Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We apply MAP estimation in the context of structural dynamic models, where the system response can be described by the frequency response function. To alleviate high computational demands from repeated expensive model calls, we utilize a rational polynomial chaos expansion (RPCE) surrogate model that expresses the system frequency response as a rational of two polynomials with complex coefficients. We propose an extension to an existing sparse Bayesian learning approach for RPCE based on Laplace's approximation for the posterior distribution of the denominator coefficients. Furthermore, we introduce a Bayesian optimization approach, which allows to adaptively enrich the experimental design throughout the optimization process of MAP estimation. Thereby, we utilize the expected improvement acquisition function as a means to identify sample points in the input space that are possibly associated with large objective function values. The acquisition function is estimated through Monte Carlo sampling based on the posterior distribution of the expansion coefficients identified in the sparse Bayesian learning process. By combining the sparsity-inducing learning procedure with the sequential experimental design, we effectively reduce the number of model evaluations in the MAP estimation problem. We demonstrate the applicability of the presented methods on the parameter updating problem of an algebraic two-degree-of-freedom system and the finite element model of a cross-laminated timber plate.

Bayesian Last Layer (BLL) models focus solely on uncertainty in the output layer of neural networks, demonstrating comparable performance to more complex Bayesian models. However, the use of Gaussian priors for last layer weights in Bayesian Last Layer (BLL) models limits their expressive capacity when faced with non-Gaussian, outlier-rich, or high-dimensional datasets. To address this shortfall, we introduce a novel approach that combines diffusion techniques and implicit priors for variational learning of Bayesian last layer weights. This method leverages implicit distributions for modeling weight priors in BLL, coupled with diffusion samplers for approximating true posterior predictions, thereby establishing a comprehensive Bayesian prior and posterior estimation strategy. By delivering an explicit and computationally efficient variational lower bound, our method aims to augment the expressive abilities of BLL models, enhancing model accuracy, calibration, and out-of-distribution detection proficiency. Through detailed exploration and experimental validation, We showcase the method's potential for improving predictive accuracy and uncertainty quantification while ensuring computational efficiency.

Large language models (LLM)'s are increasingly used for topic modeling outperforming classical topic models such as LDA. Commonly, pre-trained LLM encoders such as BERT are used out-of-the-box despite the fact that fine-tuning is known to improve LLMs considerably. The challenge lies in obtaining a suitable (labeled) dataset for fine-tuning. In this paper, we use the recent idea to use bag of sentences as the elementary unit in computing topics. In turn, we derive an approach FT-Topic to perform unsupervised fine-tuning relying primarily on two steps for constructing a training dataset in an automatic fashion. First, a heuristic method to identifies pairs of sentence groups that are either assumed to be of the same or different topics. Second, we remove sentence pairs that are likely labeled incorrectly. The dataset is then used to fine-tune an encoder LLM, which can be leveraged by any topic modeling approach using embeddings. However, in this work, we demonstrate its effectiveness by deriving a novel state-of-the-art topic modeling method called SenClu, which achieves fast inference through an expectation-maximization algorithm and hard assignments of sentence groups to a single topic, while giving users the possibility to encode prior knowledge on the topic-document distribution. Code is at \url{https://github.com/JohnTailor/FT-Topic}

Distribution learning finds probability density functions from a set of data samples, whereas clustering aims to group similar data points to form clusters. Although there are deep clustering methods that employ distribution learning methods, past work still lacks theoretical analysis regarding the relationship between clustering and distribution learning. Thus, in this work, we provide a theoretical analysis to guide the optimization of clustering via distribution learning. To achieve better results, we embed deep clustering guided by a theoretical analysis. Furthermore, the distribution learning method cannot always be directly applied to data. To overcome this issue, we introduce a clustering-oriented distribution learning method called Monte-Carlo Marginalization for Clustering. We integrate Monte-Carlo Marginalization for Clustering into Deep Clustering, resulting in Deep Clustering via Distribution Learning (DCDL). Eventually, the proposed DCDL achieves promising results compared to state-of-the-art methods on popular datasets. Considering a clustering task, the new distribution learning method outperforms previous methods as well.

Accurately gauging uncertainty on the underlying environment is a longstanding goal of intelligent systems. We characterize which latent concepts pre-trained sequence models are naturally able to reason with. We go back to De Finetti's predictive view of Bayesian reasoning: instead of modeling latent parameters through priors and likelihoods like topic models do, De Finetti has long advocated for modeling exchangeable (permutation invariant) sequences of observables. According to this view, pre-training autoregressive models formulates informed beliefs based on prior observations ("empirical Bayes"), and forward generation is a simulated instantiation of an environment ("posterior inference"). This connection allows extending in-context learning (ICL) beyond predictive settings, highlighting sequence models' ability to perform explicit statistical inference. In particular, we show the sequence prediction loss over exchangeable documents controls performance on downstream tasks where uncertainty quantification is key. Empirically, we propose and demonstrate several approaches for encoding exchangeability in sequence model architectures: data augmentation, regularization, and causal masking.

Artificial Intelligence (AI) is revolutionizing various fields, including public health surveillance. In Africa, where health systems frequently encounter challenges such as limited resources, inadequate infrastructure, failed health information systems and a shortage of skilled health professionals, AI offers a transformative opportunity. This paper investigates the applications of AI in public health surveillance across the continent, presenting successful case studies and examining the benefits, opportunities, and challenges of implementing AI technologies in African healthcare settings. Our paper highlights AI's potential to enhance disease monitoring and health outcomes, and support effective public health interventions. The findings presented in the paper demonstrate that AI can significantly improve the accuracy and timeliness of disease detection and prediction, optimize resource allocation, and facilitate targeted public health strategies. Additionally, our paper identified key barriers to the widespread adoption of AI in African public health systems and proposed actionable recommendations to overcome these challenges.

