[object Object]The evidence, $\mathcal{Z} = p(x | \mathcal{M})$, of a data-generating model $\mathcal{M}$ is a powerful tool in Bayesian frameworks: it enables model inference, model misspecification tests, and goodness-of-fit assessment as an alternative to standard discrepancy statistics, e.g. $χ^2$. While versatile, the evidence is notoriously difficult to compute, even when the likelihood is available. In both likelihood-based and simulation-based inference, estimating $\mathcal{Z}$ provides an immediate solution to high-dimensional goodness-of-fit or model misspecification tests: using $\mathcal{Z}(x)$ as the test statistic induces a minimum-volume level-$α$ test. Such tests are essential to assess model fidelity, which is necessary to trust simulation-based parameter inference. Existing learned approaches largely target Bayes factors, which only measure evidence ratios. Instead, we provide accura
2d ago·Kai Lehman, Jameson Dong, Carolina Cuesta-Lazaro et al.·PDF↗ [object Object]Many of the most important datasets in the physical sciences live natively on the sphere, and these data often carry no preferred position or orientation. Using methods that do not reflect this symmetry leads to far higher simulation requirements, which can be catastrophic for scientific analyses (forcing reliance on cheap, imperfect models that bias results). We present a novel spherical implementation of a gauge equivariant mesh architecture that is specifically designed for the Hierarchical Equal Area isoLatitude Pixelization (\healpix{}) of the sphere. The $\mathrm{SO}(3)$-equivariant convolution is built from steerable filters, parallel transport and spin-weighted features. The architecture supplies the exact symmetry, so the network does not spend training data learning it. The convolution operations are constructed to give provably exact equivariance, given a band-limit. Our full
2d ago·Joshua Williamson, Niall Jeffrey, Lorne Whiteway·PDF↗ [object Object]Rènyi differential privacy, based on Rènyi divergence, has become a notion of choice for privacy guarantees. However, outside the Gaussian setting, Rènyi divergence can be difficult to compute. In particular, Rènyi differential privacy guarantees that exploit task-specific information, as in Rènyi Pufferfish privacy, can be challenging. Here we use kernel Stein discrepancies based on escort distributions to provide certificates for Rènyi differential privacy. By designing the kernel to focus on the relevant privacy directions, we also derive task-aware privacy certificates. We provide exact identities for Gaussian and Laplace mechanisms and bounds for exponential mechanisms, with separate task-aware guarantees. A real data set example illustrates how the protected comparison set and the released subspace jointly determine the resulting certificates.
2d ago·Leoni Carla Wirth, Tara Trautwein, Gesine Reinert·PDF↗ [object Object]Primal-dual methods for constrained Markov decision processes are analyzed under a two-timescale assumption, with non-stationarity entering through two channels. In the additive channel, where the constraint level oscillates, the dual oscillation saturates at a floor set by the moving optimum and is amplified linearly by the timescale ratio. In the parametric channel, where the constraint sensitivity oscillates, a coherent modulation carries no resonant forcing at any depth: the dual update's stiffness modulation cancels the primal update's damping modulation. Instability instead comes from a mismatch between the constraint estimate used by the primal update and the measurement used by the dual update, producing a parametric resonance at twice the pair's natural frequency. The tolerated mismatch grows with the square root of the forcing bandwidth and collapses with the square root of the
2d ago·Maxime Baelde·PDF↗ 