arXiv:2606. 17014v1 Announce Type: new Abstract: Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence.
arXiv:2608. 08826v1 Announce Type: new Abstract: Adaptive procedures must work without nuisance information an oracle may use, such as a gradient scale or smoothness index, and robust procedures may have to answer queries whose coordinate and inspection time are chosen only after the data are seen.
arXiv:2607. 26577v1 Announce Type: new Abstract: Adaptive conformal inference (ACI) of Gibbs and Cand{\`e}s and its variants are the standard approach to online conformal prediction under distribution shift, but they suffer from three fundamental limitations.
The paper introduces a new representation‑adaptive kernel class that, on a fixed sample, yields a union of reproducing‑kernel Hilbert‑space ellipsoids instead of a single ellipsoid. It defines a minimum‑trace common covariance dominating the empirical union generated by Brownian kernel ladders, and derives exact formulations, statistical and computational consequences, and a universal Gaussian‑complexity bound. The work further develops geometric reductions, deterministic depth laws, and exact empirical Kolmogorov‑width formulas, providing both lower and upper certificates for covariance certification and illustrating the distinction between successful covariance certification and predictive selection.
SPACE is a conformal wrapper that creates ellipsoidal joint prediction regions for multivariate time‑series forecasts by estimating time‑local covariance directly from the current forecast sample cloud. It calibrates the region’s radius using a dynamic backward window‑selection scheme, avoiding reliance on historical residuals. Experiments on diverse datasets show that SPACE improves joint and rolling coverage, achieving better coverage‑efficiency tradeoffs than existing wrappers.
arXiv:2604. 06464v2 Announce Type: replace Abstract: Conformal prediction provides distribution-free prediction intervals with finite-sample coverage guarantees, and recent work by Snell \& Griffiths reframes it as Bayesian Quadrature (BQ-CP), yielding powerful data-conditional guarantees via Dirichlet posteriors over thresholds.
The paper introduces a tail‑aware geometry learning framework for multivariate conformal prediction using ellipsoids. It decouples tail sensitivity from coverage guarantees by learning a metric matrix through volume minimization under a CVaR constraint, followed by standard conformal calibration. The approach is convex, prioritizes high‑residual samples, and theoretically balances ellipsoidal volume against tail severity, with experiments confirming its effectiveness.
arXiv:2606. 26497v1 Announce Type: new Abstract: Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system, given observations, in an online fashion.
arXiv:2608. 06206v1 Announce Type: cross Abstract: Conformal prediction endows arbitrary black-box predictors with finite-sample, distribution-free marginal coverage, yet marginal validity can hide severe covariate-specific miscalibration, while exact distribution-free conditional coverage is finite-sample unattainable.
arXiv:2607. 18559v1 Announce Type: cross Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process.
arXiv:2607. 20239v1 Announce Type: cross Abstract: Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream.
SPARC (Single-Pass Adaptive Risk Calibration) is a Bayesian‑conformal uncertainty layer for human motion forecasting that adds an analytic epistemic scale to a deterministic MLP backbone’s Gaussian covariance. The scale, κ_t(x), inflates the covariance without altering its correlation structure, enabling 95% marginal prediction tubes with finite‑sample validity via split conformal calibration. Across nine dataset‑protocol blocks, SPARC outperforms baselines on NLL and a combined MPJPE+NLL metric while maintaining competitive point accuracy and efficient calibrated tubes.
arXiv:2606. 02232v1 Announce Type: new Abstract: Learning a Markov transition model is not merely conditional density estimation: the learned object must be a valid transition kernel before it is iterated in downstream dynamics.