  We study the problem of approximately transforming a sample from a source
statistical model to a sample from a target statistical model without knowing
the parameters of the source model, and construct several computationally
efficient such reductions between statistical experiments. In particular, we
provide computationally efficient procedures that approximately reduce uniform,
Erlang, and Laplace location models to general target families. We illustrate
our methodology by establishing nonasymptotic reductions between some canonical
high-dimensional problems, spanning mixtures of experts, phase retrieval, and
signal denoising. Notably, the reductions are structure preserving and can
accommodate missing data. We also point to a possible application in
transforming one differentially private mechanism to another.
