Efficient Bayesian Optimization for Target Vector Estimation

We consider the problem of estimating a target vector by querying an unknown multi-output function which is stochastic and expensive to evaluate. Through sequential experimental design the aim is to minimize the squared Euclidean distance between the output of the function and the target vector. Applying standard single-objective Bayesian optimization to this problem is both wasteful, since individual output components are never observed, and imprecise since the predictive distribution for new inputs will be symmetric and have negative support. We address this issue by proposing a Gaussian process model that considers the individual function outputs and derive a distribution over the resulting 2-norm. Furthermore we derive computationally efficient acquisition functions and evaluate the resulting optimization framework on several synthetic problems and a real-world problem. The results demonstrate a significant improvement over Bayesian optimization based on both standard and warped Gaussian processes

Assumptions and efficiency in Gaussian process modelling

No abstract available

Nephrocalcinosis in rabbits – a case study

Varying degrees of kidney calcification have been found in New Zealand White rabbits used for in vitro  physiological studies in our animal unit over the past 4 years. Histologically, the lesion is characterised by  the deposition of calcified deposits inside tubular structures in the cortical and (cortico)medullary region  of the rabbit kidney. The kidney calcifications could be so severe, that the isolation of renal resistance vessels,  dissected for intended in vitro studies, was no longer possible. Because 40% of the rabbit kidneys had  to be discarded at the start of the year 2000, since then, a routine histological check of all rabbit kidneys  used until 1 January 2004, was performed. The yearly incidence of numbers of animals having kidneys  with calcified deposits in cortex and/or medulla as compared to the total number of rabbits used, ranged  from 16 % to 63%. Kidney calcifications were seen in both sexes. A large interindividual variation in the  degree of nephrocalcinosis was found. Of the dietary factors involved in the ethiopathogenesis in rats,  phosphorus (P) concentration is an important determinant for kidney calcification. Also in rabbits it has  been proven that dietary phosphate supplements and increased dietary P-levels in semipurified diets will  lead to kidney calcifications in higher frequencies and degrees of severity. The recommended dietary Plevel  for growing rabbits is 0.22%, according to the National Research Council guidelines of 1977.  Commercial, natural-ingredient rabbit diets always have dietary P levels that exceed 0.22%. It is therefore  considered recommendable to lower dietary P concentration in marketed rabbit diets, in order to reduce or  prevent nephrocalcinosis in rabbits.