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1. Assessing Classification Models of Pharmaceuticals With Conformal Prediction

   https://doi.org/10.1002/cem.70017  

   Booksh, Karl S; Celani, Caelin P; Ralbovsky, Nicole M; Smith, Joseph P (March 2025, Journal of Chemometrics)

   ABSTRACT Conformal predictions transform a measurable, heuristic notion of uncertainty into statistically valid confidence intervals such that, for a future sample, the true class prediction will be included in the conformal prediction set at a predetermined confidence. In a Bayesian perspective, common estimates of uncertainty in multivariate classification, namelyp‐values, only provide the probability that the data fits the presumed class model,P(D|M). Conformal predictions, on the other hand, address the more meaningful probability that a model fits the data,P(M|D). Herein, two methods to perform inductive conformal predictions are investigated—the traditional Split Conformal Prediction that uses an external calibration set and a novel Bagged Conformal Prediction, closely related to Cross Conformal Predictions, that utilizes bagging to calibrate the heuristic notions of uncertainty. Methods for preprocessing the conformal prediction scores to improve performance are discussed and investigated. These conformal prediction strategies are applied to identifying four non‐steroidal anti‐inflammatory drugs (NSAIDs) from hyperspectral Raman imaging data. In addition to assigning meaningful confidence intervals on the model results, we herein demonstrate how conformal predictions can add additional diagnostics for model quality and method stability. 

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2. Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems

   https://doi.org/10.1002/cpa.22044  

   Li, Yanyan; Nguyen, Luc (August 2023, Communications on Pure and Applied Mathematics)

   Abstract For a given finite subsetSof a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric onM\Ssuch that each point ofScorresponds to an asymptotically flat end and that the Schouten tensor of the conformal metric belongs to the boundary of the given cone. As a by‐product, we define a purely local notion of Ricci lower bounds for continuous metrics that are conformal to smooth metrics and prove a corresponding volume comparison theorem. © 2022 The Authors.Communications on Pure and Applied Mathematicspublished by Wiley Periodicals LLC. 

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3. JANET: Joint Adaptive predictioN-region Estimation for Time-series

   https://doi.org/10.1007/s10994-025-06812-2  

   English, Eshant; Wong-Toi, Eliot; Fontana, Matteo; Mandt, Stephan; Smyth, Padhraic; Lippert, Christoph (August 2025, Machine Learning)

   Abstract Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (JointAdaptive predictioN-regionEstimation forTime-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlledK-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET’s superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data. 

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4. Three travel time inverse problems on simple Riemannian manifolds

   https://doi.org/10.1090/proc/16453  

   Ilmavirta, Joonas; Liu, Boya; Saksala, Teemu (June 2023, Proceedings of the American Mathematical Society)

   Jiaping Wang (Ed.)

   We provide new proofs based on the Myers–Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics. 

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5. Stability of saddles and choices of contour in the Euclidean path integral for linearized gravity: dependence on the DeWitt parameter

   https://doi.org/10.1007/JHEP05(2024)087  

   Liu, Xiaoyi; Marolf, Donald; Santos, Jorge E (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Due to the conformal factor problem, the definition of the Euclidean gravitational path integral requires a non-trivial choice of contour. The present work examines a generalization of a recently proposed rule-of-thumb [1] for selecting this contour at quadratic order about a saddle. The original proposal depended on the choice of an indefinite-signature metric on the space of perturbations, which was taken to be a DeWitt metric with parameterα= – 1. This choice was made to match previous results, but was otherwise admittedlyad hoc. To begin to investigate the physics associated with the choice of such a metric, we now explore contours defined using analogous prescriptions forα≠ – 1. We study such contours for Euclidean gravity linearized about AdS-Schwarzschild black holes in reflecting cavities with thermal (canonical ensemble) boundary conditions, and we compare path-integral stability of the associated saddles with thermodynamic stability of the classical spacetimes. While the contour generally depends on the choice of DeWitt parameterα, the precise agreement between these two notions of stability found atα= – 1 continues to hold over the finite interval (– 2, – 2/d), wheredis the dimension of the bulk spacetime. This agreement manifestly fails forα> – 2/dwhen the DeWitt metric becomes positive definite. However, we also find dramatic failures forα< – 2 that correlate with breakdowns of the de Donder-like gauge condition defined byα, and at which the relevant fluctuation operator fails to be diagonalizable. This provides criteria that may be useful in predicting metrics on the space of perturbations that give physically-useful contours in more general settings. Along the way, we also identify an interesting error in [1], though we show this error to be harmless. 

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