Finite-Rank Logistic Gaussian Processes with Exact Likelihood for Conditional Density Estimation
Year: 2026
Type: preprint
Abstract: Conditional density estimation describes how the entire distribution of a response changes with covariates, and in imaging studies also with location. Logistic Gaussian processes (LGP) give a flexible prior for such densities. However, the normalizing constant of an LGP has no closed form, so existing methods approximate or replace the likelihood. 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. Each function is assigned a finite-rank Gaussian process prior that is piecewise linear on a regular grid, enabling the normalizing constant, the conditional mean and the quantiles to enjoy closed form representations. Posterior samples are drawn from the exact posterior under this prior via a Gibbs sampler that updates the Gaussian components by elliptical slice sampling. 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. Numerical experiments using synthetic data demonstrate the effectiveness of ExFR-LGP in conditional density estimation. 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: U.S. Department of Defense, Alzheimer's Association, Bristol-Myers Squibb, Eli Lilly and Company, Pfizer, Biogen, University of Southern California, F. Hoffmann-La Roche, Meso Scale Diagnostics, Alzheimer's Disease Neuroimaging Initiative, BioClinica, Novartis Pharmaceuticals Corporation, Northern California Institute for Research and Education, Eisai, Servier, H. Lundbeck A/S, IXICO, National Institutes of Health, Genentech, Canadian Institutes of Health Research, National Institute of Dental and Craniofacial Research
Awards: G1012222616, G1298807586, G1554142629, G1593117279, G1650819308, G1880935189, G2100670906, G2152643862, G2189010064, G2340207221, G2423387114, G2471646051, G2522063444, G2835601961, G29951154, G3131374986, G3216574877, G3553156159, G3710456697, G3752451908, G3870774570, G3908963977, G3966393351, G43180419, G4501223628, G4800177743, G5207404921, G5209990037, G528601746, G5365730499, G5654639750, G5740349702, G613619302, G6173816828, G6210868510, G6371410416, G6412110892, G6447063303, G6719828067, G6792506723, G6899163935, G6948409098, G72415811, G7298697282, G764699806, G7799614282, G781725486, G8228018387, G8281378126, A pragmatic risk index evaluating the elderly with comorbidity for oral health event times, G839208290, G8852128998, G8895907669, G8897063270, G8957659042, G9000039018, G9000122335, Sex influences on periodontal disease and diabetes: A population science approach, with software
OpenAlex ID: W7221002457