Capturing nonlinear relationships without sacrificing interpretability remains a persistent challenge in regression modeling. We introduce SplitWise, a novel framework that enhances stepwise regression. It adaptively transforms numeric predictors into threshold-based binary features using shallow decision trees, but only when such transformations improve model fit, as assessed by the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC). This approach preserves the transparency of linear models while flexibly capturing nonlinear effects. Implemented as a user-friendly R package, SplitWise is evaluated on both synthetic and real-world datasets. The results show that it consistently produces more parsimonious and generalizable models than traditional stepwise and penalized regression techniques.

In statistical learning, models are classified as regular or singular depending on whether the mapping from parameters to probability distributions is injective. Most models with hierarchical structures or latent variables are singular, for which conventional criteria such as the Akaike Information Criterion and the Bayesian Information Criterion are inapplicable due to the breakdown of normal approximations for the likelihood and posterior. To address this, the Widely Applicable Information Criterion (WAIC) and the Widely Applicable Bayesian Information Criterion (WBIC) have been proposed. Since WAIC and WBIC are computed using posterior distributions at different temperature settings, separate posterior sampling is generally required. In this paper, we theoretically derive an asymptotic equation that links WAIC and WBIC, despite their dependence on different posteriors. This equation yields an asymptotically unbiased expression of WAIC in terms of the posterior distribution used for WBIC. The result clarifies the structural relationship between these criteria within the framework of singular learning theory, and deepens understanding of their asymptotic behavior. This theoretical contribution provides a foundation for future developments in the computational efficiency of model selection in singular models.

We revisit the classical problem of Bayesian ensembles and address the challenge of learning optimal combinations of Bayesian models in an online, continual learning setting. To this end, we reinterpret existing approaches such as Bayesian model averaging (BMA) and Bayesian stacking through a novel empirical Bayes lens, shedding new light on the limitations and pathologies of BMA. Further motivated by insights from online optimization, we propose Online Bayesian Stacking (OBS), a method that optimizes the log-score over predictive distributions to adaptively combine Bayesian models. A key contribution of our work is establishing a novel connection between OBS and portfolio selection, bridging Bayesian ensemble learning with a rich, well-studied theoretical framework that offers efficient algorithms and extensive regret analysis. We further clarify the relationship between OBS and online BMA, showing that they optimize related but distinct cost functions. Through theoretical analysis and empirical evaluation, we identify scenarios where OBS outperforms online BMA and provide principled guidance on when practitioners should prefer one approach over the other.

Knowing the uncertainty associated with the output of a deep neural network is of paramount importance in making trustworthy decisions, particularly in high-stakes fields like medical diagnosis and autonomous systems. Monte Carlo Dropout (MCD) is a widely used method for uncertainty quantification, as it can be easily integrated into various deep architectures. However, conventional MCD often struggles with providing well-calibrated uncertainty estimates. To address this, we introduce innovative frameworks that enhances MCD by integrating different search solutions namely Grey Wolf Optimizer (GWO), Bayesian Optimization (BO), and Particle Swarm Optimization (PSO) as well as an uncertainty-aware loss function, thereby improving the reliability of uncertainty quantification. We conduct comprehensive experiments using different backbones, namely DenseNet121, ResNet50, and VGG16, on various datasets, including Cats vs. Dogs, Myocarditis, Wisconsin, and a synthetic dataset (Circles). Our proposed algorithm outperforms the MCD baseline by 2-3% on average in terms of both conventional accuracy and uncertainty accuracy while achieving significantly better calibration. These results highlight the potential of our approach to enhance the trustworthiness of deep learning models in safety-critical applications.

Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially harmful samples. We propose Laplace Sample Information (LSI) measure of sample informativeness grounded in information theory widely applicable across model architectures and learning settings. LSI leverages a Bayesian approximation to the weight posterior and the KL divergence to measure the change in the parameter distribution induced by a sample of interest from the dataset. We experimentally show that LSI is effective in ordering the data with respect to typicality, detecting mislabeled samples, measuring class-wise informativeness, and assessing dataset difficulty. We demonstrate these capabilities of LSI on image and text data in supervised and unsupervised settings. Moreover, we show that LSI can be computed efficiently through probes and transfers well to the training of large models.

