Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

Optimizing the Correction of Memory Errors

People are always at risk of making errors when they attempt to retrieve information from memory. An important question is how to create the optimal learning conditions so that, over time, the correct information is learned and the number of mistakes declines. Feedback is a powerful tool, both for reinforcing new learning and correcting memory errors. In 5 experiments, I sought to understand the best procedures for administering feedback during learning. First, I evaluated the popular recommendation that feedback is most effective when given immediately, and I showed that this recommendation does not always hold when correcting errors made with educational materials in the classroom. Second, I asked whether immediate feedback is more effective in a particular case—when correcting false memories, or strongly-held errors that may be difficult to notice even when the learner is confronted with the feedback message. Third, I examined whether varying levels of learner motivation might help to explain cross-experimental variability in feedback timing effects: Are unmotivated learners less likely to benefit from corrective feedback, especially when it is administered at a delay? Overall, the results revealed that there is no best “one-size-fits-all” recommendation for administering feedback; the optimal procedure depends on various characteristics of learners and their errors. As a package, the data are consistent with the spacing hypothesis of feedback timing, although this theoretical account does not successfully explain all of the data in the larger literature.