The data augmentation (DA) algorithms are popular Markov chain Monte Carlo (MCMC) algorithms often used for sampling from intractable probability distributions. This review article comprehensively surveys DA MCMC algorithms, highlighting their theoretical foundations, methodological implementations, and diverse applications in frequentist and Bayesian statistics. The article discusses tools for studying the convergence properties of DA algorithms. Furthermore, it contains various strategies for accelerating the speed of convergence of the DA algorithms, different extensions of DA algorithms and outlines promising directions for future research. This paper aims to serve as a resource for researchers and practitioners seeking to leverage data augmentation techniques in MCMC algorithms by providing key insights and synthesizing recent developments.

Leveraging human preferences for steering the behavior of Large Language Models (LLMs) has demonstrated notable success in recent years. Nonetheless, data selection and labeling are still a bottleneck for these systems, particularly at large scale. Hence, selecting the most informative points for acquiring human feedback may considerably reduce the cost of preference labeling and unleash the further development of LLMs. Bayesian Active Learning provides a principled framework for addressing this challenge and has demonstrated remarkable success in diverse settings. However, previous attempts to employ it for Preference Modeling did not meet such expectations. In this work, we identify that naive epistemic uncertainty estimation leads to the acquisition of redundant samples. We address this by proposing the Bayesian Active Learner for Preference Modeling (BAL-PM), a novel stochastic acquisition policy that not only targets points of high epistemic uncertainty according to the preference model but also seeks to maximize the entropy of the acquired prompt distribution in the feature space spanned by the employed LLM. Notably, our experiments demonstrate that BAL-PM requires 33% to 68% fewer preference labels in two popular human preference datasets and exceeds previous stochastic Bayesian acquisition policies.

To develop rigorous knowledge about ML models -- and the systems in which they are embedded -- we need reliable measurements. But reliable measurement is fundamentally challenging, and touches on issues of reproducibility, scalability, uncertainty quantification, epistemology, and more. This dissertation addresses criteria needed to take reliability seriously: both criteria for designing meaningful metrics, and for methodologies that ensure that we can dependably and efficiently measure these metrics at scale and in practice. In doing so, this dissertation articulates a research vision for a new field of scholarship at the intersection of machine learning, law, and policy. Within this frame, we cover topics that fit under three different themes: (1) quantifying and mitigating sources of arbitrariness in ML, (2) taming randomness in uncertainty estimation and optimization algorithms, in order to achieve scalability without sacrificing reliability, and (3) providing methods for evaluating generative-AI systems, with specific focuses on quantifying memorization in language models and training latent diffusion models on open-licensed data. By making contributions in these three themes, this dissertation serves as an empirical proof by example that research on reliable measurement for machine learning is intimately and inescapably bound up with research in law and policy. These different disciplines pose similar research questions about reliable measurement in machine learning. They are, in fact, two complementary sides of the same research vision, which, broadly construed, aims to construct machine-learning systems that cohere with broader societal values.

Product assortment selection is a critical challenge facing physical retailers. Effectively aligning inventory with the preferences of shoppers can increase sales and decrease out-of-stocks. However, in real-world settings the problem is challenging due to the combinatorial explosion of product assortment possibilities. Consumer preferences are typically heterogeneous across space and time, making inventory-preference alignment challenging. Additionally, existing strategies rely on syndicated data, which tends to be aggregated, low resolution, and suffer from high latency. To solve these challenges, we introduce a real-time recommendation system, which we call EdgeRec3D. Our system utilizes recent advances in 3D computer vision for perception and automatic, fine grained sales estimation. These perceptual components run on the edge of the network and facilitate real-time reward signals. Additionally, we develop a Bayesian payoff model to account for noisy estimates from 3D LIDAR data. We rely on spatial clustering to allow the system to adapt to heterogeneous consumer preferences, and a graph-based candidate generation algorithm to address the combinatorial search problem. We test our system in real-world stores across two, 6-8 week A/B tests with beverage products and demonstrate a 35% and 27% increase in sales respectively. Finally, we monitor the deployed system for a period of 28 weeks with an observational study and show a 9.4% increase in sales.

Sepsis is a life-threatening and serious global health issue. This study combines knowledge with available hospital data to investigate the potential causes of Sepsis that can be affected by policy decisions. We investigate the underlying causal structure of this problem by combining clinical expertise with score-based, constraint-based, and hybrid structure learning algorithms. A novel approach to model averaging and knowledge-based constraints was implemented to arrive at a consensus structure for causal inference. The structure learning process highlighted the importance of exploring data-driven approaches alongside clinical expertise. This includes discovering unexpected, although reasonable, relationships from a clinical perspective. Hypothetical interventions on Chronic Obstructive Pulmonary Disease, Alcohol dependence, and Diabetes suggest that the presence of any of these risk factors in patients increases the likelihood of Sepsis. This finding, alongside measuring the effect of these risk factors on Sepsis, has potential policy implications. Recognising the importance of prediction in improving Sepsis related health outcomes, the model built is also assessed in its ability to predict Sepsis. The predictions generated by the consensus model were assessed for their accuracy, sensitivity, and specificity. These three indicators all had results around 70%, and the AUC was 80%, which means the causal structure of the model is reasonably accurate given that the models were trained on data available for commissioning purposes only.

