Javier González

David Janz, David R. Burt, Javier González

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter $ν$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $π$-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $ν>1$ and $d \geq 1$. Empirical validation suggests better performance and drastically improved computational scalablity compared with its predecessor, Improved GP-UCB.

Javier Gonzalez, Zhenwen Dai, Andreas Damianou et al.

Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimizing black-box functions where direct queries of the objective are expensive. In this paper we consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) which allows us to find the optimum of a latent function that can only be queried through pairwise comparisons, the so-called duels. PBO extends the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the winner of each duel by means of a Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments, showing that PBO needs drastically fewer comparisons for finding the optimum. According to our experiments, the way of modeling correlations in PBO is key in obtaining this advantage.

Javier González, Ivan Vujačić, Ernst Wit

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models in many branches of science they have not been the focus of systematic statistical analysis until recently. In this work we propose a general approach to estimate the parameters of systems of differential equations measured with noise. Our methodology is based on the maximization of the penalized likelihood where the system of differential equations is used as a penalty. To do so, we use a Reproducing Kernel Hilbert Space approach that allows to formulate the estimation problem as an unconstrained numeric maximization problem easy to solve. The proposed method is tested with synthetically simulated data and it is used to estimate the unobserved transcription factor CdaR in Steptomyes coelicolor using gene expression data of the genes it regulates.