While reliable data-driven decision-making hinges on high-quality labeled
data, the acquisition of quality labels often involves laborious human
annotations or slow and expensive scientific measurements. Machine learning is
becoming an appealing alternative as sophisticated predictive techniques are
being used to quickly and cheaply produce large amounts of predicted labels;
e.g., predicted protein structures are used to supplement experimentally
derived structures, predictions of socioeconomic indicators from satellite
imagery are used to supplement accurate survey data, and so on. Since
predictions are imperfect and potentially biased, this practice brings into
question the validity of downstream inferences. We introduce cross-prediction:
a method for valid inference powered by machine learning. With a small labeled
dataset and a large unlabeled dataset, cross-prediction imputes the missing
labels via machine learning and applies a form of debiasing to remedy the
prediction inaccuracies. The resulting inferences achieve the desired error
probability and are more powerful than those that only leverage the labeled
data. Closely related is the recent proposal of prediction-powered inference,
which assumes that a good pre-trained model is already available. We show that
cross-prediction is consistently more powerful than an adaptation of
prediction-powered inference in which a fraction of the labeled data is split
off and used to train the model. Finally, we observe that cross-prediction
gives more stable conclusions than its competitors; its confidence intervals
typically have significantly lower variability.

通过交叉预测方法进行有效机器学习推断，通过利用小规模标记数据集和大规模未标记数据集，来修正预测不准确性和潜在偏见，并获得更强大且置信区间更稳定的推断结果。

基于交叉预测的推理

Cross-Prediction-Powered Inference

We develop a general approach to valid inference after model selection. At
the core of our framework is a result that characterizes the distribution of a
post-selection estimator conditioned on the selection event. We specialize the
approach to model selection by the lasso to form valid confidence intervals for
the selected coefficients and test whether all relevant variables have been
included in the model.

我们提出了一种通用的模型选择后有效推断方法，通过一个结果对选择事件条件下的后选估计分布进行刻画，并将其专门应用于基于套索算法的模型选择中，形成了有效的系数置信区间，并测试了是否已将所有相关变量包含在模型中。

精确的后选择推断，以套索为例应用

Exact post-selection inference, with application to the lasso

The concept of missing at random is central in the literature on statistical
analysis with missing data. In general, inference using incomplete data should
be based not only on observed data values but should also take account of the
pattern of missing values. However, it is often said that if data are missing
at random, valid inference using likelihood approaches (including Bayesian) can
be obtained ignoring the missingness mechanism. Unfortunately, the term
"missing at random" has been used inconsistently and not always clearly; there
has also been a lack of clarity around the meaning of "valid inference using
likelihood". These issues have created potential for confusion about the exact
conditions under which the missingness mechanism can be ignored, and perhaps
fed confusion around the meaning of "analysis ignoring the missingness
mechanism". Here we provide standardised precise definitions of "missing at
random" and "missing completely at random", in order to promote unification of
the theory. Using these definitions we clarify the conditions that suffice for
"valid inference" to be obtained under a variety of inferential paradigms.

本研究提供了 “随机缺失” 和 “完全随机缺失” 的规范精确定义，以明确缺失机制被忽略的条件，从而在各种推理范式下获得有效推论。