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Distribution learning via neural differential equations: a nonparametric statistical perspective
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions.
Infinite-Dimensional Diffusion Models
For image distributions, these guidelines are in line with the canonical choices currently made for diffusion models.
On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions
We exhibit examples of high-dimensional unimodal posterior distributions arising in non-linear regression models with Gaussian process priors for which MCMC methods can take an exponential run-time to enter the regions where the bulk of the posterior measure concentrates.
On minimax density estimation via measure transport
We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport.
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