scary

paper/src/chapters/03-methodology.tex

@@ -304,7 +304,7 @@ $\mathcal{A}_{\text{filter}}$ & \texttt{search}, \texttt{filter\_date}, \texttt{
 This partition enables the weight function $\omega$ from Eq.~\ref{eq:qhat} to assign category-specific signal strengths, with $\omega(\mathcal{A}_{\text{cart}}) > \omega(\mathcal{A}_{\text{dwell}}) > \omega(\mathcal{A}_{\text{nav}}) > \omega(\mathcal{A}_{\text{filter}})$ reflecting decreasing commitment.
 It's important to acknowledge that this creates a very blatant assumption in the weighting, and we motivate the scale of each weight by the per-category observed divergence between each behavioral profile.
 In the simulator baseline this order is encoded with a compact fixed scale: cart $=4.0$, dwell $=2.0$, nav $=1.0$, filter $=0.5$. Unknown actions are mapped by prefix heuristics to the nearest category.
-We back this up by saying that each weight was assigned by observing an initial small dataset and computing KL divergence between each interaction type; the ones with the highest divergence receive a proportionately high weight in our demand estimation.
+We back this up by saying that each weight was assigned by observing an initial small dataset and computing KL divergence between each interaction type; the ones with the highest divergence receive a proportionately high weight in our demand estimation. From the order which we observe in divergences, we assign a multiple of 2 increase in weight ascending form the lowest weight of $0.5$ in rare filtering operations.
 
 The metadata record $\mu$ varies by action type. For product views, $\mu$ contains the observed price $p_{\text{obs}}$ and product attributes. For dwell events, $\mu$ includes the element text and accumulated hover duration. This heterogeneous structure is captured via a schema-on-read approach in our Kafka ingestion pipeline, where events are validated against type-specific schemas before storage.