论文标题
测试用内核的条件密度模型的拟合优度
Testing Goodness of Fit of Conditional Density Models with Kernels
论文作者
论文摘要
我们提出了两个适合条件分布的拟合优度的非参数统计测试：给定条件概率密度函数$ p（y | x）$和一个联合样本，请确定是否从$ p（y | x）r_x（x）r_x（x）$ for Some Longontion $ r_x $中绘制样品。我们的测试由Stein操作员配制，可以应用于任何可区分的条件密度模型，并且不需要知道归一化常数。我们表明1）我们的测试与任何固定的替代条件模型保持一致； 2）可以轻松估算统计数据，不需要密度估计作为中间步骤； 3）我们的第二次测试提供了可解释的测试结果，提供了有关条件模型在协变量领域不太适合位置的洞察力。我们证明了测试的可解释性，即在提货点上建模纽约市出租车下车地点的分布的任务。据我们所知，我们的工作是第一个提出此类有条件拟合优度测试的工作，同时具有所有这些理想的特性。
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some density $r_x$. Our tests, formulated with a Stein operator, can be applied to any differentiable conditional density model, and require no knowledge of the normalizing constant. We show that 1) our tests are consistent against any fixed alternative conditional model; 2) the statistics can be estimated easily, requiring no density estimation as an intermediate step; and 3) our second test offers an interpretable test result providing insight on where the conditional model does not fit well in the domain of the covariate. We demonstrate the interpretability of our test on a task of modeling the distribution of New York City's taxi drop-off location given a pick-up point. To our knowledge, our work is the first to propose such conditional goodness-of-fit tests that simultaneously have all these desirable properties.
