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John Tipton

Publications and source records attributed to John Tipton.

2 recordsLinked to original sources

Ribbon: Scalable Approximation and Robust Uncertainty Quantification

Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models. Both fully Bayesian and bootstrap resampling methods provide principled uncertainty estimates but are often too expensive for modern machine-learning models because they require posterior sampling or repeated model refitting. We introduce Ribbon, a scalable approximation to Dirichlet-reweighted bootstrap uncertainty. Ribbon replaces repeated refitting with an influence-function linearization around a single fitted model, preserving the first-order data-reweighting structure of the Bayesian bootstrap while requiring only post-hoc linear algebra. Ribbon approximates the Bayesian-bootstrap or weighted-likelihood-bootstrap refitting target. With a general concentration parameter, Ribbon gives a calibrated Dirichlet-reweighting family whose uncertainty scale can be tuned on validation data. We show that Ribbon is asymptotically equivalent to a flat-prior Laplace approximation under correct likelihood specification and recovers the robust sandwich covariance under misspecification. Across synthetic regression, MNIST classification, and California Housing benchmarks, Ribbon provides competitive predictive performance and improved calibration in several settings while avoiding repeated model retraining.

stat.ML

Reduced Order Modeling for Tsunami Forecasting with Bayesian Hierarchical Pooling

Reduced-order models (ROMs) can represent spatiotemporal processes in significantly fewer dimensions and can often be solved many orders of magnitude faster than their governing partial differential equations (PDEs). For example, proper orthogonal decomposition yields a ROM in which the state is represented as a low-dimensional linear combination of fixed spatial modes and time-dependent coefficients, but this representation remains constrained by the process used to construct the basis. In this work, we explore a new type of ROM that is not restricted to a single fixed coefficient trajectory. Specifically, we consider a corrected Galerkin-projection ROM, formulated as an initial value problem that encodes the physics of the governing PDEs and is calibrated through operator corrections to more accurately reproduce the coefficient dynamics. By combining this corrected reduced model with a Bayesian hierarchical pooling framework over the initial reduced coefficients, we obtain new, statistically interpretable and physically grounded coefficient trajectories that generalize across related scenarios. When recombined with the spatial modes, these trajectories define a complete probabilistic physics surrogate, called a randPROM, for generating simulations that are distributionally consistent with a neighborhood of initial conditions near those used to construct the ROM. We apply the randPROM framework to tsunami modeling, a setting involving unpredictable, catastrophic, and strongly nonlinear dynamics, using both a synthetic case study near Fiji and the real-world 2011 Tohoku tsunami. We demonstrate that randPROMs can substantially reduce the number of full simulations required while providing statistically calibrated and physically defensible predictions of tsunami wave arrival times and heights.

cs.LG