Rethinking Click Models in Light of Carousel Interfaces: Theory-Based Categorization and Design of Click Models

Abstract: Click models are a well-established for modeling user interactions with web interfaces. Previous work has mainly focused on traditional single-list web search settings; this includes existing surveys that introduced categorizations based on the first generation of probabilistic graphical model (PGM) click models that have become standard. However, these categorizations have become outdated, as their conceptualizations are unable to meaningfully compare PGM with neural network (NN) click models nor generalize to newer interfaces, such as carousel interfaces. We argue that this outdated view fails to adequately explain the fundamentals of click model designs, thus hindering the development of novel click models. This work reconsiders what should be the fundamental concepts in click model design, grounding them - unlike previous approaches - in their mathematical properties. We propose three fundamental key-design choices that explain what statistical patterns a click model can capture, and thus indirectly, what user behaviors they can capture. Based on these choices, we create a novel click model taxonomy that allows a meaningful comparison of all existing click models; this is the first taxonomy of single-list, grid and carousel click models that includes PGMs and NNs. Finally, we show how our conceptualization provides a foundation for future click model design by an example derivation of a novel design for carousel interfaces.

• The paper introduces a theory-based taxonomy that redefines click models using explicit observable dependencies.
• It critiques existing models for single-list interfaces and addresses gaps for carousel layouts.
• The study offers actionable design guidelines for implementing adaptable click models in complex, multi-list user interfaces.

Rethinking Click Models in Light of Carousel Interfaces

This paper presents a reexamination of the foundations underlying click modeling within modern information retrieval systems, with a particular emphasis on interfaces that employ carousels, such as those prevalent in streaming media platforms like Netflix and Spotify. The authors argue that prevailing click model taxonomies—largely derived from probabilistic graphical model (PGM) frameworks—are insufficient for encompassing contemporary neural or hybrid approaches and are ultimately ill-suited to capture complex, multi-list interfaces like carousels. To address these limitations, the paper introduces a principled, theory-grounded taxonomy that organizes click models based on explicit mathematical dependencies between observed variables, rather than relying on behavioral or latent variable assumptions.

Critique of Prevailing Taxonomies

Existing click model surveys primarily categorize models according to genealogies of user behavior or the structure of latent variables (e.g., examination, satisfaction). This leads to two central shortcomings:

1. Exclusion of Neural Models: Neural network-based click models (NN-based) and PGMs are conceptually separated into disjoint taxonomies, preventing coherent comparison despite functional overlap.
2. Interface Inflexibility: Current frameworks are tailored to single-list (e.g., vertical search engine results) layouts and do not generalize naturally to grid or carousel formats, nor do they scale to support the combinatorial browsing actions introduced by these more sophisticated interfaces.

Fundamental Recommendations

The authors propose that a robust, comprehensive taxonomy must instead categorize click models by the observable statistical relationships they model—specifically, how clicks are conditioned on other observed variables such as displayed items, topics (as in carousels), and the sequence of past clicks.

Three Core Design Choices:

1. Global Dependencies: Identifies which collections of observed variables (topics, items, and/or prior clicks) each click probability is conditioned on.
2. Sequentiality: Specifies which sub-sequences or indices within those collections condition a specific click event (e.g., dependence on preceding items or only the current item).
3. Factorization: Describes the functional form or decomposition of those dependencies—whether the model, for example, multiplies independent position and item factors, or uses more expressive/combinatorial functions.

This formalization leads to a hierarchical taxonomy where, for example, all models that condition clicks on both topics and items (but not other clicks) are grouped independently of the machine learning paradigm (PGM, NN, etc.) or any behavioral narrative.

