Scalable Logistic Gaussian Process Density Regression with Kinetic Langevin Sampling

Key points

• Conditional density estimation targets the full distribution of a response given covariates, as required, for example, for per-galaxy photometric redshifts.1
• 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.1
• 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.1
• Marginal-likelihood gradients follow from Fisher's identity as posterior expectations.1

Sources (1)

• [1]Scalable Logistic Gaussian Process Density Regression with Kinetic Langevin Sampling
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 07:35 AM

  We develop a scalable Bayesian estimator based on the logistic Gaussian process.

  Conditional density estimation targets the full distribution of a response given covariates, as required, for example, for per-galaxy photometric redshifts.

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