We explore the top-K rank aggregation problem in which one aims to recover a consistent ordering that focuses on top-K ranked items based on partially revealed preference information. We examine an M-wise comparison model that builds on the Plackett-Luce (PL) model where for each sample, M items are ranked according to their perceived utilities modeled as noisy observations of their underlying true utilities. As our result, we characterize the minimax optimality on the sample size for top-K ranking. The optimal sample size turns out to be inversely proportional to M. We devise an algorithm that effectively converts M-wise samples into pairwise ones and employs a spectral method using the refined data. In demonstrating its optimality, we develop a novel technique for deriving tight $\ell_\infty$ estimation error bounds, which is key to accurately analyzing the performance of top-K ranking algorithms, but has been challenging. Recent work relied on an additional maximum-likelihood estimation (MLE) stage merged with a spectral method to attain good estimates in $\ell_\infty$ error to achieve the limit for the pairwise model. In contrast, although it is valid in slightly restricted regimes, our result demonstrates a spectral method alone to be sufficient for the general M-wise model. We run numerical experiments using synthetic data and confirm that the optimal sample size decreases at the rate of 1/M. Moreover, running our algorithm on real-world data, we find that its applicability extends to settings that may not fit the PL model.

Neural Information Processing Systems http://nips.cc/

Theoretical analysis confirms that the proposed algorithm achieves sub-linear regret in relation to the number of rounds and arms.

We explore the top-K rank aggregation problem in which one aims to recover a consistent ordering that focuses on top-K ranked items based on partially revealed preference information. We examine an M-wise comparison model that builds on the Plackett-Luce (PL) model where for each sample, M items are ranked according to their perceived utilities modeled as noisy observations of their underlying true utilities. As our result, we characterize the minimax optimality on the sample size for top-K ranking. The optimal sample size turns out to be inversely proportional to M. We devise an algorithm that effectively converts M-wise samples into pairwise ones and employs a spectral method using the refined data.

Various kinds of uncertainty can occur in event logs, e.g., due to flawed recording, data quality issues, or the use of probabilistic models for activity recognition. Stochastically known event logs make these uncertainties transparent by encoding multiple possible realizations for events. However, the number of realizations encoded by a stochastically known log grows exponentially with its size, making exhaustive exploration infeasible even for moderately sized event logs. Thus, considering only the top-K most probable realizations has been proposed in the literature. In this paper, we implement an efficient algorithm to calculate a top-K realization ranking of an event log under event independence within O(Kn), where n is the number of uncertain events in the log. This algorithm is used to investigate the benefit of top-K rankings over top-1 interpretations of stochastically known event logs. Specifically, we analyze the usefulness of top-K rankings against different properties of the input data. We show that the benefit of a top-K ranking depends on the length of the input event log and the distribution of the event probabilities. The results highlight the potential of top-K rankings to enhance uncertainty-aware process mining techniques.

Recency bias in a sequential recommendation system refers to the overly high emphasis placed on recent items within a user session. This bias can diminish the serendipity of recommendations and hinder the system's ability to capture users' long-term interests, leading to user disengagement. We propose a simple yet effective novel metric specifically designed to quantify recency bias. Our findings also demonstrate that high recency bias measured in our proposed metric adversely impacts recommendation performance too, and mitigating it results in improved recommendation performances across all models evaluated in our experiments, thus highlighting the importance of measuring recency bias.

This paper is concerned with the consistency analysis on listwise ranking methods. Among various ranking methods, the listwise methods have competitive performances on benchmark datasets and are regarded as one of the state-of-the-art approaches. Most listwise ranking methods manage to optimize ranking on the whole list (permutation) of objects, however, in practical applications such as information retrieval, correct ranking at the top k positions is much more important. This paper aims to analyze whether existing listwise ranking methods are statistically consistent in the top-k setting. For this purpose, we define a top-k ranking framework, where the true loss (and thus the risks) are defined on the basis of top-k subgroup of permutations.

In this paper, we consider mixtures of two Mallows models for top-$k$ rankings, both with the same location parameter but with different scale parameters, i.e., a mixture of concentric Mallows models. This situation arises when we have a heterogeneous population of voters formed by two homogeneous populations, one of which is a subpopulation of expert voters while the other includes the non-expert voters. We propose efficient sampling algorithms for Mallows top-$k$ rankings. We show the identifiability of both components, and the learnability of their respective parameters in this setting by, first, bounding the sample complexity for the Borda algorithm with top-$k$ rankings and second, proposing polynomial time algorithm for the separation of the rankings in each component. Finally, since the rank aggregation will suffer from a large amount of noise introduced by the non-expert voters, we adapt the Borda algorithm to be able to recover the ground truth consensus ranking which is especially consistent with the expert rankings.

This paper is concerned with the consistency analysis on listwise ranking methods. Among various ranking methods, the listwise methods have competitive performances on benchmark datasets and are regarded as one of the state-of-the-art approaches. Most listwise ranking methods manage to optimize ranking on the whole list (permutation) of objects, however, in practical applications such as information retrieval, correct ranking at the top k positions is much more important. This paper aims to analyze whether existing listwise ranking methods are statistically consistent in the top-k setting. For this purpose, we define a top-k ranking framework, where the true loss (and thus the risks) are defined on the basis of top-k subgroup of permutations.