发表机构
Nanyang Technological University; Eötvös Loránd University (ELTE); HUN-REN Institute for Computer Science and Control (SZTAKI)（南洋理工大学; 厄特沃什·罗兰大学（ELTE）; 匈牙利国家研究网络计算机科学与控制研究所（SZTAKI））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于逻辑高斯过程的可扩展贝叶斯条件密度估计器，采用动力学朗之万采样高效推断，在光度红移基准上媲美最先进模型。
AI 中文摘要
条件密度估计旨在给定协变量时预测响应的完整分布，例如在逐个星系的光度红移估计中就需要这种估计。我们开发了一种基于逻辑高斯过程的可扩展贝叶斯估计器。对数条件密度具有可分离的协方差：沿响应方向使用马特恩核，在圆上的截断傅里叶基中表示；协变量核则通过Nyström特征表示，能够适应具有输入依赖振幅和长度尺度的非平稳核。我们不对潜在场采用拉普拉斯或变分近似，而是直接对该有限特征模型的潜在场进行采样。在给定超参数的情况下，其后验是强对数凹的，且Hessian矩阵一致有界，我们通过模拟动力学朗之万动力学来从中采样，在Kronecker白化坐标中使用对称小批量分裂。边际似然梯度通过Fisher恒等式作为后验期望获得。在我们的分析条件下，其偏差受采样器步长和运行长度的控制，预测平均值基于非高斯潜在后验，而非围绕其众数的高斯近似。在光度红移基准测试中，使用多达390万个训练样本，在单个GPU上训练，该估计器在密度和校准指标上与最先进的表格基础模型相当。
英文摘要
Conditional density estimation targets the full distribution of a response given covariates, as required, for example, for per-galaxy photometric redshifts. We develop a scalable Bayesian estimator based on the logistic Gaussian process. The log conditional density has a separable covariance: a Matérn kernel along the response, represented in a truncated Fourier basis on a circle, and a covariate kernel represented by Nyström features, which accommodate non-stationary kernels with input-dependent amplitudes and length scales. Instead of a Laplace or variational approximation, we sample the latent field of this finite-feature model. Given the hyperparameters, its posterior is strongly log-concave with a uniformly bounded Hessian, and we draw from it by simulating kinetic Langevin dynamics with symmetric minibatch splitting in Kronecker-whitened coordinates. Marginal-likelihood gradients follow from Fisher's identity as posterior expectations. Under the conditions of our analysis their bias is controlled by the sampler's step size and run length, and the predictive averages over the non-Gaussian latent posterior instead of a Gaussian around its mode. On photometric-redshift benchmarks with up to 3.9 million training observations, trained on a single GPU, the estimator is competitive with state-of-the-art tabular foundation models on density and calibration metrics.
Comments27 pages, 3 figures