We investigate the application of active inference in developing energy-efficient control agents for manufacturing systems. Active inference, rooted in neuroscience, provides a unified probabilistic framework integrating perception, learning, and action, with inherent uncertainty quantification elements. Our study explores deep active inference, an emerging field that combines deep learning with the active inference decision-making framework. Leveraging a deep active inference agent, we focus on controlling parallel and identical machine workstations to enhance energy efficiency. We address challenges posed by the problem's stochastic nature and delayed policy response by introducing tailored enhancements to existing agent architectures. Specifically, we introduce multi-step transition and hybrid horizon methods to mitigate the need for complex planning. Our experimental results demonstrate the effectiveness of these enhancements and highlight the potential of the active inference-based approach.

Offline reinforcement learning (RL) can learn optimal policies from pre-collected offline datasets without interacting with the environment, but the sampled actions of the agent cannot often cover the action distribution under a given state, resulting in the extrapolation error issue. Recent works address this issue by employing generative adversarial networks (GANs). However, these methods often suffer from insufficient constraints on policy exploration and inaccurate representation of behavior policies. Moreover, the generator in GANs fails in fooling the discriminator while maximizing the expected returns of a policy. Inspired by the diffusion, a generative model with powerful feature expressiveness, we propose a new offline RL method named Diffusion Policies with Generative Adversarial Networks (Diff-PoGAN). In this approach, the diffusion serves as the policy generator to generate diverse distributions of actions, and a regularization method based on maximum likelihood estimation (MLE) is developed to generate data that approximate the distribution of behavior policies. Besides, we introduce an additional regularization term based on the discriminator output to effectively constrain policy exploration for policy improvement. Comprehensive experiments are conducted on the datasets for deep data-driven reinforcement learning (D4RL), and experimental results show that DiffPoGAN outperforms state-of-the-art methods in offline RL.

State of the art large language models (LLMs) have shown impressive performance on a variety of benchmark tasks and are increasingly used as components in larger applications, where LLM-based predictions serve as proxies for human judgements or decision. This raises questions about the human-likeness of LLM-derived information, alignment with human intuition, and whether LLMs could possibly be considered (parts of) explanatory models of (aspects of) human cognition or language use. To shed more light on these issues, we here investigate the human-likeness of LLMs' predictions for multiple-choice decision tasks from the perspective of Bayesian statistical modeling. Using human data from a forced-choice experiment on pragmatic language use, we find that LLMs do not capture the variance in the human data at the item-level. We suggest different ways of deriving full distributional predictions from LLMs for aggregate, condition-level data, and find that some, but not all ways of obtaining condition-level predictions yield adequate fits to human data. These results suggests that assessment of LLM performance depends strongly on seemingly subtle choices in methodology, and that LLMs are at best predictors of human behavior at the aggregate, condition-level, for which they are, however, not designed to, or usually used to, make predictions in the first place.

Neural networks that can produce accurate, input-conditional uncertainty representations are critical for real-world applications. Recent progress on heteroscedastic continuous regression has shown great promise for calibrated uncertainty quantification on complex tasks, like image regression. However, when these methods are applied to discrete regression tasks, such as crowd counting, ratings prediction, or inventory estimation, they tend to produce predictive distributions with numerous pathologies. We propose to address these issues by training a neural network to output the parameters of a Double Poisson distribution, which we call the Deep Double Poisson Network (DDPN). In contrast to existing methods that are trained to minimize Gaussian negative log likelihood (NLL), DDPNs produce a proper probability mass function over discrete output. Additionally, DDPNs naturally model under-, over-, and equi-dispersion, unlike networks trained with the more rigid Poisson and Negative Binomial parameterizations. We show DDPNs 1) vastly outperform existing discrete models; 2) meet or exceed the accuracy and flexibility of networks trained with Gaussian NLL; 3) produce proper predictive distributions over discrete counts; and 4) exhibit superior out-of-distribution detection. DDPNs can easily be applied to a variety of count regression datasets including tabular, image, point cloud, and text data.

Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal Differential Equations (UDEs) are used to combine prior knowledge in the form of mechanistic formulations with universal function approximators, like neural networks. Integral to the efficacy of UDEs is the joint estimation of parameters within mechanistic formulations and the universal function approximators using empirical data. The robustness and applicability of resultant models, however, hinge upon the rigorous quantification of uncertainties associated with these parameters, as well as the predictive capabilities of the overall model or its constituent components. With this work, we provide a formalisation of uncertainty quantification (UQ) for UDEs and investigate important frequentist and Bayesian methods. By analysing three synthetic examples of varying complexity, we evaluate the validity and efficiency of ensembles, variational inference and Markov chain Monte Carlo sampling as epistemic UQ methods for UDEs.