Laplace-Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation

• URL: http://arxiv.org/abs/2606.25169v2
• Date: Wed, 01 Jul 2026 03:30:46 GMT
• Title: Laplace-Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation
• Abstract summary: Laplace-Fisher Gate Identity (LFGI)<n> finite-reference LFGI estimator to normalized density evaluation for Bayesian inverse problems.<n>Experiments using LFGI with known model evidence check absolute evidence calibration in both Gaussian and non-Gaussian settings.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Sampling from an unnormalized target by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal. Tweedie's identity and a target-score identity give unbiased finite-reference estimators for this score. Scalar blends can reduce variance, but are too rigid for singular or strongly anisotropic targets. We cast blended score estimation as conditional risk minimization over matrix-valued blending coefficients, or gates, and derive the variance-optimal gate G*(y,t) = alpha_t^2 (alpha_t^2 I_d + gamma_t E[H_0(X_0) | Y_t = y])^{-1}, H_0 = -nabla^2 log p_0. Here alpha_t = e^{-t} and gamma_t = 1 - e^{-2t}. We call this formula the Laplace-Fisher Gate Identity (LFGI). Since the Tweedie-TSI disagreement has conditional mean zero, the gate changes estimator variance without changing its expected value. We give the Gaussian special case and prove finite-reference consistency and stability bounds for estimating the gate from weighted reference samples. We apply the finite-reference LFGI estimator to normalized density evaluation for Bayesian inverse problems. When MCMC pilot samples and derivative information are available, LFGI uses these byproducts to construct a normalized posterior-density surrogate. The surrogate enables posterior-energy evaluation, model-evidence estimation, and downstream density-based diagnostics. On a PDE-constrained inverse-problem benchmark, the LFGI surrogate improves posterior-density calibration and sampling diagnostics relative to the other tested score-estimator classes. Experiments using LFGI with known model evidence check absolute evidence calibration in both Gaussian and non-Gaussian settings.

Related papers

• EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale [9.562123195246393]
  EGGROLL makes evolution strategies practical for LLMs by replacing dense Gaussian weight perturbations with low-rank Gaussian products.<n>We analyze the error of its finite-population estimator.<n>LOO-ROLL, a leave-one-out estimator, preserves the finite-rank population field while replacing EGGROLL's two antithetic evaluations per direction by one.
  arXiv  Detail & Related papers  (2026-09-10T01:58:02Z)
• Sample-Adaptive Latent Rewards for Uncertainty-Guided Diffusion Post-Training [51.18425726646089]
  We propose textscSURE, a unified latent-space framework for image and video diffusion models.<n>It learns reward distributions and directly uses their reliability to guide dense post-training.<n>textscSURE-REFL achieves the highest VBench quality, semantic, and total scores among the evaluated methods.
  arXiv  Detail & Related papers  (2026-08-06T14:55:42Z)
• Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model [0.554780083433538]
  We study ridge-regularized log-density-ratio estimation in the Gaussian location model.<n>The variational estimator is the empirical Kullback-Leibler (KL) log-normalized fit with a squared L2-penalty on its nonconstant coefficient.
  arXiv  Detail & Related papers  (2026-07-02T08:46:52Z)
• Information Hidden in Gradients of Regression with Target Noise [2.8911861322232686]
  We show that the gradients alone can reveal the Hessian.<n>We provide non-asymptotic operator-norm guarantees under sub-Gaussian inputs.
  arXiv  Detail & Related papers  (2026-01-26T14:50:16Z)
• Variance-Reduced Diffusion Sampling via Target Score Identity [0.0]
  We study variance reduction for score estimation and diffusion-based sampling in settings where the clean (target) score is available or can be approximated.<n>We develop a plug-and-play nonparametric self-normalized importance sampling estimator compatible with standard reverse-time solvers.<n> Experiments on synthetic targets and PDE-governed inverse problems demonstrate improved sample quality for a fixed simulation budget.
  arXiv  Detail & Related papers  (2026-01-04T16:46:31Z)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• On the Wasserstein Convergence and Straightness of Rectified Flow [54.580605276017096]
  Rectified Flow (RF) is a generative model that aims to learn straight flow trajectories from noise to data.<n>We provide a theoretical analysis of the Wasserstein distance between the sampling distribution of RF and the target distribution.<n>We present general conditions guaranteeing uniqueness and straightness of 1-RF, which is in line with previous empirical findings.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Batch and match: black-box variational inference with a score-based divergence [26.873037094654826]
  We propose batch and match (BaM) as an alternative approach to blackbox variational inference (BBVI) based on a score-based divergence. We show that BaM converges in fewer evaluations than leading implementations of BBVI based on ELBO.
  arXiv  Detail & Related papers  (2024-02-22T18:20:22Z)
• Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference [0.8388591755871735]
  This study presents a Bayesian maximum textitaposteriori (MAP) framework for dynamical system identification from time-series data.
  arXiv  Detail & Related papers  (2024-01-30T12:16:52Z)
• TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression [109.69084997173196]
  Deepscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. Recent works show that this may result in sub-optimal convergence due to the challenges associated with covariance estimation. We study two questions: (1) Does the predicted covariance truly capture the randomness of the predicted mean? Our results show that not only does TIC accurately learn the covariance, it additionally facilitates an improved convergence of the negative log-likelihood.
  arXiv  Detail & Related papers  (2023-10-29T09:54:03Z)
• Auto-Encoding Goodness of Fit [9.560668678348579]
  We develop a new type of generative autoencoder called the Goodness-of-Fit Autoencoder (GoFAE)<n>At the minibatch level, it uses GoF test statistics as regularization objectives.<n>At a more global level, it selects a regularization coefficient based on higher criticism.
  arXiv  Detail & Related papers  (2022-10-12T19:21:57Z)
• Gradient Estimation for Binary Latent Variables via Gradient Variance Clipping [6.234350105794441]
  gradient estimation is often necessary for fitting generative models with discrete latent variables. DisARM and other estimators have potentially exploding variance near the boundary of the parameter space. We propose a new gradient estimator textitbitflip-1 that has lower variance at the boundaries of the parameter space.
  arXiv  Detail & Related papers  (2022-08-12T05:37:52Z)
• Optimal Extragradient-Based Bilinearly-Coupled Saddle-Point Optimization [116.89941263390769]
  We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $min_mathbfxmax_mathbfyF(mathbfx) + H(mathbfx,mathbfy)$, where one has access to first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. We present a emphaccelerated gradient-extragradient (AG-EG) descent-ascent algorithm that combines extragrad
  arXiv  Detail & Related papers  (2022-06-17T06:10:20Z)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator [93.05919133288161]
  We show that the variance of the straight-through variant of the popular Gumbel-Softmax estimator can be reduced through Rao-Blackwellization. This provably reduces the mean squared error. We empirically demonstrate that this leads to variance reduction, faster convergence, and generally improved performance in two unsupervised latent variable models.
  arXiv  Detail & Related papers  (2020-10-09T22:54:38Z)

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.