Determinantal sampling on general spaces: fast approximation via diffusion geometry

arXiv:2607.06644 · stat.ML, cs.LG, math.PR · Submitted 2026-07-07 · Read on arXiv

stat.ML, cs.LG, math.PR

Submitted: 2026-07-07

Updated: 2026-10-24

Comments: Preliminary version - to be updated

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Variance Reduction — 27× in this paper · explained in 2 episodes
• Core — 8× in this paper · explained in 2 episodes
• Generator — 8× in this paper · explained in 2 episodes
• Benchmark — 5× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Intrinsic Dimension — 4× in this paper · explained in 3 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Orthogonal Projection — 2× in this paper · explained in 2 episodes
• Point Clouds — 2× in this paper · explained in 2 episodes
• Reduction Theorem — 2× in this paper · explained in 2 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Geometric interpretation — 1× in this paper · explained in 2 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Infinitesimal Generator — 1× in this paper · explained in 2 episodes
• Monotonicity — 1× in this paper · explained in 2 episodes
• Monte Carlo Sampling — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Spectral Clustering — 1× in this paper · explained in 3 episodes
• Spectral Geometry — 1× in this paper · explained in 3 episodes

Sources

• Monte Carlo integration of non-differentiable functions on $[0,1]^\iota$, $\iota=1,\dots,d$, using a single determinantal point pattern defined on $[0,1]^d$
• State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives

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