Convergence of sparse variational inference in gaussian processes regression

Gaussian processes are distributions over functions that are versatile and mathematically convenient priors in Bayesian modelling. However, their use is often impeded for data with large numbers of observations, N, due to the cubic (in N) cost of matrix operations used in exact inference. Many solutions have been proposed that rely on M << N inducing variables to form an approximation at a cost of O(NM^2). While the computational cost appears linear in N, the true complexity depends on how M must scale with N to ensure a certain quality of the approximation. In this work, we investigate upper and lower bounds on how M needs to grow with N to ensure high quality approximations. We show that we can make the KL-divergence between the approximate model and the exact posterior arbitrarily small for a Gaussian-noise regression model with M<<N. Specifically, for the popular squared exponential kernel and D-dimensional Gaussian distributed covariates, M=O((log N)^D) suffice and a method with an overall computational cost of O(N(log N)^{2D}(\log\log N)^2) can be used to perform inference

Bayesian Optimization Approaches for Massively Multi-modal Problems

The optimization of massively multi-modal functions is a challenging task, particularly for problems where the search space can lead the op- timization process to local optima. While evolutionary algorithms have been extensively investigated for these optimization problems, Bayesian Optimization algorithms have not been explored to the same extent. In this paper, we study the behavior of Bayesian Optimization as part of a hybrid approach for solving several massively multi-modal functions. We use well-known benchmarks and metrics to evaluate how different variants of Bayesian Optimization deal with multi-modality.TIN2016-78365-

Differential regulation of a MYB transcription factor is correlated with transgenerational epigenetic inheritance of trichome density in Mimulus guttatus

This is the peer reviewed version of the following article: Scoville, A. G., Barnett, L. L., Bodbyl-Roels, S., Kelly, J. K. and Hileman, L. C. (2011), Differential regulation of a MYB transcription factor is correlated with transgenerational epigenetic inheritance of trichome density in Mimulus guttatus. New Phytologist, 191: 251–263. doi:10.1111/j.1469-8137.2011.03656.x, which has been published in final form at http://doi.org/10.1111/j.1469-8137.2011.03656.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Epigenetic inheritance, transgenerational transmission of traits not proximally determined by DNA sequence, has been linked to transmission of chromatin modifications and gene regulation, which are known to be sensitive to environmental factors. Mimulus guttatus increases trichome (plant hair) density in response to simulated herbivore damage. Increased density is expressed in progeny even if progeny do not experience damage. To better understand epigenetic inheritance of trichome production, we tested the hypothesis that candidate gene expression states are inherited in response to parental damage. Using M. guttatus recombinant inbred lines, offspring of leaf-damaged and control plants were raised without damage. Relative expression of candidate trichome development genes was measured in offspring. Line and parental damage effects on trichome density were measured. Associations between gene expression, trichome density, and response to parental damage were determined. We identified M. guttatus MYB MIXTA-like 8 as a possible negative regulator of trichome development. We found that parental leaf damage induces down-regulation of MYB MIXTA-like 8 in progeny, which is associated with epigenetically inherited increased trichome density. Our results link epigenetic transmission of an ecologically important trait with differential gene expression states – providing insight into a mechanism underlying environmentally induced ‘soft inheritance’

Bayesian optimization for materials design

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality

Quality or equality? The Norwegian experience with medical monopolies

BACKGROUND: In order to maintain both quality and efficiency of health services in a small country with a scattered population, Norway established a monopoly system for 38 highly specialized medical services. The geographical distributions of these services, which are provided by one or two university hospitals only, were analysed. METHODS: The counties of residence for 2 711 patients admitted for the first time in 2001 to these 31 monopolies and 7 duopolies were identified. RESULTS: The general tendency observed was that with increasing distance from residential home to monopoly hospitals there was a declining coverage of these health services. The same pattern was found even with regard to explicit diagnoses or treatments such as organ transplantations (except renal transplantations). Duopolies seemed to yield a more even geographical distribution of the services. CONCLUSION: Monopolies may serve as a useful means for maintaining quality in highly specialized medical services, but seem to have an inherent tendency to do this at the expense of geographical equality

