We propose Top-N-Rank, a novel family of list-wise Learning-to-Rank models for reliably recommending the N top-ranked items. The proposed models optimize a variant of the widely used discounted cumulative gain (DCG) objective function which differs from DCG in two important aspects: (i) It limits the evaluation of DCG only on the top N items in the ranked lists, thereby eliminating the impact of low-ranked items on the learned ranking function; and (ii) it incorporates weights that allow the model to leverage multiple types of implicit feedback with differing levels of reliability or trustworthiness. Because the resulting objective function is non-smooth and hence challenging to optimize, we consider two smooth approximations of the objective function, using the traditional sigmoid function and the rectified linear unit (ReLU). We propose a family of learning-to-rank algorithms (Top-N-Rank) that work with any smooth objective function. Then, a more efficient variant, Top-N-Rank.ReLU, is introduced, which effectively exploits the properties of ReLU function to reduce the computational complexity of Top-N-Rank from quadratic to linear in the average number of items rated by users. The results of our experiments using two widely used benchmarks, namely, the MovieLens data set and the Amazon Video Games data set demonstrate that: (i) The top-N truncation' of the objective function substantially improves the ranking quality of the top N recommendations; (ii) using the ReLU for smoothing the objective function yields significant improvement in both ranking quality as well as runtime as compared to using the sigmoid; and (iii) Top-N-Rank.ReLU substantially outperforms the well-performing list-wise ranking methods in terms of ranking quality.
Existing LTR approaches suffer from several limitations. Although, in practical applications, only the top (say N) items in the ranked list are of interest, and the lower-ranked ratings in the list are less reliable, most existing LTR methods are optimized on the ranks of the entire lists, which, could potentially reduce the ranking quality of the top-ranked items. Furthermore, the computational complexity of straightforward approaches to optimizing ranking measures (e.g., DCG @cite_5 , MRR @cite_20 , AUC @cite_11 or MAP @cite_6 ), scale quadratically with @math (the average number of observed items across all users), which renders such methods impractical in large-scale real-world settings.
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The ranking problem has become increasingly important in modern applications of statistical methods in automated decision making systems. In particular, we consider a formulation of the statistical ranking problem which we call subset ranking, and focus on the discounted cumulated gain (DCG) criterion that measures the quality of items near the top of the rank-list. Similar to error minimization for binary classification, direct optimization of natural ranking criteria such as DCG leads to a nonconvex optimization problems that can be NP-hard. Therefore, a computationally more tractable approach is needed. We present bounds that relate the approximate optimization of DCG to the approximate minimization of certain regression errors. These bounds justify the use of convex learning formulations for solving the subset ranking problem. The resulting estimation methods are not conventional, in that we focus on the estimation quality in the top-portion of the rank-list. We further investigate the asymptotic statistical behavior of these formulations. Under appropriate conditions, the consistency of the estimation schemes with respect to the DCG metric can be derived. We study the subset ranking problem, motivated by its important application in web-search. In this context, we consider the standard DCG criterion (discounted cumulated gain) that measures the quality of items near the top of the rank-list. Similar to error minimization for binary classification, the DCG criterion leads to a non-convex optimization problem that can be NP-hard. Therefore a computationally more tractable approach is needed. We present bounds that relate the approximate optimization of DCG to the approximate minimization of certain regression errors. These bounds justify the use of convex learning formulations for solving the subset ranking problem. The resulting estimation methods are not conventional, in that we focus on the estimation quality in the top-portion of the rank-list. We further investigate the generalization ability of these formulations. Under appropriate conditions, the consistency of the estimation schemes with respect to the DCG metric can be derived. Algorithms that favor popular items are used to help us select among many choices, from top-ranked search engine results to highly-cited scientific papers. The goal of these algorithms is to identify high-quality items such as reliable news, credible information sources, and important discoveriesin short, high-quality content should rank at the top. Prior work has shown that choosing what is popular may amplify random fluctuations and lead to sub-optimal rankings. Nonetheless, it is often assumed that recommending what is popular will help high-quality content bubble up in practice. Here we identify the conditions in which popularity may be a viable proxy for quality content by studying a simple model of a cultural market endowed with an intrinsic notion of quality. A parameter representing the cognitive cost of exploration controls the trade-off between quality and popularity. Below and above a critical exploration cost, popularity bias is more likely to hinder quality. But we find a narrow intermediate regime of user attention where an optimal balance exists: choosing what is popular can help promote high-quality items to the top. These findings clarify the effects of algorithmic popularity bias on quality outcomes, and may inform the design of more principled mechanisms for techno-social cultural markets. This paper explores the preference-based top- @math rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top- @math ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model that postulates a set of latent preference scores underlying all items, where the odds of paired comparisons depend only on the relative scores of the items involved. We characterize the minimax limits on identifiability of top- @math ranked items, in the presence of random and non-adaptive sampling. Our results highlight a separation measure that quantifies the gap of preference scores between the @math and @math ranked items. The minimum sample complexity required for reliable top- @math ranking scales inversely with the separation measure irrespective of other preference distribution metrics. To approach this minimax limit, we propose a nearly linear-time ranking scheme, called , that returns the indices of the top- @math items in accordance to a careful score estimate. In a nutshell, Spectral MLE starts with an initial score estimate with minimal squared loss (obtained via a spectral method), and then successively refines each component with the assistance of coordinate-wise MLEs. Encouragingly, Spectral MLE allows perfect top- @math item identification under minimal sample complexity. The practical applicability of Spectral MLE is further corroborated by numerical experiments.