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.

翻译：我们研究了在未知源统计模型参数的情况下，将源统计模型的样本近似转化为目标统计模型样本的问题，并构建了统计实验之间若干计算高效的此类约简。具体而言，我们提供了将均匀分布、埃尔朗分布和拉普拉斯位置模型近似约简为一般目标族的计算高效流程。通过建立涵盖专家混合、相位恢复和信号去噪等经典高维问题之间的非渐近约简，我们展示了该方法。值得注意的是，这些约简具有结构保持特性，并能处理缺失数据。我们还指出了该方法在将一种差分隐私机制转化为另一种差分隐私机制方面的潜在应用。