Energy cost and return for hunting in African wild dogs and Cheetahs

African wild dogs (Lycaon pictus) are reported to hunt with energetically costly long chase distances. We used high-resolution GPS and inertial technology to record 1,119 high-speed chases of all members of a pack of six adult African wild dogs in northern Botswana. Dogs performed multiple short, high-speed, mostly unsuccessful chases to capture prey, while cheetahs (Acinonyx jubatus) undertook even shorter, higher-speed hunts. We used an energy balance model to show that the energy return from group hunting and feeding substantially outweighs the cost of multiple short chases, which indicates that African wild dogs are more energetically robust than previously believed. Comparison with cheetah illustrates the trade-off between sheer athleticism and high individual kill rate characteristic of cheetahs, and the energetic robustness of frequent opportunistic group hunting and feeding by African wild dogs

On Bayesian Search for the Feasible Space Under Computationally Expensive Constraints

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of exploration would be prohibitive. Bayesian search is data-efficient for such problems: starting from a small dataset, the central concept is to use Bayesian models of constraints with an acquisition function to locate promising solutions that may improve predictions of feasibility when the dataset is augmented. At the end of this sequential active learning approach with a limited number of expensive evaluations, the models can accurately predict the feasibility of any solution obviating the need for full simulations. In this paper, we propose a novel acquisition function that combines the probability that a solution lies at the boundary between feasible and infeasible spaces (representing exploitation) and the entropy in predictions (representing exploration). Experiments confirmed the efficacy of the proposed function

Multiple reassortment events in the evolutionary history of H1N1 influenza A virus since 1918

The H1N1 subtype of influenza A virus has caused substantial morbidity and mortality in humans, first documented in the global pandemic of 1918 and continuing to the present day. Despite this disease burden, the evolutionary history of the A/H1N1 virus is not well understood, particularly whether there is a virological basis for several notable epidemics of unusual severity in the 1940s and 1950s. Using a data set of 71 representative complete genome sequences sampled between 1918 and 2006, we show that segmental reassortment has played an important role in the genomic evolution of A/H1N1 since 1918. Specifically, we demonstrate that an A/H1N1 isolate from the 1947 epidemic acquired novel PB2 and HA genes through intra-subtype reassortment, which may explain the abrupt antigenic evolution of this virus. Similarly, the 1951 influenza epidemic may also have been associated with reassortant A/H1N1 viruses. Intra-subtype reassortment therefore appears to be a more important process in the evolution and epidemiology of H1N1 influenza A virus than previously realized

Computer Controlled Automated Assay for Comprehensive Studies of Enzyme Kinetic Parameters

Stability and biological activity of proteins is highly dependent on their physicochemical environment. The development of realistic models of biological systems necessitates quantitative information on the response to changes of external conditions like pH, salinity and concentrations of substrates and allosteric modulators. Changes in just a few variable parameters rapidly lead to large numbers of experimental conditions, which go beyond the experimental capacity of most research groups. We implemented a computer-aided experimenting framework (“robot lab assistant”) that allows us to parameterize abstract, human-readable descriptions of micro-plate based experiments with variable parameters and execute them on a conventional 8 channel liquid handling robot fitted with a sensitive plate reader. A set of newly developed R-packages translates the instructions into machine commands, executes them, collects the data and processes it without user-interaction. By combining script-driven experimental planning, execution and data-analysis, our system can react to experimental outcomes autonomously, allowing outcome-based iterative experimental strategies. The framework was applied in a response-surface model based iterative optimization of buffer conditions and investigation of substrate, allosteric effector, pH and salt dependent activity profiles of pyruvate kinase (PYK). A diprotic model of enzyme kinetics was used to model the combined effects of changing pH and substrate concentrations. The 8 parameters of the model could be estimated from a single two-hour experiment using nonlinear least-squares regression. The model with the estimated parameters successfully predicted pH and PEP dependence of initial reaction rates, while the PEP concentration dependent shift of optimal pH could only be reproduced with a set of manually tweaked parameters. Differences between model-predictions and experimental observations at low pH suggest additional protonation-sites at the enzyme or substrates critical for enzymatic activity. The developed framework is a powerful tool to investigate enzyme reaction specifics and explore biological system behaviour in a wide range of experimental conditions