This study analyzes hybrid AI systems' design patterns and their effectiveness in clinical decision-making using the boxology framework. It categorizes and copares various architectures combining machine learning and rule-based reasoning to provide insights into their structural foundations and healthcare applications. Addressing two main questions, how to categorize these systems againts established design patterns and how to extract insights through comparative analysis, the study uses design patterns from software engineering to understand and optimize healthcare AI systems. Boxology helps identify commonalities and create reusable solutions, enhancing these systems' scalability, reliability, and performance. Five primary architectures are examined: REML, MLRB, RBML, RMLT, and PERML. Each has unique strengths and weaknesses, highlighting the need for tailored approaches in clinical tasks. REML excels in high-accuracy prediction for datasets with limited data; MLRB in handling large datasets and complex data integration; RBML in explainability and trustworthiness; RMLT in managing high-dimensional data; and PERML, though limited in analysis, shows promise in urgent care scenarios. The study introduces four new patterns, creates five abstract categorization patterns, and refines those five further to specific systems. These contributions enhance Boxlogy's taxonomical organization and offer novel approaches to integrating expert knowledge with machine learning. Boxology's structured, modular apporach offers significant advantages in developing and analyzing hybrid AI systems, revealing commonalities, and promoting reusable solutions. In conclusion, this study underscores hybrid AI systems' crucial role in advancing healthcare and Boxology's potential to drive further innovation in AI integration, ultimately improving clinical decision support and patient outcomes.

Because of its strong predictive skills, deep learning has emerged as an essential tool in many industries, including healthcare. Traditional deep learning models, on the other hand, frequently lack interpretability and omit to take prediction uncertainty into account two crucial components of clinical decision making. In order to produce explainable and uncertainty aware predictions, this study presents a novel framework called Bayesian Kolmogorov Arnold Networks (BKANs), which combines the expressive capacity of Kolmogorov Arnold Networks with Bayesian inference. We employ BKANs on two medical datasets, which are widely used benchmarks for assessing machine learning models in medical diagnostics: the Pima Indians Diabetes dataset and the Cleveland Heart Disease dataset. Our method provides useful insights into prediction confidence and decision boundaries and outperforms traditional deep learning models in terms of prediction accuracy. Moreover, BKANs' capacity to represent aleatoric and epistemic uncertainty guarantees doctors receive more solid and trustworthy decision support. Our Bayesian strategy improves the interpretability of the model and considerably minimises overfitting, which is important for tiny and imbalanced medical datasets, according to experimental results. We present possible expansions to further use BKANs in more complicated multimodal datasets and address the significance of these discoveries for future research in building reliable AI systems for healthcare. This work paves the way for a new paradigm in deep learning model deployment in vital sectors where transparency and reliability are crucial.

Most machine learning classifiers are designed to output posterior probabilities for the classes given the input sample. These probabilities may be used to make the categorical decision on the class of the sample; provided as input to a downstream system; or provided to a human for interpretation. Evaluating the quality of the posteriors generated by these system is an essential problem which was addressed decades ago with the invention of proper scoring rules (PSRs). Unfortunately, much of the recent machine learning literature uses calibration metrics -- most commonly, the expected calibration error (ECE) -- as a proxy to assess posterior performance. The problem with this approach is that calibration metrics reflect only one aspect of the quality of the posteriors, ignoring the discrimination performance. For this reason, we argue that calibration metrics should play no role in the assessment of posterior quality. Expected PSRs should instead be used for this job, preferably normalized for ease of interpretation. In this work, we first give a brief review of PSRs from a practical perspective, motivating their definition using Bayes decision theory. We discuss why expected PSRs provide a principled measure of the quality of a system's posteriors and why calibration metrics are not the right tool for this job. We argue that calibration metrics, while not useful for performance assessment, may be used as diagnostic tools during system development. With this purpose in mind, we discuss a simple and practical calibration metric, called calibration loss, derived from a decomposition of expected PSRs. We compare this metric with the ECE and with the expected score divergence calibration metric from the PSR literature and argue, using theoretical and empirical evidence, that calibration loss is superior to these two metrics.

The Hilbert-space Gaussian Process (HGP) approach offers a hyperparameter-independent basis function approximation for speeding up Gaussian Process (GP) inference by projecting the GP onto M basis functions. These properties result in a favorable data-independent $\mathcal{O}(M^3)$ computational complexity during hyperparameter optimization but require a dominating one-time precomputation of the precision matrix costing $\mathcal{O}(NM^2)$ operations. In this paper, we lower this dominating computational complexity to $\mathcal{O}(NM)$ with no additional approximations. We can do this because we realize that the precision matrix can be split into a sum of Hankel-Toeplitz matrices, each having $\mathcal{O}(M)$ unique entries. Based on this realization we propose computing only these unique entries at $\mathcal{O}(NM)$ costs. Further, we develop two theorems that prescribe sufficient conditions for the complexity reduction to hold generally for a wide range of other approximate GP models, such as the Variational Fourier Feature (VFF) approach. The two theorems do this with no assumptions on the data and no additional approximations of the GP models themselves. Thus, our contribution provides a pure speed-up of several existing, widely used, GP approximations, without further approximations.