From low to high-dimensional moments without magic
This work addresses the problem of moment recovery for high-dimensional random vectors, offering a principled approach for dimensionality reduction in statistical estimation.
The paper provides explicit reconstruction formulas and a computational framework to compute high-dimensional moments from low-dimensional projections, with randomized projections enabling approximate recovery.
We aim to compute the first few moments of a high-dimensional random vector from the first few moments of a number of its low-dimensional projections. To this end, we identify algebraic conditions on the set of low-dimensional projectors that yield explicit reconstruction formulas. We also provide a computational framework, with which suitable projectors can be derived by solving an optimization problem. Finally, we show that randomized projections permit approximate recovery.