Multiscale models
Publication
Zago, D., Canale, A., Stefanucci, M. (2022). Bayesian multiscale mixtures of multivariate Gaussian kernels for density estimation. Proceedings of the 36th International Workshop on Statistical Modelling.
Description
In this research project we developed a Bayesian multivariate stick-breaking multiscale mixture model based on a binary-tree expansion,
\[f(y) = \sum_{s=0}^{\infty }\sum_{h=1}^{2^{s}} \pi_{s,h} \mathcal{K}(y | \mathbf{\vartheta}_{s,h}).\]Although the dimension of the target space \(\mathcal{Y} \subseteq \mathbb{R}^{d}\) can be greater than one, we managed to maintain a binary tree structure by leveraging the Hilbert curve during the construction of the underlying stochastic processes. The building block of the proposed approach is a base measure defined by exploiting the Hilbert space-filling curve, which allows the partitioning scheme for the univariate parameter to be adapted to the multivariate case with minor adjustments.