Inductive Conformal Prediction (ICP) provides a practical and effective
approach for equipping deep learning models with uncertainty estimates in the
form of set-valued predictions which are guaranteed to contain the ground truth
with high probability. Despite the appeal of this coverage guarantee, these
sets may not be efficient: the size and contents of the prediction sets are not
directly controlled, and instead depend on the underlying model and choice of
score function. To remedy this, recent work has proposed learning model and
score function parameters using data to directly optimize the efficiency of the
ICP prediction sets. While appealing, the generalization theory for such an
approach is lacking: direct optimization of empirical efficiency may yield
prediction sets that are either no longer efficient on test data, or no longer
obtain the required coverage on test data. In this work, we use PAC-Bayes
theory to obtain generalization bounds on both the coverage and the efficiency
of set-valued predictors which can be directly optimized to maximize efficiency
while satisfying a desired test coverage. In contrast to prior work, our
framework allows us to utilize the entire calibration dataset to learn the
parameters of the model and score function, instead of requiring a separate
hold-out set for obtaining test-time coverage guarantees. We leverage these
theoretical results to provide a practical algorithm for using calibration data
to simultaneously fine-tune the parameters of a model and score function while
guaranteeing test-time coverage and efficiency of the resulting prediction
sets. We evaluate the approach on regression and classification tasks, and
outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on
ICP, especially in the low-data regime.

在这项工作中，我们使用 PAC-Bayes 理论获得了关于集合值预测器的覆盖率和效率的泛化界限，可以直接优化以最大化效率，同时满足所需的测试覆盖率，并利用这些理论结果提供了一种利用校准数据对模型和评分函数的参数进行微调，并确保所得预测集的测试覆盖率和效率的实际算法。

学习归纳态度预测的 PAC-Bayes 泛化证明

PAC-Bayes Generalization Certificates for Learned Inductive Conformal  Prediction

With a goal of understanding what drives generalization in deep networks, we
consider several recently suggested explanations, including norm-based control,
sharpness and robustness. We study how these measures can ensure
generalization, highlighting the importance of scale normalization, and making
a connection between sharpness and PAC-Bayes theory. We then investigate how
well the measures explain different observed phenomena.

研究深度网络通用性的驱动因素，在考虑到规范基础控制、锐度和鲁棒性等因素后，发现尺度归一化对于通用性至关重要，并建立锐度与 PAC-Bayes 理论之间的联系，进一步探究这些措施如何解释已观察到的现象。