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.
@cite_5 @cite_6 @cite_20 @cite_11
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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. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. 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. In this paper we tackle the problem of recommendation in the scenarios with binary relevance data, when only a few (k) items are recommended to individual users. Past work on Collaborative Filtering (CF) has either not addressed the ranking problem for binary relevance datasets, or not specifically focused on improving top-k recommendations. To solve the problem we propose a new CF approach, Collaborative Less-is-More Filtering (CLiMF). In CLiMF the model parameters are learned by directly maximizing the Mean Reciprocal Rank (MRR), which is a well-known information retrieval metric for measuring the performance of top-k recommendations. We achieve linear computational complexity by introducing a lower bound of the smoothed reciprocal rank metric. Experiments on two social network datasets demonstrate the effectiveness and the scalability of CLiMF, and show that CLiMF significantly outperforms a naive baseline and two state-of-the-art CF methods.