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Obtaining solutions to optimal transportation (OT) problems is typically intractable when marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d. sampling, and this has shown convergence as the sample size increases. However, obtaining OT solutions with large sample sizes requires intensive computation effort, which can be prohibitive in practice. In this paper, we propose an algorithm for calculating discretizations with a given number of weighted points for marginal distributions by minimizing the (entropy-regularized) Wasserstein distance and providing bounds on the performance. The results suggest that our plans are comparable to those obtained with much larger numbers of i.i.d. samples and are more efficient than existing alternatives. Moreover, we propose a local, parallelizable version of such discretizations for applications, which we demonstrate by approximating adorable images. 

Children do not just learn in the classroom. They engage in “informal learning” every day just by spending time with their family and peers. However, while researchers know this occurs, less is known about the science of this learning—how this learning works. This is so because investigators lack access to those moments of informal learning. In this mini-review we present a technical solution: a mobile-based research platform called “Talk of the Town” that will provide a window into children’s informal learning. The tool will be open to all researchers and educators and is flexibly adaptable to these needs. It allows access to data that have never been studied before, providing a means for developing and testing vast educational interventions, and providing access to much more diverse samples than are typically studied in laboratories, homes, and science museums. The review details the promise and challenges associated with these new methods of data collection and family engagement in STEM learning sciences. 

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference. 

Abstract State-of-the-art deep-learning systems use decision rules that are challenging for humans to model. Explainable AI (XAI) attempts to improve human understanding but rarely accounts for how people typically reason about unfamiliar agents. We propose explicitly modelling the human explainee via Bayesian teaching, which evaluates explanations by how much they shift explainees’ inferences toward a desired goal. We assess Bayesian teaching in a binary image classification task across a variety of contexts. Absent intervention, participants predict that the AI’s classifications will match their own, but explanations generated by Bayesian teaching improve their ability to predict the AI’s judgements by moving them away from this prior belief. Bayesian teaching further allows each case to be broken down into sub-examples (here saliency maps). These sub-examples complement whole examples by improving error detection for familiar categories, whereas whole examples help predict correct AI judgements of unfamiliar cases. 

In studies involving human subjects, voluntary participation may lead to sampling bias, thus limiting the generalizability of findings. This effect may be especially pronounced in developmental studies, where parents serve as both the primary environmental input and decision maker of whether their child participates in a study. We present a novel empirical and modeling approach to estimate how parental consent may bias measurements of children’s behavior. Specifically, we coupled naturalistic observations of parent–child interactions in public spaces with a behavioral test with children, and used modeling methods to impute the behavior of children who did not participate. Results showed that parents’ tendency to use questions to teach was associated with both children’s behavior in the test and parents’ tendency to participate. Exploiting these associations with a model-based multiple imputation and a propensity score–matching procedure, we estimated that the means of the participating and not-participating groups could differ as much as 0.23 standard deviations for the test measurements, and standard deviations themselves are likely underestimated. These results suggest that ignoring factors associated with consent may lead to systematic biases when generalizing beyond lab samples, and the proposed general approach provides a way to estimate these biases in future research. 

Abstract What maximizes instructional impact in early childhood? We propose a simple intervention employing “Pedagogical Questions”. We explore whether swapping some instructional language with questions in psychosomatic storybooks improves preschoolers’ memory, learning, and generalization. Seventy-two preschoolers were randomly assigned to one of three conditions and were read storybooks employing eitherDirect Instruction,Pedagogical Questions, orControlcontent. Posttest measures of psychosomatic understanding, judgments about the possibility of psychosomatic events, and memory for storybook details showed that children in thePedagogical Questionscondition demonstrated greater memory for relevant storybook details and improved psychosomatic understanding. Our results suggest that pedagogical questions are a relatively simple educational manipulation to improve memory, learning, and transfer of theory-rich content.