Amortized Bandwidth Learning for Kernel Density Estimation under Logarithmic Score

• URL: http://arxiv.org/abs/2608.20445v1
• Date: Thu, 20 Aug 2026 15:56:59 GMT
• Title: Amortized Bandwidth Learning for Kernel Density Estimation under Logarithmic Score
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kernel density estimation converts finite samples into probability densities, but its performance depends critically on bandwidth selection. Classical selectors prescribe the sample-to-bandwidth rule analytically or asymptotically, or solve a new optimization for each sample. An amortized framework is proposed that instead learns this mapping across a distribution of density-estimation tasks by optimizing the logarithmic score. A truncated-and-renormalized bounded-support formulation enables stable learning across heterogeneous tasks, while affine standardization allows a selector trained on a single reference interval to transfer across bounded intervals. 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, the Sheather--Jones selector, and least-squares cross-validation, with especially large gains in small and heterogeneous samples. Finite Gaussian mixtures provide a generic training mechanism supported by their $L^1$ approximation property. Selectors trained in this way generalize strongly across different density structures, allowing the same trained selector to be applied directly to finite samples from unknown densities without specifying or fitting a distributional family. This combination of broad applicability and strong empirical performance makes the framework attractive for a wide range of applications in which finite samples or ensembles must be converted into continuous probability densities.

Related papers

• Total Variation Guarantees for Sampling with Stochastic Localization [0.0]
  We present a rigorous convergence analysis of SLIPS, a sampling algorithm based on localization.<n>We establish the first guarantee for SLIPS in total variation distance.<n>We further provide theoretical insights into the empirically observed optimal choice of discretization points.
  arXiv  Detail & Related papers  (2026-03-31T10:34:42Z)
• Learnable Chernoff Baselines for Inference-Time Alignment [64.81256817158851]
  We introduce Learnable Chernoff Baselines as a method for efficiently and approximately sampling from exponentially tilted kernels.<n>We establish total-variation guarantees to the ideal aligned model, and demonstrate in both continuous and discrete diffusion settings that LCB sampling closely matches ideal rejection sampling.
  arXiv  Detail & Related papers  (2026-02-08T00:09:40Z)
• Combating Noisy Labels through Fostering Self- and Neighbor-Consistency [120.4394402099635]
  Label noise is pervasive in various real-world scenarios, posing challenges in supervised deep learning.<n>We propose a noise-robust method named Jo-SNC (textbfJoint sample selection and model regularization based on textbfSelf- and textbfNeighbor-textbfConsistency)<n>We design a self-adaptive, data-driven thresholding scheme to adjust per-class selection thresholds.
  arXiv  Detail & Related papers  (2026-01-19T07:55:29Z)
• Improved Sample Complexity for Full Coverage in Compact and Continuous Spaces [0.0]
  We study uniform random sampling on the $d$-dimensional unit hypercube.<n>We derive a sample complexity bound with a logarithmic dependence on the failure probability.<n>Our findings offer a sharper theoretical tool for algorithms that rely on grid-based coverage guarantees.
  arXiv  Detail & Related papers  (2025-11-21T21:06:14Z)
• Assessing One-Dimensional Cluster Stability by Extreme-Point Trimming [0.0]
  We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional i.i.d. samples.<n>We derive analytical expressions, including finite-sample corrections, for the expected shrinkage under both the uniform and Gaussian hypotheses.<n>We further integrate our criterion into a clustering pipeline (e.g. DBSCAN), demonstrating its ability to validate one-dimensional clusters without any density estimation or parameter tuning.
  arXiv  Detail & Related papers  (2025-08-29T21:52:15Z)
• 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 Nonparametric Estimation: from Sparse to Dense Samples per Terminal [9.766173684831324]
  We characterize the minimax optimal rates for all regimes, and identify phase transitions of the optimal rates as the samples per terminal vary from sparse to dense.<n>This fully solves the problem left open by previous works, whose scopes are limited to regimes with either dense samples or a single sample per terminal.<n>The optimal rates are immediate for various special cases such as density estimation, Gaussian, binary, Poisson and heteroskedastic regression models.
  arXiv  Detail & Related papers  (2025-01-14T06:41:55Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• 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)
• Sobolev Space Regularised Pre Density Models [51.558848491038916]
  We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive validation model clear and consistent.
  arXiv  Detail & Related papers  (2023-07-25T18:47:53Z)
• 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)
• Reliable Categorical Variational Inference with Mixture of Discrete Normalizing Flows [10.406659081400354]
  Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one.
  arXiv  Detail & Related papers  (2020-06-28T10:39:39Z)

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.