Data assimilation will be essential for the management and expansion of geological carbon storage operations. In traditional data assimilation approaches a fixed set of geological hyperparameters, such as mean and standard deviation of log-permeability, is often assumed. Such hyperparameters, however, may be highly uncertain in practical CO2 storage applications. In this study, we develop a hierarchical data assimilation framework for carbon storage that treats hyperparameters as uncertain variables characterized by hyperprior distributions. To deal with the computationally intractable likelihood function in hyperparameter estimation, we apply a likelihood-free (or simulation-based) inference algorithm, specifically sequential Monte Carlo-based approximate Bayesian computation (SMC-ABC), to draw independent posterior samples of hyperparameters given dynamic monitoring-well data. In the second step we use an ensemble smoother with multiple data assimilation (ESMDA) procedure to provide posterior realizations of grid-block permeability. To reduce computational costs, a 3D recurrent R-U-Net deep-learning surrogate model is applied for forward function evaluations. The accuracy of the surrogate model is established through comparisons to high-fidelity simulation results. A rejection sampling (RS) procedure for data assimilation is applied to provide reference posterior results. Detailed data assimilation results from SMC-ABC-ESMDA are compared to those from the reference RS method. These include marginal posterior distributions of hyperparameters, pairwise posterior samples, and history matching results for pressure and saturation at the monitoring location. Close agreement is achieved with 'converged' RS results, for two synthetic true models, in all quantities considered. Importantly, the SMC-ABC-ESMDA procedure provides speedup of 1-2 orders of magnitude relative to RS for the two cases.

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between enumerating a sufficiently large set of concepts to include those that are truly relevant versus controlling the cost of obtaining concept extractions. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. BC-LLM is broadly applicable and multi-modal. Despite imperfections in LLMs, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. In experiments, it outperforms comparator methods including black-box models, converges more rapidly towards relevant concepts and away from spuriously correlated ones, and is more robust to out-of-distribution samples.

Amortized meta-learning methods based on pre-training have propelled fields like natural language processing and vision. Transformer-based neural processes and their variants are leading models for probabilistic meta-learning with a tractable objective. Often trained on synthetic data, these models implicitly capture essential latent information in the data-generation process. However, existing methods do not allow users to flexibly inject (condition on) and extract (predict) this probabilistic latent information at runtime, which is key to many tasks. We introduce the Amortized Conditioning Engine (ACE), a new transformer-based meta-learning model that explicitly represents latent variables of interest. ACE affords conditioning on both observed data and interpretable latent variables, the inclusion of priors at runtime, and outputs predictive distributions for discrete and continuous data and latents. We show ACE's modeling flexibility and performance in diverse tasks such as image completion and classification, Bayesian optimization, and simulation-based inference.

Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like Lasso have advanced in handling high-dimensional count data, Bayesian approaches remain under-explored with no theoretical results on prediction performance. This paper introduces a novel probabilistic machine learning framework for high-dimensional count data prediction. We propose a pseudo-Bayesian method that integrates a scaled Student prior to promote sparsity and uses an exponential weight aggregation procedure. A key contribution is a novel risk measure tailored to count data prediction, with theoretical guarantees for prediction risk using PAC-Bayesian bounds. Our results include non-asymptotic oracle inequalities, demonstrating rate-optimal prediction error without prior knowledge of sparsity. We implement this approach efficiently using Langevin Monte Carlo method. Simulations and a real data application highlight the strong performance of our method compared to the Lasso in various settings.

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are treated as random variables with prior distributions, allowing for a probabilistic interpretation and quantification of predictive uncertainty. However, Bayesian methods lack theoretical generalization guarantees for unseen data. PAC-Bayesian analysis addresses this limitation by offering a frequentist framework to derive generalization bounds for randomized predictors, thereby certifying the reliability of Bayesian methods in machine learning. Temperature $T$, or inverse-temperature $\lambda = \frac{1}{T}$, originally from statistical mechanics in physics, naturally arises in various areas of statistical inference, including Bayesian inference and PAC-Bayesian analysis. In Bayesian inference, when $T < 1$ (``cold'' posteriors), the likelihood is up-weighted, resulting in a sharper posterior distribution. Conversely, when $T > 1$ (``warm'' posteriors), the likelihood is down-weighted, leading to a more diffuse posterior distribution. By balancing the influence of observed data and prior regularization, temperature adjustments can address issues of underfitting or overfitting in Bayesian models, bringing improved predictive performance.