This dissertation addresses achieving causal interpretability in Deep Learning for Software Engineering (DL4SE). While Neural Code Models (NCMs) show strong performance in automating software tasks, their lack of transparency in causal relationships between inputs and outputs limits full understanding of their capabilities. To build trust in NCMs, researchers and practitioners must explain code predictions. Associational interpretability, which identifies correlations, is often insufficient for tasks requiring intervention and change analysis. To address this, the dissertation introduces DoCode, a novel post hoc interpretability method for NCMs. DoCode uses causal inference to provide programming language-oriented explanations of model predictions. It follows a four-step pipeline: modeling causal problems using Structural Causal Models (SCMs), identifying the causal estimand, estimating effects with metrics like Average Treatment Effect (ATE), and refuting effect estimates. Its framework is extensible, with an example that reduces spurious correlations by grounding explanations in programming language properties. A case study on deep code generation across interpretability scenarios and various deep learning architectures demonstrates DoCode's benefits. Results show NCMs' sensitivity to code syntax changes and their ability to learn certain programming concepts while minimizing confounding bias. The dissertation also examines associational interpretability as a foundation, analyzing software information's causal nature using tools like COMET and TraceXplainer for traceability. It highlights the need to identify code confounders and offers practical guidelines for applying causal interpretability to NCMs, contributing to more trustworthy AI in software engineering.

For future human-autonomous vehicle (AV) interactions to be effective and smooth, human-aware systems that analyze and align human needs with automation decisions are essential. Achieving this requires systems that account for human cognitive states. We present a novel computational model in the form of a Dynamic Bayesian Network (DBN) that infers the cognitive states of both AV users and other road users, integrating this information into the AV's decision-making process. Specifically, our model captures the well-being of both an AV user and an interacting road user as cognitive states alongside trust. Our DBN models infer beliefs over the AV user's evolving well-being, trust, and intention states, as well as the possible well-being of other road users, based on observed interaction experiences. Using data collected from an interaction study, we refine the model parameters and empirically assess its performance. Finally, we extend our model into a causal inference model (CIM) framework for AV decision-making, enabling the AV to enhance user well-being and trust while balancing these factors with its own operational costs and the well-being of interacting road users. Our evaluation demonstrates the model's effectiveness in accurately predicting user's states and guiding informed, human-centered AV decisions.

Ensuring the reliability and safety of machine learning models in open-world deployment is a central challenge in AI safety. This thesis develops both algorithmic and theoretical foundations to address key reliability issues arising from distributional uncertainty and unknown classes, from standard neural networks to modern foundation models like large language models (LLMs). Traditional learning paradigms, such as empirical risk minimization (ERM), assume no distribution shift between training and inference, often leading to overconfident predictions on out-of-distribution (OOD) inputs. This thesis introduces novel frameworks that jointly optimize for in-distribution accuracy and reliability to unseen data. A core contribution is the development of an unknown-aware learning framework that enables models to recognize and handle novel inputs without labeled OOD data. We propose new outlier synthesis methods, VOS, NPOS, and DREAM-OOD, to generate informative unknowns during training. Building on this, we present SAL, a theoretical and algorithmic framework that leverages unlabeled in-the-wild data to enhance OOD detection under realistic deployment conditions. These methods demonstrate that abundant unlabeled data can be harnessed to recognize and adapt to unforeseen inputs, providing formal reliability guarantees. The thesis also extends reliable learning to foundation models. We develop HaloScope for hallucination detection in LLMs, MLLMGuard for defending against malicious prompts in multimodal models, and data cleaning methods to denoise human feedback used for better alignment. These tools target failure modes that threaten the safety of large-scale models in deployment. Overall, these contributions promote unknown-aware learning as a new paradigm, and we hope it can advance the reliability of AI systems with minimal human efforts.

This work introduces a new method called scalable Bayesian Monte Carlo (SBMC). The model interpolates between a point estimator and the posterior, and the algorithm is a parallel implementation of a consistent (asymptotically unbiased) Bayesian deep learning algorithm: sequential Monte Carlo (SMC) or Markov chain Monte Carlo (MCMC). The method is motivated theoretically, and its utility is demonstrated on practical examples: MNIST, CIFAR, IMDb. A systematic numerical study reveals that parallel implementations of SMC and MCMC are comparable to serial implementations in terms of performance and total cost, and they achieve accuracy at or beyond the state-of-the-art (SOTA) methods like deep ensembles at convergence, along with substantially improved uncertainty quantification (UQ)--in particular, epistemic UQ. But even parallel implementations are expensive, with an irreducible time barrier much larger than the cost of the MAP estimator. Compressing time further leads to rapid degradation of accuracy, whereas UQ remains valuable. By anchoring to a point estimator we can recover accuracy, while retaining valuable UQ, ultimately delivering strong performance across metrics for a cost comparable to the SOTA.

Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular data sets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian ideas, they do not provide any uncertainty quantification for predictive means, quantiles, or similar quantities. We propose a principled and efficient sampling procedure to construct Bayesian posteriors for such estimates based on Martingale posteriors, and prove its convergence. Several simulated and real-world data examples showcase the uncertainty quantification of our method in inference applications.