Post-selection inference studies how to perform valid statistical inference after a model, variable set, or hypothesis has been chosen using the same data. Classical theory assumes the model is fixed in advance, but modern workflows first select features, tune hyperparameters, or choose networks, which introduces hidden bias. Post-selection theory corrects for this by conditioning on the selection event and using tools from probability, such as truncated distributions, martingales, and selective likelihoods, to recover valid p-values and confidence intervals. In statistics, it enables honest inference after LASSO, stepwise regression, and data-driven model choice. In machine learning, it is crucial for feature selection, neural architecture search, and adaptive pipelines, where naĆÆve uncertainty estimates are misleading. In deep learning, post-selection ideas support reliable evaluation and interpretability. By accounting for data reuse, post-selection inference restores trust in conclusions drawn from complex, adaptive learning systems.
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