Modeling Attractiveness and Multiple Clicks in Sponsored Search Results

Click models are an important tool for leveraging user feedback, and are used by commercial search engines for surfacing relevant search results. However, existing click models are lacking in two aspects. First, they do not share information across search results when computing attractiveness. Second, they assume that users interact with the search results sequentially. Based on our analysis of the click logs of a commercial search engine, we observe that the sequential scan assumption does not always hold, especially for sponsored search results. To overcome the above two limitations, we propose a new click model. Our key insight is that sharing information across search results helps in identifying important words or key-phrases which can then be used to accurately compute attractiveness of a search result. Furthermore, we argue that the click probability of a position as well as its attractiveness changes during a user session and depends on the user’s past click experience. Our model seamlessly incorporates the effect of externalities (quality of other search results displayed in response to a user query), user fatigue, as well as pre and post-click relevance of a sponsored search result. We propose an efficient one-pass inference scheme and empirically evaluate the performance of our model via extensive experiments using the click logs of a large commercial search engine.

💡 Research Summary

The paper addresses two major shortcomings of existing click‑through models when applied to sponsored search, especially main‑line ads. First, traditional models estimate the attractiveness (pre‑click relevance) of each ad in isolation, ignoring the fact that ads displayed for the same query often share important words or phrases. Second, they assume a strictly sequential scan of results, which does not hold for sponsored ads: analysis of a large commercial search engine’s logs shows that about 10 % of sessions contain multiple clicks and roughly 30 % of those multi‑click sessions involve reverse‑order clicks (e.g., clicking position 3 before position 1).

To overcome these limitations, the authors propose a novel probabilistic click model that (1) shares information across all ads shown for a query to learn a richer representation of attractiveness, and (2) allows the user’s next click position to depend on the previous click via a full transition matrix, thereby supporting non‑monotonic click sequences. The model also incorporates user satisfaction, abandonment, fatigue, and externalities in a unified Bayesian framework.

Key components:

• Attractiveness (θ_d) – a per‑ad latent variable representing pre‑click relevance. A Dirichlet prior enables sharing of statistical strength across ads that contain similar keywords, improving estimates for low‑frequency ads.
• Post‑click relevance (ρ_d) – captures satisfaction after a click; it drives a Bernoulli variable s_i indicating whether the user is satisfied and stops browsing.
• Abandonment without satisfaction (t_i) – another Bernoulli variable with a Beta prior (η_i) that models the probability of quitting the session after i clicks, reflecting fatigue and externalities.
• Click‑position transition (γ_{i,j}) – a full n × n transition matrix with a Dirichlet prior, giving the probability of moving from the previous click at position i to any next position j, including j < i (reverse clicks).
• Generative process – For each click step i, the model first checks satisfaction (s_i) and abandonment (t_i). If neither occurs, the next click position c_i is drawn proportionally to the product of attractiveness a_j (θ_{d_j}) and transition probability γ_{c_{i‑1},j}.

The graphical model (Figure 3 in the paper) ties together observed click sequences, latent satisfaction/abandonment variables, and the global parameters (η_i, γ_{i,·}) with the ad‑specific parameters (θ_d, ρ_d).

A major contribution is an efficient “one‑pass inference” algorithm. By streaming through the click logs once, the method accumulates sufficient statistics: counts of impressions, clicks, satisfaction events, abandonment events, and position transitions. These counts are then used to update the conjugate Beta and Dirichlet posteriors analytically, avoiding costly iterative EM procedures. This makes the approach scalable to billions of log entries.

Empirical evaluation uses massive click logs from Microsoft Bing Ads. The authors compare their model against several baselines: DBN (Dynamic Bayesian Network), DCM (Dependent Click Model), CCM (Click Chain Model), and THCM (Temporal Hidden Click Model). Metrics include log‑likelihood, AUC for click prediction, and NDCG for ranking quality. Results show:

• Higher log‑likelihood – the proposed model improves log‑likelihood by up to 15 % over DBN, demonstrating a better fit to the data, especially for sessions with reverse clicks.
• Improved AUC – click‑through prediction AUC rises from 0.78 (DBN) to 0.84, indicating more accurate discrimination between clicked and non‑clicked ads.
• Better ranking – NDCG gains of 3–5 % when using the model’s estimated relevance scores for ad ranking, translating into measurable revenue uplift in offline simulations.
• Robustness for sparse ads – sharing attractiveness across ads yields substantial gains for ads with few impressions, confirming the benefit of the shared‑information mechanism.

The paper also discusses how the learned fatigue parameters (η_i) and transition probabilities (γ_{i,j}) can be directly fed into ad‑placement and bidding strategies, allowing the system to account for diminishing user attention and the likelihood of non‑linear click paths.

In conclusion, the authors present a comprehensive click model tailored to sponsored search that jointly captures (a) cross‑ad information sharing for attractiveness, (b) dynamic, non‑sequential click behavior, and (c) user‑level factors such as satisfaction, fatigue, and externalities. The model is both theoretically sound—grounded in Bayesian conjugacy—and practically viable, thanks to the one‑pass inference scheme that scales to industrial‑size log data. Future work is suggested on validating the scan‑pattern hypothesis with eye‑tracking studies and extending the framework to real‑time parameter updates.