On a Mallows-type Model for Preference Learning From (Ranked) Choices
Dr. Yifan Feng
Department of Analytics & Operations, NUS Business School
National University of Singapore
In this talk, we study a preference learning setting where participants choose their top-$k$ preferred items from individualized display sets. We present a distance-based ranking model, akin to the Mallows model, using a new distance function called Reverse Major Index (RMJ). The RMJ-based ranking model allows simple closed-form expressions for (ranked) choice probabilities. As a result, it enables efficient methods to infer model parameters with provable consistency. Comprehensive numerical studies demonstrate the model’s favorable generalization power, robustness, and computational efficiency.
We also use the model to examine the relationship between feedback structure richness (represented by $k$) and feedback collection efficiency. We formulate an active preference learning problem: A company sequentially determines display sets and collects top-$k$ ranked choices from customers, aiming to find the top-ranked candidate with minimal samples. We evaluate the informational efficiency of various $k$ values using sample complexity under optimal sequential feedback collection procedures. Our results indicate that while information efficiency increases with $k$, a small value of $k=2$ is close to (and sometimes equals) the full-efficiency value.