Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process.

In many problem settings, parameter vectors are not merely sparse, but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity". Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop efficient approximate inference methods and show substantial improvements over comparable methods (e.g., group lasso and smooth RVM) for both simulated and real datasets from brain imaging.

Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative Poisson topic model with long documents, dropout training improves the exponent in the generalization bound for empirical risk minimization. Dropout achieves this gain much like a marathon runner who practices at altitude: once a classifier learns to perform reasonably well on training examples that have been artificially corrupted by dropout, it will do very well on the uncorrupted test set. We also show that, under similar conditions, dropout preserves the Bayes decision boundary and should therefore induce minimal bias in high dimensions.

Hard computing generally deals with precise data, which provides ideal solutions to problems. However, in the civil engineering field, amongst other disciplines, that is not always the case as real-world systems are continuously changing. Here lies the need to explore soft computing methods and artificial intelligence to solve civil engineering shortcomings. The integration of advanced computational models, including Artificial Neural Networks (ANNs), Fuzzy Logic, Genetic Algorithms (GAs), and Probabilistic Reasoning, has revolutionized the domain of civil engineering. These models have significantly advanced diverse sub-fields by offering innovative solutions and improved analysis capabilities. Sub-fields such as: slope stability analysis, bearing capacity, water quality and treatment, transportation systems, air quality, structural materials, etc. ANNs predict non-linearities and provide accurate estimates. Fuzzy logic uses an efficient decision-making process to provide a more precise assessment of systems. Lastly, while GAs optimizes models (based on evolutionary processes) for better outcomes, probabilistic reasoning lowers their statistical uncertainties.

The choroid, a highly vascular layer behind the retina, is an extension of the central nervous system and has parallels with the renal cortex, with blood flow far exceeding that of the brain and kidney. Thus, there has been growing interest of choroidal blood flow reflecting physiological status of systemic disease. Optical coherence tomography (OCT) enables high-resolution imaging of the choroid, but conventional analysis methods remain manual or semi-automatic, limiting reproducibility, standardisation and clinical utility. In this thesis, I develop several new methods to analyse the choroid in OCT image sequences, with each successive method improving on its predecessors. I first develop two semi-automatic approaches for choroid region (Gaussian Process Edge Tracing, GPET) and vessel (Multi-scale Median Cut Quantisation, MMCQ) analysis, which improve on manual approaches but remain user-dependent. To address this, I introduce DeepGPET, a deep learning-based region segmentation method which improves on execution time, reproducibility, and end-user accessibility, but lacks choroid vessel analysis and automatic feature measurement. Improving on this, I developed Choroidalyzer, a deep learning-based pipeline to segment the choroidal space and vessels and generate fully automatic, clinically meaningful and reproducible choroidal features. I provide rigorous evaluation of these four approaches and consider their potential clinical value in three applications into systemic health: OCTANE, assessing choroidal changes in renal transplant recipients and donors; PREVENT, exploring choroidal associations with Alzheimer's risk factors at mid-life; D-RISCii, assessing choroidal variation and feasibility of OCT in critical care. In short, this thesis contributes many open-source tools for standardised choroidal measurement and highlights the choroid's potential as a biomarker in systemic health.

Earthquake forecasting remains a significant scientific challenge, with current methods falling short of achieving the performance necessary for meaningful societal benefits. Traditional models, primarily based on past seismicity and geomechanical data, struggle to capture the complexity of seismic patterns and often overlook valuable non-seismic precursors such as geophysical, geochemical, and atmospheric anomalies. The integration of such diverse data sources into forecasting models, combined with advancements in AI technologies, offers a promising path forward. AI methods, particularly deep learning, excel at processing complex, large-scale datasets, identifying subtle patterns, and handling multidimensional relationships, making them well-suited for overcoming the limitations of conventional approaches. This review highlights the importance of combining AI with geophysical knowledge to create robust, physics-informed forecasting models. It explores current AI methods, input data types, loss functions, and practical considerations for model development, offering guidance to both geophysicists and AI researchers. While many AI-based studies oversimplify earthquake prediction, neglecting critical features such as data imbalance and spatio-temporal clustering, the integration of specialized geophysical insights into AI models can address these shortcomings. We emphasize the importance of interdisciplinary collaboration, urging geophysicists to experiment with AI architectures thoughtfully and encouraging AI experts to deepen their understanding of seismology. By bridging these disciplines, we can develop more accurate, reliable, and societally impactful earthquake forecasting tools.

Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the high computational complexity of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose the Bayesian Optimization by Kernel regression and density-based Exploration (BOKE) algorithm. BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and the improved kernel regression upper confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE and ensures its robustness. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.

Reverberant speech, denoting the speech signal degraded by the process of reverberation, contains crucial knowledge of both anechoic source speech and room impulse response (RIR). This work proposes a variational Bayesian inference (VBI) framework with neural speech prior (VINP) for joint speech dereverberation and blind RIR identification. In VINP, a probabilistic signal model is constructed in the time-frequency (T-F) domain based on convolution transfer function (CTF) approximation. For the first time, we propose using an arbitrary discriminative dereverberation deep neural network (DNN) to predict the prior distribution of anechoic speech within a probabilistic model. By integrating both reverberant speech and the anechoic speech prior, VINP yields the maximum a posteriori (MAP) and maximum likelihood (ML) estimations of the anechoic speech spectrum and CTF filter, respectively. After simple transformations, the waveforms of anechoic speech and RIR are estimated. Moreover, VINP is effective for automatic speech recognition (ASR) systems, which sets it apart from most deep learning (DL)-based single-channel dereverberation approaches. Experiments on single-channel speech dereverberation demonstrate that VINP reaches an advanced level in most metrics related to human perception and displays unquestionable state-of-the-art (SOTA) performance in ASR-related metrics. For blind RIR identification, experiments indicate that VINP attains the SOTA level in blind estimation of reverberation time at 60 dB (RT60) and direct-to-reverberation ratio (DRR). Codes and audio samples are available online.

Cancer evolves continuously over time through a complex interplay of genetic, epigenetic, microenvironmental, and phenotypic changes. This dynamic behavior drives uncontrolled cell growth, metastasis, immune evasion, and therapy resistance, posing challenges for effective monitoring and treatment. However, today's data-driven research in oncology has primarily focused on cross-sectional analysis using data from a single modality, limiting the ability to fully characterize and interpret the disease's dynamic heterogeneity. Advances in multiscale data collection and computational methods now enable the discovery of longitudinal multimodal biomarkers for precision oncology. Longitudinal data reveal patterns of disease progression and treatment response that are not evident from single-timepoint data, enabling timely abnormality detection and dynamic treatment adaptation. Multimodal data integration offers complementary information from diverse sources for more precise risk assessment and targeting of cancer therapy. In this review, we survey methods of longitudinal and multimodal modeling, highlighting their synergy in providing multifaceted insights for personalized care tailored to the unique characteristics of a patient's cancer. We summarize the current challenges and future directions of longitudinal multimodal analysis in advancing precision oncology.

High-risk artificial intelligence and machine learning classification tasks, such as healthcare diagnosis, require accurate and interpretable prediction models. However, classifier algorithms typically sacrifice individual case-accuracy for overall model accuracy, limiting analysis of class overlap areas regardless of task significance. The Adaptive Boosting meta-algorithm, which won the 2003 G\"odel Prize, analytically assigns higher weights to misclassified cases to reclassify. However, it relies on weaker base classifiers that are iteratively strengthened, limiting improvements from base classifiers. Combining visual and computational approaches enables selecting stronger base classifiers before boosting. This paper proposes moving boosting methodology from focusing on only misclassified cases to all cases in the class overlap areas using Computational and Interactive Visual Learning (CIVL) with a Human-in-the-Loop. It builds classifiers in lossless visualizations integrating human domain expertise and visual insights. A Divide and Classify process splits cases to simple and complex, classifying these individually through computational analysis and data visualization with lossless visualization spaces of Parallel Coordinates or other General Line Coordinates. After finding pure and overlap class areas simple cases in pure areas are classified, generating interpretable sub-models like decision rules in Propositional and First-order Logics. Only multidimensional cases in the overlap areas are losslessly visualized simplifying end-user cognitive tasks to identify difficult case patterns, including engineering features to form new classifiable patterns. Demonstration shows a perfectly accurate and losslessly interpretable model of the Iris dataset, and simulated data shows generalized benefits to accuracy and interpretability of models, increasing end-user confidence in discovered models.