Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches

A new framework called min-max Functional Bayesian Optimization (MM-FBO) has been proposed to optimize functional responses under min-max criteria, addressing limitations of traditional Bayesian optimization methods that focus on scalar responses. This approach minimizes the maximum error across the functional domain, utilizing functional principal component analysis and Gaussian process surrogates for improved performance.

A novel hierarchical Bayesian framework for semiparametric mixture cure models has been proposed, enhancing survival analysis by accommodating frailty components. This approach aims to provide a more accurate representation of long-term survival dynamics, particularly for patients considered cured, and utilizes Markov chain Monte Carlo methods for posterior distribution sampling.

A novel framework called self-diffusion has been proposed for solving inverse problems, which operates without the need for pretrained generative models. This approach involves an iterative process of alternating noising and denoising steps, refining estimates of solutions using a self-denoiser that is a randomly initialized convolutional network.

A new study revisits the ski rental problem using a Bayesian decision-making framework, proposing a discrete Bayesian approach that maintains exact posterior distributions over time. This method allows for principled uncertainty quantification and the integration of expert priors, achieving competitive guarantees that balance worst-case and fully-informed scenarios.

A new study has focused on the estimation of conditional independence graphs (CIGs) from high-dimensional multivariate Gaussian time series using multi-attribute data. This research introduces a theoretical framework for graph learning that employs a penalized log-likelihood objective function in the frequency domain, utilizing the discrete Fourier transform of time-domain data.