In generative models with obscured likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter trials to keep only a small fraction that passes an acceptance test. To accelerate ABC rejection sampling, this paper develops a self-aware framework that learns from past trials and errors. We apply recursive partitioning classifiers on the ABC lookup table to sequentially refine high-likelihood regions into boxes. Each box is regarded as an arm in a binary bandit problem treating ABC acceptance as a reward. Each arm has a proclivity for being chosen for the next ABC evaluation, depending on the prior distribution and past rejections. The method places more splits in those areas where the likelihood resides, shying away from low-probability regions destined for ABC rejections. We provide two versions: (1) ABC-Tree for posterior sampling, and (2) ABC-MAP for maximum a posteriori estimation. We demonstrate accurate ABC approximability at much lower simulation cost. We justify the use of our tree-based bandit algorithms with nearly optimal regret bounds. Finally, we successfully apply our approach to the problem of masked image classification using deep generative models.

The growing capabilities of AI raise questions about their trustworthiness in healthcare, particularly due to opaque decision-making and limited data availability. This paper proposes a novel approach to address these challenges, introducing a Bayesian Monte Carlo Dropout model with kernel modelling. Our model is designed to enhance reliability on small medical datasets, a crucial barrier to the wider adoption of AI in healthcare. This model leverages existing language models for improved effectiveness and seamlessly integrates with current workflows. We demonstrate significant improvements in reliability, even with limited data, offering a promising step towards building trust in AI-driven medical predictions and unlocking its potential to improve patient care.

Clinical data informs the personalization of health care with a potential for more effective disease management. In practice, this is achieved by subgrouping, whereby clusters with similar patient characteristics are identified and then receive customized treatment plans with the goal of targeting subgroup-specific disease dynamics. In this paper, we propose a novel mixture hidden Markov model for subgrouping patient trajectories from chronic diseases. Our model is probabilistic and carefully designed to capture different trajectory phases of chronic diseases (i.e., "severe", "moderate", and "mild") through tailored latent states. We demonstrate our subgrouping framework based on a longitudinal study across 847 patients with non-specific low back pain. Here, our subgrouping framework identifies 8 subgroups. Further, we show that our subgrouping framework outperforms common baselines in terms of cluster validity indices. Finally, we discuss the applicability of the model to other chronic and long-lasting diseases.

Learning from human feedback plays an important role in aligning generative models, such as large language models (LLM). However, the effectiveness of this approach can be influenced by adversaries, who may intentionally provide misleading preferences to manipulate the output in an undesirable or harmful direction. To tackle this challenge, we study a specific model within this problem domain--contextual dueling bandits with adversarial feedback, where the true preference label can be flipped by an adversary. We propose an algorithm namely robust contextual dueling bandit (\algo), which is based on uncertainty-weighted maximum likelihood estimation. Our algorithm achieves an $\tilde O(d\sqrt{T}+dC)$ regret bound, where $T$ is the number of rounds, $d$ is the dimension of the context, and $ 0 \le C \le T$ is the total number of adversarial feedback. We also prove a lower bound to show that our regret bound is nearly optimal, both in scenarios with and without ($C=0$) adversarial feedback. Additionally, we conduct experiments to evaluate our proposed algorithm against various types of adversarial feedback. Experimental results demonstrate its superiority over the state-of-the-art dueling bandit algorithms in the presence of adversarial feedback.

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high-dimensional settings. In this paper, we propose a framework for Bayesian posterior estimation by mapping data to posteriors of parameters using a neural network trained on data simulated from the complex model. Posterior distributions of model parameters are efficiently obtained by feeding observed data into the trained neural network. We show theoretically that our posteriors converge to the true posteriors in Kullback-Leibler divergence. Our approach yields computationally efficient and theoretically justified uncertainty quantification, which is lacking in existing simulation-based neural network approaches. Comprehensive simulation studies highlight our method's robustness and accuracy.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

