arXiv Statistics ML
Seeing the Forest for the Trees: The Gaussian Process Limit of BART
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arXiv Machine Learning
Aug 27
Fast rates in Bayesian online learning with approximate posteriors
The paper investigates how fast predictive regret guarantees of exact Bayesian online learning can be maintained when using approximate posterior methods. It establishes a general theorem linking the cumulative cost of posterior approximation to the contraction radius of the exact Gibbs posterior and the Wasserstein distance between approximate and exact posteriors. Three concrete online learning scenarios—linear models, infinite‑dimensional exponential families, and Gaussian process regression—illustrate that appropriately accurate approximations (projected Langevin, truncation, and sparse variational posteriors) preserve fast regret bounds while reducing computational demands.
arXiv Machine Learning
Jun 30
Warm-Starting Iterative Gaussian Processes for Faster Sequential Inference
arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
arXiv Machine Learning
Sep 10
Differentiable Causal Discovery for Singular Linear Models under Confounding
arXiv:2601.01368v2 Announce Type: replace Abstract: Score-based causal discovery in the presence of unobserved confounders requires both a consistent scoring criterion and an efficient search over gr...
arXiv Machine Learning
Aug 28
Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences
The monograph explores the relationships between Gaussian processes and reproducing kernel Hilbert spaces (RKHS), two widely used approaches that rely on positive definite kernels. It examines how these frameworks connect and are equivalent across key topics such as regression, interpolation, numerical integration, distributional discrepancies, statistical dependence, and Gaussian process sample path properties. By establishing a unifying perspective based on the equivalence between the Gaussian Hilbert space and the RKHS, the work aims to bridge methods developed independently by the machine learning, statistics, and numerical analysis communities.
arXiv AI
Jun 2
Transferring Information Across Interventions in Causal Bayesian Optimization
arXiv:2606. 01457v1 Announce Type: new Abstract: Bayesian optimization is a popular way to optimize expensive systems, where every experiment, simulation, or intervention costs time or money.
arXiv Machine Learning
Jul 27
Scalable Gaussian process inference via neural feature maps
arXiv:2605. 10285v2 Announce Type: replace-cross Abstract: We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels.