In this paper, we propose an active algorithm to find the graph with high probability and analyze its query complexity.

We will elaborate on works relevant to the noiseless triplet setting in the related work section. Thank you also for pointing out the typos. That is an interesting way of looking at the problem. If the dataset consists of hierarchical clusters as in the condition for Theorem 4.6, This is made more explicit in the discussion following Theorem 4.4. Houle, Michael E., and Michael Nett (2013), Rank cover trees for nearest neighbor search, International Conference on

We study the secure stochastic convex optimization problem.

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Ranking items is a central task in many information retrieval and recommender systems. User input for the ranking task often comes in the form of ratings on a coarse discrete scale. We ask whether it is possible to recover a fine-grained item ranking from such coarse-grained ratings. We model items as having scores and users as having thresholds; a user rates an item positively if the item's score exceeds the user's threshold. Although all users agree on the total item order, estimating that order is challenging when both the scores and the thresholds are latent. Under our model, any ranking method naturally partitions the $n$ items into bins; the bins are ordered, but the items inside each bin are still unordered. Users arrive sequentially, and every new user can be queried to refine the current ranking. We prove that achieving a near-perfect ranking, measured by Spearman distance, requires $Θ(n^2)$ users (and therefore $Ω(n^2)$ queries). This is significantly worse than the $O(n\log n)$ queries needed to rank from comparisons; the gap reflects the additional queries needed to identify the users who have the appropriate thresholds. Our bound also quantifies the impact of a mismatch between score and threshold distributions via a quadratic divergence factor. To show the tightness of our results, we provide a ranking algorithm whose query complexity matches our bound up to a logarithmic factor. Our work reveals a tension in online ranking: diversity in thresholds is necessary to merge coarse ratings from many users into a fine-grained ranking, but this diversity has a cost if the thresholds are a priori unknown.

Thanks for the valuable comments and questions. 1) We understand the reviewer's concern that the ratio of Besides, there are various methods specially for data imbalance to alleviate the issues. Flawfinder and a commercial tool CXXX which we hide the name for legal concern. Static analyzers tend to miss most vulnerable functions and have high false positives, e.g., Cppcheck found 0 One important note is that [19] didn't To verify it, we tested trained models with different sizes of the combined dataset, i.e., 1/3, 2/3 As shown in Table 2, both accuracy and F1 increases as the data volume increases.

Moreover, our work explores this problem in the context of complex image scenes containing multiple objects.

A version of the dueling bandit problem is addressed in which a Condorcet winner may not exist. Two algorithms are proposed that instead seek to minimize regret with respect to the Copeland winner, which, unlike the Condorcet winner, is guaranteed to exist. The first, Copeland Confidence Bound (CCB), is designed for small numbers of arms, while the second, Scalable Copeland Bandits (SCB), works better for large-scale problems. We provide theoretical results bounding the regret accumulated by CCB and SCB, both substantially improving existing results.

Although the importance of feedback in neural information processing has been widely recognized in the field, the detailed mechanism of how it works remains largely unknown. Here, we investigate the role of feedback in hierarchical information retrieval.

In the adaptive setting, many multi-armed bandit applications allow the learner to adaptively draw samples and adjust sampling strategy in rounds. In many real applications, not only the query complexity but also the round complexity need to be optimized.