Manifold Sampling via Entropy Maximization

• URL: http://arxiv.org/abs/2605.12338v1
• Date: Tue, 12 May 2026 16:19:32 GMT
• Title: Manifold Sampling via Entropy Maximization
• Abstract summary: We propose MAnifold Sampling via Entropy Maximization (MASEM) for sampling on a manifold with an unknown number of disconnected components.<n>We show that MASEM decreases the KL-divergence between the empirical distribution and the maximum-entropy target exponentially in the number of resampling steps.
• Score: 10.198969609811323
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible set is connected. However, in practice, the feasible set often decomposes into multiple disconnected components, which makes efficient sampling under constraints challenging. In this paper, we propose MAnifold Sampling via Entropy Maximization (MASEM) for sampling on a manifold with an unknown number of disconnected components, implicitly defined by smooth equality and inequality constraints. The presented method uses a resampling scheme to maximize the entropy of the empirical distribution based on k-nearest neighbor density estimation. We show that, in the mean field, MASEM decreases the KL-divergence between the empirical distribution and the maximum-entropy target exponentially in the number of resampling steps. We instantiate MASEM with multiple local samplers and demonstrate its versatility and efficiency on synthetic and robotics-based benchmarks. MASEM enables fast and scalable mixing across a range of constrained sampling problems, improving over alternatives by an order of magnitude in Sinkhorn distance with competitive runtime.

Related papers

• Amortized Bandwidth Learning for Kernel Density Estimation under Logarithmic Score [0.0]
  An amortized framework is proposed that learns mapping across a distribution of density-estimation tasks by optimizing the logarithmic score.<n>Experiments under Gaussian sampling, a multi-family benchmark, and randomized Gaussian-mixture training show that the amortized selector consistently and substantially outperforms Silverman's rule.
  arXiv  Detail & Related papers  (2026-08-20T15:56:59Z)
• Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging [22.40017989720178]
  High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities.<n>We propose emphHyperbolic Secant-squared Gibbs-Sampling (HiSS), a novel family of sampling algorithms that integrates a emphMetropolis-within-Gibbs framework to enhance mixing efficiency.
  arXiv  Detail & Related papers  (2026-04-12T21:23:35Z)
• Score-based sampling without diffusions: Guidance from a simple and modular scheme [0.0]
  We show how to design forward trajectories that both (a) the terminal distribution, and (b) each of the backward conditional distribution is defined by a strongly log concave (SLC) distribution.<n>This modular reduction allows us to exploit emphany SLC sampling algorithm in order to traverse the backwards path.<n>The use of high-accuracy routines yields $varepsilon$-accurate answers, in either KL or Wasserstein distances.
  arXiv  Detail & Related papers  (2025-12-30T11:34:59Z)
• Restricted Spectral Gap Decomposition for Simulated Tempering Targeting Mixture Distributions [8.366536762687492]
  We consider simulated tempering combined with an arbitrary local chain Monte Carlo sampler.<n>We present a new decomposition theorem that provides a lower bound on the restricted spectral gap of the Metropolis for sampling from mixture distributions.
  arXiv  Detail & Related papers  (2025-05-21T03:28:55Z)
• Adaptive Sampled Softmax with Inverted Multi-Index: Methods, Theory and Applications [79.53938312089308]
  The MIDX-Sampler is a novel adaptive sampling strategy based on an inverted multi-index approach.<n>Our method is backed by rigorous theoretical analysis, addressing key concerns such as sampling bias, gradient bias, convergence rates, and generalization error bounds.
  arXiv  Detail & Related papers  (2025-01-15T04:09:21Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Sampling with Mollified Interaction Energy Descent [57.00583139477843]
  We present a new optimization-based method for sampling called mollified interaction energy descent (MIED) MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs) We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD.
  arXiv  Detail & Related papers  (2022-10-24T16:54:18Z)
• A Proximal Algorithm for Sampling [14.909442791255042]
  We study problems associated with potentials that lack smoothness. The potentials can be either convex or non-smooth. Our algorithm is based on a special case of rejection sampling.
  arXiv  Detail & Related papers  (2022-02-28T17:26:09Z)
• Ensemble Slice Sampling: Parallel, black-box and gradient-free inference for correlated & multimodal distributions [0.0]
  Slice Sampling has emerged as a powerful Markov Chain Monte Carlo algorithm that adapts to the characteristics of the target distribution with minimal hand-tuning. This paper introduces Ensemble Slice Sampling (ESS), a new class of algorithms that bypasses such difficulties by adaptively tuning the initial length scale. These affine-invariant algorithms are trivial to construct, require no hand-tuning, and can easily be implemented in parallel computing environments.
  arXiv  Detail & Related papers  (2020-02-14T19:00:12Z)
• Generative Modeling with Denoising Auto-Encoders and Langevin Sampling [88.83704353627554]
  We show that both DAE and DSM provide estimates of the score of the smoothed population density. We then apply our results to the homotopy method of arXiv:1907.05600 and provide theoretical justification for its empirical success.
  arXiv  Detail & Related papers  (2020-01-31T23:50:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.