On the impact of covariance functions in multi-objective Bayesian optimization for engineering design

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordMulti-objective Bayesian optimization (BO) is a highly useful class of methods that can effectively solve computationally expensive engineering design optimization problems with multiple objectives. However, the impact of covariance function, which is an important part of multi-objective BO, is rarely studied in the context of engineering optimization. We aim to shed light on this issue by performing numerical experiments on engineering design optimization problems, primarily low-fidelity problems so that we are able to statistically evaluate the performance of BO methods with various covariance functions. In this paper, we performed the study using a set of subsonic airfoil optimization cases as benchmark problems. Expected hypervolume improvement was used as the acquisition function to enrich the experimental design. Results show that the choice of the covariance function give a notable impact on the performance of multi-objective BO. In this regard, Kriging models with Matern-3/2 is the most robust method in terms of the diversity and convergence to the Pareto front that can handle problems with various complexities.Natural Environment Research Council (NERC

A Geometric Variational Approach to Bayesian Inference

We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the manifold can be identified with the positive orthant of the unit hypersphere in L2, and the Fisher-Rao metric reduces to the standard L2 metric. Exploiting such a Riemannian structure, we formulate the task of approximating the posterior distribution as a variational problem on the hypersphere based on the alpha-divergence. This provides a tighter lower bound on the marginal distribution when compared to, and a corresponding upper bound unavailable with, approaches based on the Kullback-Leibler divergence. We propose a novel gradient-based algorithm for the variational problem based on Frechet derivative operators motivated by the geometry of the Hilbert sphere, and examine its properties. Through simulations and real-data applications, we demonstrate the utility of the proposed geometric framework and algorithm on several Bayesian models

On the Use of Upper Trust Bounds in Constrained Bayesian Optimization Infill Criterion

In order to handle constrained optimization problems with a large number of design variables, a new approach has been proposed to address constraints in a surrogate-based optimization framework. This approach focuses on sequential enrichment using adaptive surrogate models based on Bayesian optimization approach, and Gaussian process models. A constraints criterion using the uncertainty estimation of the Gaussian process models is introduced. Different evolutions of the algorithm, based on the accuracy of the constraints surrogate models, are used for selecting the infill sample points. The resulting algorithm has been tested on the well known modified Branin optimization problem

The Variational Garrote

In this paper, we present a new variational method for sparse regression using $L_0$ regularization. The variational parameters appear in the approximate model in a way that is similar to Breiman's Garrote model. We refer to this method as the variational Garrote (VG). We show that the combination of the variational approximation and $L_0$ regularization has the effect of making the problem effectively of maximal rank even when the number of samples is small compared to the number of variables. The VG is compared numerically with the Lasso method, ridge regression and the recently introduced paired mean field method (PMF) (M. Titsias & M. L\'azaro-Gredilla., NIPS 2012). Numerical results show that the VG and PMF yield more accurate predictions and more accurately reconstruct the true model than the other methods. It is shown that the VG finds correct solutions when the Lasso solution is inconsistent due to large input correlations. Globally, VG is significantly faster than PMF and tends to perform better as the problems become denser and in problems with strongly correlated inputs. The naive implementation of the VG scales cubic with the number of features. By introducing Lagrange multipliers we obtain a dual formulation of the problem that scales cubic in the number of samples, but close to linear in the number of features.Comment: 26 pages, 11 figure

Characterization of Indoor Extremely Low Frequency and Low Frequency Electromagnetic Fields in the INMA-Granada Cohort

Objective: To characterize the exposure to electric fields and magnetic fields of non-ionizing radiation in the electromagnetic spectrum (15 Hz to 100 kHz) in the dwellings of children from the Spanish Environment and Childhood-“INMA” population-based birth cohort. Methodology: The study sample was drawn from the INMA-Granada cohort. Out of 300 boys participating in the 9–10 year follow-up, 123 families agreed to the exposure assessment at home and completed a specific ad hoc questionnaire gathering information on sources of non-ionizing radiation electric and magnetic fields inside the homes and on patterns of use. Long-term indoor measurements were carried out in the living room and bedroom. Results: Survey data showed a low exposure in the children's homes according to reference levels of the International Commission on Non-Ionizing Radiation Protection but with large differences among homes in mean and maximum values. Daytime electrostatic and magnetic fields were below the quantification limit in 78.6% (92 dwellings) and 92.3% (108 dwellings) of houses, with an arithmetic mean value (± standard deviation) of 7.31±9.32 V/m and 162.30±91.16 nT, respectively. Mean magnetic field values were 1.6 lower during the night than the day. Nocturnal electrostatic values were not measured. Exposure levels were influenced by the area of residence (higher values in urban/semi-urban versus rural areas), type of dwelling, age of dwelling, floor of the dwelling, and season. Conclusion: Given the greater sensitivity to extremely low-frequency electromagnetic fields of children and following the precautionary principle, preventive measures are warranted to reduce their exposure.This work was supported by the Spanish Ministry of Health (CIBERESP and FIS PI11/0610) and the Andalusia Regional Government, Council of Innovation, Science and Enterprise (Excellence Project P09-CTS-5488) and Council of Health (SAS PI-0675-2010)

