Trending in Methodology
Robust Bayesian Optimization via Tempered Posteriors
Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function such as expected improvement (EI). In practice, BO often concentrates evaluations near the current incumbent, causing the surrogate to become overconfident and to understate predictive uncertainty in the region guiding subsequent decisions. We develop a robust GP-based BO via tempered posterior updates, which downweight the likelihood by a power $α\in (0,1]$ to mitigate overconfidence under local misspecification. We establish cumulative regret bounds for tempered BO under a family of generalized improvement rules, including EI, and show that tempering yields strictly sharper worst-case regret guarantees than the standard posterior $(α=1)$, with the most favorable guarantees occurring near the classical EI choice. Motivated by our theoretic findings, we propose a prequential procedure for selecting $α$ online: it decreases $α$ when realized prediction errors exceed model-implied uncertainty and returns $α$ toward one as calibration improves. Empirical results demonstrate that tempering provides a practical yet theoretically grounded tool for stabilizing BO surrogates under localized sampling.
2601.07094
Jan 2026Methodology
Spatially Varying Gene Regulatory Networks via Bayesian Nonparametric Covariate-Dependent Directed Cyclic Graphical Models
Spatial transcriptomics technologies enable the measurement of gene expression with spatial context, providing opportunities to understand how gene regulatory networks vary across tissue regions. However, existing graphical models focus primarily on undirected graphs or directed acyclic graphs, limiting their ability to capture feedback loops that are prevalent in gene regulation. Moreover, ensuring the so-called stability condition of cyclic graphs, while allowing graph structures to vary continuously with spatial covariates, presents significant statistical and computational challenges. We propose BNP-DCGx, a Bayesian nonparametric approach for learning spatially varying gene regulatory networks via covariate-dependent directed cyclic graphical models. Our method introduces a covariate-dependent random partition as an intermediary layer in a hierarchical model, which discretizes the covariate space into clusters with cluster-specific stable directed cyclic graphs. Through partition averaging, we obtain smoothly varying graph structures over space while maintaining theoretical guarantees of stability. We develop an efficient parallel tempered Markov chain Monte Carlo algorithm for posterior inference and demonstrate through simulations that our method accurately recovers both piecewise constant and continuously varying graph structures. Application to spatial transcriptomics data from human dorsolateral prefrontal cortex reveals spatially varying regulatory networks with feedback loops, identifies potential cell subtypes within established cell types based on distinct regulatory mechanisms, and provides new insights into spatial organization of gene regulation in brain tissue.
2512.11732
Dec 2025Methodology
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