussed above when introducing the references [4,33,23,18]. In [26,22], several approximations of the distribution in (4) by multidimensional Gaussian distributions are presented (in particular, the Laplace and EP approximations, the variational method and the Kullback-Leibler method).…”

Section: Comparison With Classical Gpcmentioning

confidence: 99%

Gaussian process optimization with failures: classification and convergence proof

Bachoc

Helbert

Picheny³

2020

J Glob Optim

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We consider the optimization of a computer model where each simulation either fails or returns a valid output performance. We first propose a new joint Gaussian process model for classification of the inputs (computation failure or success) and for regression of the performance function. We provide results that allow for a computationally efficient maximum likelihood estimation of the covariance parameters, with a stochastic approximation of the likelihood gradient. We then extend the classical improvement criterion to our setting of joint classification and regression. We provide an efficient computation procedure for the extended criterion and its gradient. We prove the almost sure convergence of the global optimization algorithm following from this extended criterion. We also study the practical performances of this algorithm, both on simulated data and on a real computer model in the context of automotive fan design.

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Finite-Dimensional Gaussian Approximation with Linear Inequality Constraints

Cited by 60 publications

References 28 publications

Physically-Inspired Gaussian Process Models for Post-Transcriptional Regulation in Drosophila

Physically-Inspired Gaussian Process Models for Post-Transcriptional Regulation in Drosophila

Gaussian process metamodeling of functional-input code for coastal flood hazard assessment

Gaussian process optimization with failures: classification and convergence proof

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