What Makes A Good Fisherman? Linear Regression under Self-Selection Bias. (arXiv:2205.03246v1 [math.ST])

In the classical setting of self-selection, the goal is to learn $k$ models,
simultaneously from observations $(x^{(i)}, y^{(i)})$ where $y^{(i)}$ is the
output of one of $k$ underlying models on input $x^{(i)}$. In contrast to
mixture models, where we observe the output of a randomly selected model, here
the observed model depends on the outputs themselves, and is determined by some
known selection criterion. For example, we might observe the highest output,
the smallest output, or the median output of …

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