Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. The experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

Language models have demonstrated the ability to generate highly fluent text; however, it remains unclear whether their output retains coherent high-level structure (e.g., story progression). Here, we propose to apply a statistical tool, model criticism in latent space, to evaluate the high-level structure of the generated text. Model criticism compares the distributions between real and generated data in a latent space obtained according to an assumptive generative process. Different generative processes identify specific failure modes of the underlying model. We perform experiments on three representative aspects of high-level discourse -- coherence, coreference, and topicality -- and find that transformer-based language models are able to capture topical structures but have a harder time maintaining structural coherence or modeling coreference.

Constrained random test generation is one of the most widely adopted methods for generating stimuli for simulation-based verification. Randomness leads to test diversity, but tests tend to repeatedly exercise the same design logic. Constraints are written (typically manually) to bias random tests towards interesting, hard-to-reach, and yet-untested logic. However, as verification progresses, most constrained random tests yield little to no effect on functional coverage. If stimuli generation consumes significantly less resources than simulation, then a better approach involves randomly generating a large number of tests, selecting the most effective subset, and only simulating that subset. In this paper, we introduce a novel method for automatic constraint extraction and test selection. This method, which we call coverage-directed test selection, is based on supervised learning from coverage feedback. Our method biases selection towards tests that have a high probability of increasing functional coverage, and prioritises them for simulation. We show how coverage-directed test selection can reduce manual constraint writing, prioritise effective tests, reduce verification resource consumption, and accelerate coverage closure on a large, real-life industrial hardware design.

We propose a general framework to design posterior sampling methods for model-based RL. We show that the proposed algorithms can be analyzed by reducing regret to Hellinger distance in conditional probability estimation. We further show that optimistic posterior sampling can control this Hellinger distance, when we measure model error via data likelihood. This technique allows us to design and analyze unified posterior sampling algorithms with state-of-the-art sample complexity guarantees for many model-based RL settings. We illustrate our general result in many special cases, demonstrating the versatility of our framework.

The cooperative Multi-A gent R einforcement Learning (MARL) with permutation invariant agents framework has achieved tremendous empirical successes in real-world applications. Unfortunately, the theoretical understanding of this MARL problem is lacking due to the curse of many agents and the limited exploration of the relational reasoning in existing works. In this paper, we verify that the transformer implements complex relational reasoning, and we propose and analyze model-free and model-based offline MARL algorithms with the transformer approximators. We prove that the suboptimality gaps of the model-free and model-based algorithms are independent of and logarithmic in the number of agents respectively, which mitigates the curse of many agents. These results are consequences of a novel generalization error bound of the transformer and a novel analysis of the Maximum Likelihood Estimate (MLE) of the system dynamics with the transformer. Our model-based algorithm is the first provably efficient MARL algorithm that explicitly exploits the permutation invariance of the agents. Our improved generalization bound may be of independent interest and is applicable to other regression problems related to the transformer beyond MARL.

The ability to generate synthetic data has a variety of use cases across different domains. In education research, there is a growing need to have access to synthetic data to test certain concepts and ideas. In recent years, several deep learning architectures were used to aid in the generation of synthetic data - but with varying results. In the education context, the sophistication of implementing different models requiring large datasets is becoming very important. This study aims to compare the application of synthetic tabular data generation between a probabilistic model specifically a Bayesian Network, and a deep learning model, specifically a Generative Adversarial Network using a classification task. The results of this study indicate that synthetic tabular data generation is better suited for the education context using probabilistic models (overall accuracy of 75%) than deep learning architecture (overall accuracy of 38%) because of probabilistic interdependence. Lastly, we recommend that other data types, should be explored and evaluated for their application in generating synthetic data for education use cases.

Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to the posterior approximation's error. Meanwhile, alternatives to MC integration tend to be more expensive or biased. In this work, we experimentally show that the key to good MC-approximated predictive distributions is the quality of the approximate posterior itself. However, previous methods for obtaining accurate posterior approximations are expensive and non-trivial to implement. We, therefore, propose to refine Gaussian approximate posteriors with normalizing flows. When applied to last-layer BNNs, it yields a simple \emph{post hoc} method for improving pre-existing parametric approximations. We show that the resulting posterior approximation is competitive with even the gold-standard full-batch Hamiltonian Monte Carlo.

This research aims to develop machine learning models for students academic performance and study strategies prediction which could be generalized to all courses in higher education. Key learning attributes (intrinsic, extrinsic, autonomy, relatedness, competence, and self-esteem) essential for students learning process were used in building the models. Determining the broad effect of these attributes on students' academic performance and study strategy is the center of our interest. To investigate this, we used Scikit-learn in python to build five machine learning models (Decision Tree, K-Nearest Neighbour, Random Forest, Linear/Logistic Regression, and Support Vector Machine) for both regression and classification tasks to perform our analysis. The models were trained, evaluated, and tested for accuracy using 924 university dentistry students' data collected by Chilean authors through quantitative research design. A comparative analysis of the models revealed that the tree-based models such as the random forest (with prediction accuracy of 94.9%) and decision tree show the best results compared to the linear, support vector, and k-nearest neighbours. The models built in this research can be used in predicting student performance and study strategy so that appropriate interventions could be implemented to improve student learning progress. Thus, incorporating strategies that could improve diverse student learning attributes in the design of online educational systems may increase the likelihood of students continuing with their learning tasks as required. Moreover, the results show that the attributes could be modelled together and used to adapt/personalize the learning process.

Speakers repeat constructions frequently in dialogue. Due to their peculiar information-theoretic properties, repetitions can be thought of as a strategy for cost-effective communication. In this study, we focus on the repetition of lexicalised constructions -- i.e., recurring multi-word units -- in English open-domain spoken dialogues. We hypothesise that speakers use construction repetition to mitigate information rate, leading to an overall decrease in utterance information content over the course of a dialogue. We conduct a quantitative analysis, measuring the information content of constructions and that of their containing utterances, estimating information content with an adaptive neural language model. We observe that construction usage lowers the information content of utterances. This facilitating effect (i) increases throughout dialogues, (ii) is boosted by repetition, (iii) grows as a function of repetition frequency and density, and (iv) is stronger for repetitions of referential constructions.

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.