Finite-Rank Logistic Gaussian Processes with Exact Likelihood for Conditional Density Estimation

Key points

• Conditional density estimation describes how the entire distribution of a response changes with covariates, and in imaging studies also with location.1
• Logistic Gaussian processes (LGP) give a flexible prior for such densities.1
• When the true log density is the sum of two such bivariate functions, we show that the posterior contracts at the minimax rate of an $α$-smooth bivariate density up to a logarithmic factor.1
• Furthermore, application to fractional anisotropy responses along the corpus callosum in the Alzheimer's Disease Neuroimaging Initiative data yields covariate-adjusted percentile bands with uncertainty, elucidating how diagnosis changes the distribution along the tract.1

Sources (1)

• [1]Finite-Rank Logistic Gaussian Processes with Exact Likelihood for Conditional Density Estimation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 05:08 AM

  We propose the exact likelihood finite-rank LGP (ExFR-LGP), which writes the log density as the sum of two bivariate functions, one of the response and a location-varying linear index of the covariates, and one of the response and the location.

  Conditional density estimation describes how the entire distribution of a response changes with covariates, and in imaging studies also with location.

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