Illustrated Taxonomy

The taxonomy first distinguishes between models that do or do not condition on context (i.e., topics, items, prior clicks). Within the contextual branch, dependencies are further stratified based on which observed variables are involved:

• Random: No dependencies; click probability is constant.
• Items-Only: Only the displayed item impacts click probability.
• Clicks-Only: Only other clicks impact click probability.
• Items-Clicks: Both item and click dependencies.
• Topics-Only, Topics-Clicks, Topics-Items, Fully Dependent: Variants involving topics (in carousels), with the fully dependent category combining all three observed variable groups.

An excerpt of this taxonomy is tabulated (see Table 1 in the paper), systematically categorizing established models (e.g., PBM, DCM, DBN, NCM) as well as recent neural approaches, hybrid models combining PGMs and boosted decision trees, and models designed specifically for grid or carousel interfaces.

Application to Carousel Interfaces

The framework is instantiated through the derivation of a new click model for carousel interfaces, addressing a significant gap in prior work. The design proceeds by explicit selection along the three axes:

• Global Dependencies: Model placed in the "Topics-Items" class (each click depends on both the list’s topic and the item).
• Sequentiality: Click depends on the path traversed through previous topics and items within its carousel.
• Factorization: The click probability is modeled as a product of independent functions over (a) topic sequence and (b) item sequence, or, alternately, as the interaction between the current item and history.

This deliberate and explicit design process enables systematic comparison with other models independent of whether they are based on PGMs, NNs, or hybrid approaches.

Strong Claims and Implications

The authors assert that their taxonomy satisfies key desiderata: comprehensiveness (covers all click models, past and future, across interfaces and learning paradigms), exclusivity (no overlapping categories for mathematically equivalent models), and stability (taxonomic expansion with new observed variables does not alter existing structure).

This reframing renders prior taxonomies—and the behavioral narratives they encode—secondary to the actual statistical mechanisms click models employ. The direct implication is that future click model research can prioritize mathematical expressivity and adaptability, systematically evaluating or extending models within this unified categorical structure.

Practical and Theoretical Implications

Practical:

• Model Design: System architects developing user-interaction models for novel or compound UIs (carousels, grids) can use the taxonomy to specify, compare, or justify design choices explicitly in terms of observable dependencies, facilitating modular design and isolation of confounding effects (e.g., separating topic from item or position effects).
• Implementation: The taxonomy is agnostic to learning technique, enabling direct implementation in either graphical model frameworks or neural architectures, as well as in hybrid systems combining both.
• Evaluation and Extensibility: New models—especially as user interfaces diversify—can be categorized immediately in terms of expressiveness and parameterization, simplifying both implementation and empirical benchmarking.

Theoretical:

• Unified Analysis: Enables rigorous direct comparison between models, even when behavioral motivation or model machinery (PGM vs NN) differs, by reducing all models to their explicit observable dependency structure.
• Propensity Estimation and Bias Correction: As click bias estimation and counterfactual learning are central to modern IR systems, the ability to precisely characterize model assumptions regarding dependencies and independence is critical.
• Future Research Directions: The work suggests that many click models applicable to complex UI layouts (especially carousels) remain unexplored. Further, as interface diversity increases—including mobile, touch, or multi-modal layouts—this formalism allows systematic exploration and design unencumbered by historical PGM behavioral dogma.

Future Directions

Potential next steps include:

• Development of data-mining or learning algorithms that can, given logged interaction data, identify the optimal position in the taxonomy for a new model or discover novel effective dependencies for unexplored layouts.
• Empirical benchmarking of partially or fully dependent models for carousels against existing baselines, evaluating the trade-offs between expressivity and generalization.
• Extending the taxonomy to include additional observed user activity modalities (e.g., scrolling actions, dwell times), as these become routinely logged in contemporary platforms.

Conclusion

This work provides a rigorous mathematical foundation for click model taxonomy, enabling systematic and future-proof model design across interface types and model architectures. By removing latent behavioral assumptions as the principal organizing principle, the approach encourages explicit, modular, and mathematically tractable design of click models—an essential development as IR environments and user interfaces grow in complexity and diversity.