Marker development for quality protein maize breeding and an interaction study between Opaque-2 and Ask2 genes

Quality Protein Maize (QPM) kernels contain twice the amounts of lysine and tryptophan compared to normal corn kernels. Although the opaque-2 (o2) mutation is the underlying cause of this beneficial change, other genes such as Aspartate kinase-2 (Ask2) affect the amino acid content in the endosperm to a lesser degree. To date, reports on the interaction between both loci are scarce and there are no high-throughput assays for the identification of the alleles of these genes. The objectives of this research were: 1) to study the interaction between the o2 and Ask2 genes with respect to the accumulation of amino acids in the endosperm in an F2 population, 2) to identify conserved SNPs into the o2 gene that can be used as markers, 3) to estimate the frequency of an SNP of Ask2 associated with the accumulation of lysine in the endosperm in CIMMYT germplasm, and 4) to develop high-throughput marker assays for these SNPs. The interaction study showed a preponderant effect of o2 on the accumulation of 11 amino acids (P ≤ 0.01). Ask2 appeared only to act with o2 to enhance marginally lysine, histidine and methionine levels in the double recessive homozygotes. Sequencing of amplicons at the o2 locus led to the identification of an SNP in exon 1 that discriminated all QPM (C) genotypes from non-QPM (T) genotypes. Validation of this SNP through KASP™ assays indicated that it was 92 % assertive in differentiating the o2 genotypes. In contrast, the frequency of the Ask2 SNP in CIMMYT QPM germplasm was low; however, an SSCP marker developed using this SNP detected five variants indicating that other unknown base changes may confer positive lysine-increasing responses. These markers could aid the marker-assisted selection of QPM cultivars

Efficacy and safety of autologous platelet rich plasma for the treatment of vascular ulcers in primary care: Phase III study

Background: Vascular ulcers are commonly seen in daily practice at all levels of care and have great impact at personal, professional and social levels with a high cost in terms of human and material resources. Given that the application of autologous platelet rich plasma has been shown to decrease healing times in various different studies in the hospital setting, we considered that it would be interesting to assess the efficacy and feasibility of this treatment in primary care. The objectives of this study are to assess the potential efficacy and safety of autologous platelet rich plasma for the treatment of venous ulcers compared to the conventional treatment (moist wound care) in primary care patients with chronic venous insufficiency (C, clinical class, E, aetiology, A, anatomy and P, pathophysiology classification C6). Design: We will conduct a phase III, open-label, parallel-group, multicentre, randomized study. The subjects will be 150 patients aged between 40 and 100 years of age with an at least 2-month history of a vascular venous ulcer assigned to ten primary care centres. For the treatment with autologous platelet rich plasma, all the following tasks will be performed in the primary care setting: blood collection, centrifugation, separation of platelet rich plasma, activation of coagulation adding calcium chloride and application of the PRP topically after gelification. The control group will receive standard moist wound care. The outcome variables to be measured at baseline, and at weeks 5 and 9 later include: reduction in the ulcer area, Chronic Venous Insufficiency Quality of Life Questionnaire score, and percentage of patients who require wound care only once a week. Discussion: The results of this study will be useful to improve the protocol for using platelet rich plasma in chronic vascular ulcers and to favour wider use of this treatment in primary care.This study can be undertaken thanks to the financial support of the Spanish Carlos III Health Institute. We are grateful for funding from the Department of Health and Consumer Affairs of the Government of the Basque Country, the Basque Health Service (Osakidetza) for the pilot support and the Ezkerraldea Enkarterri health region

Probabilistic machine learning and artificial intelligence.

How can a machine learn from experience? Probabilistic modelling provides a framework for understanding what learning is, and has therefore emerged as one of the principal theoretical and practical approaches for designing machines that learn from data acquired through experience. The probabilistic framework, which describes how to represent and manipulate uncertainty about models and predictions, has a central role in scientific data analysis, machine learning, robotics, cognitive science and artificial intelligence. This Review provides an introduction to this framework, and discusses some of the state-of-the-art advances in the field, namely, probabilistic programming, Bayesian optimization, data compression and automatic model discovery.The author acknowledges an EPSRC grant EP/I036575/1, the DARPA PPAML programme, a Google Focused Research Award for the Automatic Statistician and support from Microsoft Research.This is the author accepted manuscript. The final version is available from NPG at http://www.nature.com/nature/journal/v521/n7553/full/nature14541.html#abstract

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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