Abstract: The timed position of documents retrieved by learning to rank models can be seen as signals. Signals
carry useful information such as drop or rise of documents over time or user behaviors. In this work,
we propose to use the logic formalism called Signal Temporal Logic (STL) to characterize document
behaviors in ranking accordingly to the specified formulas. Our analysis shows that interesting
document behaviors can be easily formalized and detected thanks to STL formulas. We validate our
idea on a dataset of 100K product signals. Through the presented framework, we uncover interesting
patterns, such as cold start, warm start, spikes, and inspect how they affect our learning to ranks
models.
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