We propose an analytical solution for approximating the gradient of the Evidence Lower Bound (ELBO) in variational inference problems where the statistical model is a Bayesian network consisting of observations drawn from a mixture of a Gaussian distribution embedded in unrelated clutter, known as the clutter problem. The method employs the reparameterization trick to move the gradient operator inside the expectation and relies on the assumption that, because the likelihood factorizes over the observed data, the variational distribution is generally more compactly supported than the Gaussian distribution in the likelihood factors. This allows efficient local approximation of the individual likelihood factors, which leads to an analytical solution for the integral defining the gradient expectation. We integrate the proposed gradient approximation as the expectation step in an EM (Expectation Maximization) algorithm for maximizing ELBO and test against classical deterministic approaches in Bayesian inference, such as the Laplace approximation, Expectation Propagation and Mean-Field Variational Inference. The proposed method demonstrates good accuracy and rate of convergence together with linear computational complexity.

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred to as $\Xi$-variational inference ($\Xi$-VI). $\Xi$-VI has a close connection to the entropic optimal transport problem and benefits from the computationally efficient Sinkhorn algorithm. We show that $\Xi$-variational posteriors effectively recover the true posterior dependency, where the dependence is downweighted by the regularization parameter. We analyze the role of dimensionality of the parameter space on the accuracy of $\Xi$-variational approximation and how it affects computational considerations, providing a rough characterization of the statistical-computational trade-off in $\Xi$-VI. We also investigate the frequentist properties of $\Xi$-VI and establish results on consistency, asymptotic normality, high-dimensional asymptotics, and algorithmic stability. We provide sufficient criteria for achieving polynomial-time approximate inference using the method. Finally, we demonstrate the practical advantage of $\Xi$-VI over mean-field variational inference on simulated and real data.

State-of-the-art large language models (LLMs) have become indispensable tools for various tasks. However, training LLMs to serve as effective assistants for humans requires careful consideration. A promising approach is reinforcement learning from human feedback (RLHF), which leverages human feedback to update the model in accordance with human preferences and mitigate issues like toxicity and hallucinations. Yet, an understanding of RLHF for LLMs is largely entangled with initial design choices that popularized the method and current research focuses on augmenting those choices rather than fundamentally improving the framework. In this paper, we analyze RLHF through the lens of reinforcement learning principles to develop an understanding of its fundamentals, dedicating substantial focus to the core component of RLHF -- the reward model. Our study investigates modeling choices, caveats of function approximation, and their implications on RLHF training algorithms, highlighting the underlying assumptions made about the expressivity of reward. Our analysis improves the understanding of the role of reward models and methods for their training, concurrently revealing limitations of the current methodology. We characterize these limitations, including incorrect generalization, model misspecification, and the sparsity of feedback, along with their impact on the performance of a language model. The discussion and analysis are substantiated by a categorical review of current literature, serving as a reference for researchers and practitioners to understand the challenges of RLHF and build upon existing efforts.

In an era of increased climatic disasters, there is an urgent need to develop reliable frameworks and tools for evaluating and improving community resilience to climatic hazards at multiple geographical and temporal scales. Defining and quantifying resilience in the social domain is relatively subjective due to the intricate interplay of socioeconomic factors with disaster resilience. Meanwhile, there is a lack of computationally rigorous, user-friendly tools that can support customized resilience assessment considering local conditions. This study aims to address these gaps through the power of CyberGIS with three objectives: 1) To develop an empirically validated disaster resilience model - Customized Resilience Inference Measurement designed for multi-scale community resilience assessment and influential socioeconomic factors identification, 2) To implement a Platform for Resilience Inference Measurement and Enhancement module in the CyberGISX platform backed by high-performance computing, 3) To demonstrate the utility of PRIME through a representative study. CRIM generates vulnerability, adaptability, and overall resilience scores derived from empirical hazard parameters. Computationally intensive Machine Learning methods are employed to explain the intricate relationships between these scores and socioeconomic driving factors. PRIME provides a web-based notebook interface guiding users to select study areas, configure parameters, calculate and geo-visualize resilience scores, and interpret socioeconomic factors shaping resilience capacities. A representative study showcases the efficiency of the platform while explaining how the visual results obtained may be interpreted. The essence of this work lies in its comprehensive architecture that encapsulates the requisite data, analytical and geo-visualization functions, and ML models for resilience assessment.