[Paper Review] Efficient Probabilistic Inference with Partial Ranking Queries

Jonathan Huang, Ashish Kapoor+1 more|arXiv (Cornell University)|Feb 14, 2012

Game Theory and Voting Systems8 references3 citations

TL;DR

This paper proposes riffled independence factorizations as a structural assumption for modeling ranking distributions, enabling efficient probabilistic inference with partial ranking queries—common in preference modeling and recommendation systems. By exploiting conditional independence across riffled subsets of items, the method achieves significant computational gains over brute-force approaches while maintaining accuracy in ranking inference tasks.

ABSTRACT

Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distributions. We approach the modeling problem from the computational principle that one should make structural assumptions which allow for efficient calculation of typical probabilistic queries. For ranking models, "typical" queries predominantly take the form of partial ranking queries (e.g., given a user's top-k favorite movies, what are his preferences over remaining movies?). In this paper, we argue that riffled independence factorizations proposed in recent literature [7, 8] are a natural structural assumption for ranking distributions, allowing for particularly efficient processing of partial ranking queries.

Motivation & Objective

• To address the computational intractability of full ranking distribution inference due to factorial-sized ranking spaces.
• To identify structural assumptions that enable efficient processing of typical probabilistic queries in ranking systems.
• To formalize and evaluate riffled independence as a natural and effective factorization for partial ranking queries.
• To demonstrate that this approach scales better than existing methods while preserving inference accuracy.

Proposed method

• The paper introduces riffled independence factorizations, which decompose a ranking distribution into conditionally independent components over disjoint subsets of items.
• It models rankings as a combination of independent permutations over riffled (interleaved) item sets, reducing the complexity of joint distribution modeling.
• The method uses conditional probability propagation to compute posterior distributions over remaining items given a partial ranking (e.g., top-k preferences).
• It leverages the structure of riffled independence to avoid enumerating all possible full rankings, drastically reducing computational cost.
• The inference algorithm efficiently computes marginal probabilities over unobserved items using dynamic programming over riffled components.
• The approach is validated through empirical evaluation on synthetic and real-world preference datasets, showing scalability and accuracy.

Experimental results

Research questions

• RQ1 Can riffled independence factorizations enable efficient inference for partial ranking queries in large-scale ranking models?
• RQ2 How does the computational complexity of inference under riffled independence compare to standard ranking models?
• RQ3 To what extent does the method preserve accuracy in predicting unobserved preferences given partial rankings?
• RQ4 Does the structural assumption of riffled independence generalize well across diverse preference datasets?

Key findings

• The proposed method achieves significant speedups in inference time compared to full enumeration or standard probabilistic models.
• Riffled independence factorizations allow for exact inference over partial rankings without requiring full ranking enumeration.
• The method maintains high accuracy in predicting missing preferences, even with limited observed top-k rankings.
• Empirical results show the approach scales effectively to larger item sets, outperforming baseline models in both speed and precision.