Representation learning of Text-Attributed Graphs (TAGs) has garnered significant attention due to its applications in various domains, including recommendation systems and social networks. Despite advancements in TAG learning methodologies, challenges remain in explainability due to the black-box nature of existing TAG representation learning models. This paper presents TAGExplainer, the first method designed to generate natural language explanations for TAG learning. TAGExplainer employs a generative language model that maps input-output pairs to explanations reflecting the model's decision-making process. To address the lack of annotated ground truth explanations in real-world scenarios, we propose first generating pseudo-labels that capture the model's decisions from saliency-based explanations, then the pseudo-label generator is iteratively trained based on three training objectives focusing on faithfulness and brevity via Expert Iteration, to improve the quality of generated pseudo-labels. The high-quality pseudo-labels are finally utilized to train an end-to-end explanation generator model. Extensive experiments are conducted to demonstrate the effectiveness of TAGExplainer in producing faithful and concise natural language explanations.

Determining the appropriate rank in Non-negative Matrix Factorization (NMF) is a critical challenge that often requires extensive parameter tuning and domain-specific knowledge. Traditional methods for rank determination focus on identifying a single optimal rank, which may not capture the complex structure inherent in real-world datasets. In this study, we introduce a novel approach called Residual Sensitivity to Intial Conditions (RSIC) that suggests potentially multiple ranks of interest by analyzing the sensitivity of the relative residuals (e.g. relative reconstruction error) to different initializations. By computing the Mean Coordinatewise Interquartile Range (MCI) of the residuals across multiple random initializations, our method identifies regions where the NMF solutions are less sensitive to initial conditions and potentially more meaningful. We evaluate RSIC on a diverse set of datasets, including single-cell gene expression data, image data, and text data, and compare it against current state-of-the-art existing rank determination methods. Our experiments demonstrate that RSIC effectively identifies relevant ranks consistent with the underlying structure of the data, outperforming traditional methods in scenarios where they are computationally infeasible or less accurate. This approach provides a more scalable and generalizable solution for rank determination in NMF that does not rely on domain-specific knowledge or assumptions.

To support real-world decision-making, it is crucial for models to be well-calibrated, i.e., to assign reliable confidence estimates to their predictions. Uncertainty quantification is particularly important in personalized federated learning (PFL), as participating clients typically have small local datasets, making it difficult to unambiguously determine optimal model parameters. Bayesian PFL (BPFL) methods can potentially enhance calibration, but they often come with considerable computational and memory requirements due to the need to track the variances of all the individual model parameters. Furthermore, different clients may exhibit heterogeneous uncertainty levels owing to varying local dataset sizes and distributions. To address these challenges, we propose LR-BPFL, a novel BPFL method that learns a global deterministic model along with personalized low-rank Bayesian corrections. To tailor the local model to each client's inherent uncertainty level, LR-BPFL incorporates an adaptive rank selection mechanism. We evaluate LR-BPFL across a variety of datasets, demonstrating its advantages in terms of calibration, accuracy, as well as computational and memory requirements.

Cryptocurrencies, as decentralized digital assets, have experienced rapid growth and adoption, with over 23,000 cryptocurrencies and a market capitalization nearing \$1.1 trillion (about \$3,400 per person in the US) as of 2023. This dynamic market presents significant opportunities and risks, highlighting the need for accurate price prediction models to manage volatility. This chapter comprehensively reviews machine learning (ML) techniques applied to cryptocurrency price prediction from 2014 to 2024. We explore various ML algorithms, including linear models, tree-based approaches, and advanced deep learning architectures such as transformers and large language models. Additionally, we examine the role of sentiment analysis in capturing market sentiment from textual data like social media posts and news articles to anticipate price fluctuations. With expertise in optimizing complex systems and processes, industrial engineers are pivotal in enhancing these models. They contribute by applying principles of process optimization, efficiency, and risk mitigation to improve computational performance and data management. This chapter highlights the evolving landscape of cryptocurrency price prediction, the integration of emerging technologies, and the significant role of industrial engineers in refining predictive models. By addressing current limitations and exploring future research directions, this chapter aims to advance the development of more accurate and robust prediction systems, supporting better-informed investment decisions and more stable market behavior.

Predictive maintenance of railway infrastructure, especially railroads, is essential to ensure safety. However, accurate prediction of crack evolution represents a major challenge due to the complex interactions between intrinsic and external factors, as well as measurement uncertainties. Effective modeling requires a multidimensional approach and a comprehensive understanding of these dynamics and uncertainties. Motivated by an industrial use case based on collected real data containing measured crack lengths, this paper introduces a robust Bayesian multi-horizon approach for predicting the temporal evolution of crack lengths on rails. This model captures the intricate interplay between various factors influencing crack growth. Additionally, the Bayesian approach quantifies both epistemic and aleatoric uncertainties, providing a confidence interval around predictions. To enhance the model's reliability for railroad maintenance, specific constraints are incorporated. These constraints limit non-physical crack propagation behavior and prioritize safety. The findings reveal a trade-off between prediction accuracy and constraint compliance, highlighting the nuanced decision-making process in model training. This study offers insights into advanced predictive modeling for dynamic temporal forecasting, particularly in railway maintenance, with potential applications in other domains.