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 study the policy testing problem in discounted Markov decision processes (MDPs) under the fixed-confidence setting. The goal is to determine whether the value of a given policy exceeds a specified threshold while minimizing the number of observations. We begin by deriving an instance-specific lower bound that any algorithm must satisfy. This lower bound is characterized as the solution to an optimization problem with non-convex constraints. We propose a policy testing algorithm inspired by this optimization problem--a common approach in pure exploration problems such as best-arm identification, where asymptotically optimal algorithms often stem from such optimization-based characterizations. As for other pure exploration tasks in MDPs, however, the non-convex constraints in the lower-bound problem present significant challenges, raising doubts about whether statistically optimal and computationally tractable algorithms can be designed. To address this, we reformulate the lower-bound problem by interchanging the roles of the objective and the constraints, yielding an alternative problem with a non-convex objective but convex constraints. Strikingly, this reformulated problem admits an interpretation as a policy optimization task in a newly constructed reversed MDP. Leveraging recent advances in policy gradient methods, we efficiently solve this problem and use it to design a policy testing algorithm that is statistically optimal--matching the instance-specific lower bound on sample complexity--while remaining computationally tractable. We validate our approach with numerical experiments.

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.

In this work, we contribute the first approach to solve infinite-horizon discounted general-utility Markov decision processes (GUMDPs) in the single-trial regime, i.e., when the agent's performance is evaluated based on a single trajectory. First, we provide some fundamental results regarding policy optimization in the single-trial regime, investigating which class of policies suffices for optimality, casting our problem as a particular MDP that is equivalent to our original problem, as well as studying the computational hardness of policy optimization in the single-trial regime. Second, we show how we can leverage online planning techniques, in particular a Monte-Carlo tree search algorithm, to solve GUMDPs in the single-trial regime. Third, we provide experimental results showcasing the superior performance of our approach in comparison to relevant baselines.

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.

Reinforcement Learning (RL) in partially observable environments poses significant challenges due to the complexity of learning under uncertainty. While additional information, such as that available in simulations, can enhance training, effectively leveraging it remains an open problem. To address this, we introduce Guided Policy Optimization (GPO), a framework that co-trains a guider and a learner. The guider takes advantage of privileged information while ensuring alignment with the learner's policy that is primarily trained via imitation learning. We theoretically demonstrate that this learning scheme achieves optimality comparable to direct RL, thereby overcoming key limitations inherent in existing approaches. Empirical evaluations show strong performance of GPO across various tasks, including continuous control with partial observability and noise, and memory-based challenges, significantly outperforming existing methods.

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.

Reinforcement learning (RL) has seen significant advancements through the application of various neural network architectures. In this study, we systematically investigate the performance of several neural networks in RL tasks, including Long Short-Term Memory (LSTM), Multi-Layer Perceptron (MLP), Mamba/Mamba-2, Transformer-XL, Gated Transformer-XL, and Gated Recurrent Unit (GRU). Through comprehensive evaluation across continuous control, discrete decision-making, and memory-based environments, we identify architecture-specific strengths and limitations. Our results reveal that: (1) MLPs excel in fully observable continuous control tasks, providing an optimal balance of performance and efficiency; (2) recurrent architectures like LSTM and GRU offer robust performance in partially observable environments with moderate memory requirements; (3) Mamba models achieve a 4.5x higher throughput compared to LSTM and a 3.9x increase over GRU, all while maintaining comparable performance; and (4) only Transformer-XL, Gated Transformer-XL, and Mamba-2 successfully solve the most challenging memory-intensive tasks, with Mamba-2 requiring 8x less memory than Transformer-XL. These findings provide insights for researchers and practitioners, enabling more informed architecture selection based on specific task characteristics and computational constraints. Code is available at: https://github.com/SafeRL-Lab/RLBenchNet

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.