Corrected kriging update formulae for batch-sequential data assimilation

Recently, a lot of effort has been spent in the efficient computation of kriging predictors when observations are assimilated sequentially. In particular, kriging update formulae enabling significant computational savings were derived. Taking advantage of the previous kriging mean and variance computations helps avoiding a costly matrix inversion when adding one observation to the TeX already available ones. In addition to traditional update formulae taking into account a single new observation, Emery (2009) proposed formulae for the batch-sequential case, i.e. when TeX new observations are simultaneously assimilated. However, the kriging variance and covariance formulae given in Emery (2009) for the batch-sequential case are not correct. In this paper, we fix this issue and establish correct expressions for updated kriging variances and covariances when assimilating observations in parallel. An application in sequential conditional simulation finally shows that coupling update and residual substitution approaches may enable significant speed-ups.

Distance-based kriging relying on proxy simulations for inverse conditioning

Let us consider a large set of candidate parameter fields, such as hydraulic conductivity maps, on which we can run an accurate forward flow and transport simulation. We address the issue of rapidly identifying a subset of candidates whose response best match a reference response curve. In order to keep the number of calls to the accurate flow simulator computationally tractable, a recent distance-based approach relying on fast proxy simulations is revisited, and turned into a non-stationary kriging method where the covariance kernel is obtained by combining a classical kernel with the proxy. Once the accurate simulator has been run for an initial subset of parameter fields and a kriging metamodel has been inferred, the predictive distributions of misfits for the remaining parameter fields can be used as a guide to select candidate parameter fields in a sequential way. The proposed algorithm, Proxy-based Kriging for Sequential Inversion (ProKSI), relies on a variant of the Expected Improvement, a popular criterion for kriging-based global optimization. A statistical benchmark of ProKSI’s performances illustrates the efficiency and the robustness of the approach when using different kinds of proxies.

A benchmark of kriging-based infill criteria for noisy optimization

Responses of many real-world problems can only be evaluated perturbed by noise. In order to make an efficient optimization of these problems possible, intelligent optimization strategies successfully coping with noisy evaluations are required. In this article, a comprehensive review of existing kriging-based methods for the optimization of noisy functions is provided. In summary, ten methods for choosing the sequential samples are described using a unified formalism. They are compared on analytical benchmark problems, whereby the usual assumption of homoscedastic Gaussian noise made in the underlying models is meet. Different problem configurations (noise level, maximum number of observations, initial number of observations) and setups (covariance functions, budget, initial sample size) are considered. It is found that the choices of the initial sample size and the covariance function are not critical. The choice of the method, however, can result in significant differences in the performance. In particular, the three most intuitive criteria are found as poor alternatives. Although no criterion is found consistently more efficient than the others, two specialized methods appear more robust on average.

KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging

Several strategies relying on kriging have recently been proposed for adaptively estimating contour lines and excursion sets of functions under severely limited evaluation budget. The recently released R package KrigInv 3 is presented and offers a sound implementation of various sampling criteria for those kinds of inverse problems. KrigInv is based on the DiceKriging package, and thus benefits from a number of options concerning the underlying kriging models. Six implemented sampling criteria are detailed in a tutorial and illustrated with graphical examples. Different functionalities of KrigInv are gradually explained. Additionally, two recently proposed criteria for batch-sequential inversion are presented, enabling advanced users to distribute function evaluations in parallel on clusters or clouds of machines. Finally, auxiliary problems are discussed. These include the fine tuning of numerical integration and optimization procedures used within the computation and the optimization of the considered criteria.

Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package

Kriging-based optimization relying on noisy evaluations of complex systems has recently motivated contributions from various research communities. Five strategies have been implemented in the DiceOptim package. The corresponding functions constitute a user-friendly tool for solving expensive noisy optimization problems in a sequential framework, while offering some flexibility for advanced users. Besides, the implementation is done in a unified environment, making this package a useful device for studying the relative performances of existing approaches depending on the experimental setup. An overview of the package structure and interface is provided, as well as a description of the strategies and some insight about the implementation challenges and the proposed solutions. The strategies are compared to some existing optimization packages on analytical test functions and show promising performances.

Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function  f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this article we introduce several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Hypercoagulation and hyperkinetic blood pressure indicative of physiological loss-of-control despite behavioural control in Africans: The SABPA study.

OBJECTIVES A dissociation between behavioural (in-control) and physiological parameters (indicating loss-of-control) is associated with cardiovascular risk in defensive coping (DefS) Africans. We evaluated relationships between DefS, sub-clinical atherosclerosis, low-grade inflammation and hypercoagulation in a bi-ethnic sex cohort. METHODS Black (Africans) and white Africans (Caucasians) (n = 375; aged 44.6 ± 9.7 years) were included. Ambulatory BP, vascular structure (left carotid cross-sectional wall area (L-CSWA) and plaque counts), and markers of coagulation and inflammation were quantified. Ethnicity/coping style interaction was revealed only in DefS participants. RESULTS A hypertensive state, less plaque, low-grade inflammation, and hypercoagulation were more prevalent in DefS Africans (27-84%) than DefS Caucasians (18-41%). Regression analyses demonstrated associations between L-CSWA and 24 hour systolic BP (R(2) = 0.38; β = 0.78; p < 0.05) in DefS African men but not in DefS African women or Caucasians. No associations between L-CSWA and coagulation markers were evident. CONCLUSION Novel findings revealed hypercoagulation, low-grade inflammation and hyperkinetic BP (physiological loss-of-control responses) in DefS African men. Coupled to a self-reported in-control DefS behavioural profile, this reflects dissociation between behaviour and physiology. It may explain changes in vascular structure, increasing cerebrovascular disease risk in a state of hyper-vigilant coping.

Urinary Biomarkers Indicative of Apoptosis and Acute Kidney Injury in the Critically Ill.

BACKGROUND Apoptosis is a key mechanism involved in ischemic acute kidney injury (AKI), but its role in septic AKI is controversial. Biomarkers indicative of apoptosis could potentially detect developing AKI prior to its clinical diagnosis. METHODS As a part of the multicenter, observational FINNAKI study, we performed a pilot study among critically ill patients who developed AKI (n = 30) matched to critically ill patients without AKI (n = 30). We explored the urine and plasma levels of cytokeratin-18 neoepitope M30 (CK-18 M30), cell-free DNA, and heat shock protein 70 (HSP70) at intensive care unit (ICU) admission and 24h thereafter, before the clinical diagnosis of AKI defined by the Kidney Disease: Improving Global Outcomes -creatinine and urine output criteria. Furthermore, we performed a validation study in 197 consecutive patients in the FINNAKI cohort and analyzed the urine sample at ICU admission for CK-18 M30 levels. RESULTS In the pilot study, the urine or plasma levels of measured biomarkers at ICU admission, at 24h, or their maximum value did not differ significantly between AKI and non-AKI patients. Among 20 AKI patients without severe sepsis, the urine CK-18 M30 levels were significantly higher at 24h (median 116.0, IQR [32.3-233.0] U/L) than among those 20 patients who did not develop AKI (46.0 [0.0-54.0] U/L), P = 0.020. Neither urine cell-free DNA nor HSP70 levels significantly differed between AKI and non-AKI patients regardless of the presence of severe sepsis. In the validation study, urine CK-18 M30 level at ICU admission was not significantly higher among patients developing AKI compared to non-AKI patients regardless of the presence of severe sepsis or CKD. CONCLUSIONS Our findings do not support that apoptosis detected with CK-18 M30 level would be useful in assessing the development of AKI in the critically ill. Urine HSP or cell-free DNA levels did not differ between AKI and non-AKI patients.