Establishes measure-theoretic foundations for NML in regular non-smooth models and introduces the PDL-PPMH geometric MCMC sampler to compute stochastic complexity exactly.
Available: https://arxiv.org/abs/2409.08387
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Rm-NML is introduced as a geometrically invariant extension of NML to Riemannian manifolds, with explicit computation shown for normal distributions on hyperbolic spaces.
Exact Schur-Sylvester reductions lower PPMH projection and volume costs for non-smooth NML from O(N^3) to O(k^3 + N^2 k), with reported 14,100x speedups on high-dimensional data while preserving double-precision equivalence.
citing papers explorer
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The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling
Establishes measure-theoretic foundations for NML in regular non-smooth models and introduces the PDL-PPMH geometric MCMC sampler to compute stochastic complexity exactly.
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Normalized Maximum Likelihood Code-Length on Riemannian Data Spaces
Rm-NML is introduced as a geometrically invariant extension of NML to Riemannian manifolds, with explicit computation shown for normal distributions on hyperbolic spaces.
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Exact Schur-Sylvester Dimensionality Reductions for Non-Smooth Stochastic Complexity and Manifold Sampling
Exact Schur-Sylvester reductions lower PPMH projection and volume costs for non-smooth NML from O(N^3) to O(k^3 + N^2 k), with reported 14,100x speedups on high-dimensional data while preserving double-precision equivalence.