This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due to many kernels being evaluated simultaneously by our VBKS algorithm, we show that the variational lower bound of the log-marginal likelihood can be decomposed into an additive form such that each additive term depends only on a disjoint subset of the variational variables and can thus be optimized independently. Stochastic optimization is then used to maximize the variational lower bound by iteratively improving the variational approximation of the exact posterior belief via stochastic gradient ascent, which incurs constant time per iteration and hence scales to big data. We empirically evaluate the performance of our VBKS algorithm on synthetic and massive real-world datasets.
A large body of research consistently found cultural differences in cognition between Westerners and East Asians. We undertook a study to explore whether culture-specific thinking models may influence how German and Chinese children understand fairy tales. By transferring the established theoretical framework of individualism versus collectivism from cultural psychology to literary studies, we hypothesize that readers in western Europe prefer an individualistic-oriented thinking model for character evaluation, adventurous attitude to plot development, as well as concrete time and spatial perception; by contrast, their counterparts in East Asia use social-oriented interpretation styles for character judgment, a self-restrained attitude towards plot development, and a symbolic time and spatial imagination. The method we used relies on questionnaires, item-based analysis and factor analysis to learn about the most salient dimensions for cross-cultural story comprehension. We found differences in all three dimensions of story comprehension, namely character evaluation, plot development, and time/space imagination. The results reveal how culture shapes the way we read and point to the important role of embedded schematic knowledge for story comprehension.
This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learning criterion. Then, we exploit a relaxed form of submodularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for active learning of MOGP and single-output GP models.
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