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

Black-Box α-divergence minimization

Black-box alpha (BB-α) is a new approximate inference method based on the minimization of α-divergences. BB-α scales to large datasets because it can be implemented using stochastic gradient descent. BB-α can be applied to complex probabilistic models with little effort since it only requires as input the likelihood function and its gradients. These gradients can be easily obtained using automatic differentiation. By changing the divergence parameter α, the method is able to interpolate between variational Bayes (VB) (α → 0) and an algorithm similar to expectation propagation (EP) (α = 1). Experiments on probit regression and neural network regression and classification problems show that BB-a with non-standard settings of α, such as α = 0.5, usually produces better predictions than with α → 0 (VB) or α = 1 (EP).JMHL acknowledges support from the Rafael del Pino Foundation. YL thanks the Schlumberger Foundation Faculty for the Future fellowship on supporting her PhD study. MR acknowledges support from UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis. TDB thanks Google for funding his European Doctoral Fellowship. DHL acknowledge support from Plan National I+D+i, Grant TIN2013-42351-P and TIN2015- 70308-REDT, and from Comunidad de Madrid, Grant S2013/ICE-2845 CASI-CAM-CM. RET thanks EPSRC grant #EP/L000776/1 and #EP/M026957/1

Stellar equilibrium configurations of white dwarfs in the f(R,T)f(R,T) gravity

In this work we investigate the equilibrium configurations of white dwarfs in a modified gravity theory, na\-mely, $f(R,T)$ gravity, for which $R$ and $T$ stand for the Ricci scalar and trace of the energy-momentum tensor, respectively. Considering the functional form $f(R,T)=R+2\lambda T$, with $\lambda$ being a constant, we obtain the hydrostatic equilibrium equation for the theory. Some physical properties of white dwarfs, such as: mass, radius, pressure and energy density, as well as their dependence on the parameter $\lambda$ are derived. More massive and larger white dwarfs are found for negative values of $\lambda$ when it decreases. The equilibrium configurations predict a maximum mass limit for white dwarfs slightly above the Chandrasekhar limit, with larger radii and lower central densities when compared to standard gravity outcomes. The most important effect of $f(R,T)$ theory for massive white dwarfs is the increase of the radius in comparison with GR and also $f(R)$ results. By comparing our results with some observational data of massive white dwarfs we also find a lower limit for $\lambda$, namely, $\lambda >- 3\times 10^{-4}$.Comment: To be published in EPJ

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

Expressive and Instrumental Offending: Reconciling the Paradox of Specialisation and Versatility

Although previous research into specialisation has been dominated by the debate over the existence of specialisation versus versatility, it is suggested that research needs to move beyond the restrictions of this dispute. The current study explores the criminal careers of 200 offenders based on their criminal records, obtained from a police database in the North West of England, aiming to understand the patterns and nature of specialisation by determining the presence of differentiation within their general offending behaviours and examining whether the framework of Expressive and Instrumental offending styles can account for any specialised tendencies that emerge. Fifty-eight offences were subjected to Smallest Space Analysis. Results revealed that a model of criminal differentiation could be identified and that any specialisation is represented in terms of Expressive and Instrumental offending styles

Soil microbiome structure and function in ecopiles used to remediate petroleum-contaminated soil

The soil microbiome consists of a vast variety of microorganisms which contribute to essential ecosystem services including nutrient recycling, protecting soil structure, and pathogen suppression. Recalcitrant organic compounds present in soils contaminated with fuel oil can lead to a decrease in functional redundancy within soil microbiomes. Ecopiling is a passive bioremediation technique involving biostimulation of indigenous hydrocarbon degraders, bioaugmentation through inoculation with known petroleum-degrading consortia, and phytoremediation. The current study investigates the assemblage of soil microbial communities and pollutant-degrading potential in soil undergoing the Ecopiling process, through the amplicon marker gene and metagenomics analysis of the contaminated soil. The analysis of key community members including bacteria, fungi, and nematodes revealed a surprisingly diverse microbial community composition within the contaminated soil. The soil bacterial community was found to be dominated by Alphaproteobacteria (60–70%) with the most abundant genera such as Lysobacter, Dietzia, Pseudomonas, and Extensimonas. The fungal community consisted mainly of Ascomycota (50–70% relative abundance). Soil sequencing data allowed the identification of key enzymes involved in the biodegradation of hydrocarbons, providing a novel window into the function of individual bacterial groups in the Ecopile. Although the genus Lysobacter was identified as the most abundant bacterial genus (11–46%) in all of the contaminated soil samples, the metagenomic data were unable to confirm a role for this group in petrochemical degradation. Conversely, genera with relatively low abundance such as Dietzia (0.4–9.0%), Pusillimonas (0.7–2.3%), and Bradyrhizobium (0.8–1.8%) did possess genes involved in aliphatic or aromatic compound degradation