As the deep integration of machine learning and intelligent education, Computerized Adaptive Testing (CAT) has received more and more research attention. Compared to traditional paper-and-pencil tests, CAT can deliver both personalized and interactive assessments by automatically adjusting testing questions according to the performance of students during the test process. Therefore, CAT has been recognized as an efficient testing methodology capable of accurately estimating a student's ability with a minimal number of questions, leading to its widespread adoption in mainstream selective exams such as the GMAT and GRE. However, just improving the accuracy of ability estimation is far from satisfactory in the real-world scenarios, since an accurate ranking of students is usually more important (e.g., in high-stakes exams). Considering the shortage of existing CAT solutions in student ranking, this paper emphasizes the importance of aligning test outcomes (student ranks) with the true underlying abilities of students. Along this line, different from the conventional independent testing paradigm among students, we propose a novel collaborative framework, Collaborative Computerized Adaptive Testing (CCAT), that leverages inter-student information to enhance student ranking.

The primary application of collaborate filtering (CF) is to recommend a small set of items to a user, which entails ranking. Most approaches, however, formulate the CF problem as rating prediction, overlooking the ranking perspective. In this work we present a method for collaborative ranking that leverages the strengths of the two main CF approaches, neighborhood-and model-based. Our novel method is highly efficient, with only seventeen parameters to optimize and a single hyperparameter to tune, and beats the state-of-the-art collaborative ranking methods. We also show that parameters learned on datasets from one item domain yield excellent results on a dataset from very different item domain, without any retraining.

In personalized recommendation systems, it is important to predict preferences of a user on items that have not been seen by that user yet. Similarly, in revenue management, it is important to predict outcomes of comparisons among those items that have never been compared so far. The MultiNomial Logit model, a popular discrete choice model, captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

In this paper, we consider collaborative filtering as a ranking problem. We present a method which uses Maximum Margin Matrix Factorization and optimizes rank- ing instead of rating. We employ structured output prediction to optimize directly for ranking scores. Experimental results show that our method gives very good ranking scores and scales well on collaborative filtering tasks.

The recent development of online recommender systems has a focus on collaborative ranking from implicit feedback, such as user clicks and purchases. Different from explicit ratings, which reflect graded user preferences, the implicit feedback only generates positive and unobserved labels. While considerable efforts have been made in this direction, the well-known pairwise and listwise approaches have still been limited by various challenges. Specifically, for the pairwise approaches, the assumption of independent pairwise preference is not always held in practice. Also, the listwise approaches cannot efficiently accommodate "ties" due to the precondition of the entire list permutation. To this end, in this paper, we propose a novel setwise Bayesian approach for collaborative ranking, namely SetRank, to inherently accommodate the characteristics of implicit feedback in recommender system. Specifically, SetRank aims at maximizing the posterior probability of novel setwise preference comparisons and can be implemented with matrix factorization and neural networks. Meanwhile, we also present the theoretical analysis of SetRank to show that the bound of excess risk can be proportional to $\sqrt{M/N}$, where $M$ and $N$ are the numbers of items and users, respectively. Finally, extensive experiments on four real-world datasets clearly validate the superiority of SetRank compared with various state-of-the-art baselines.

Abstract--Recently, word embedding algorithms have been applied to map the entities of recommender systems, such as users and items, to new feature spaces using textual elementcontext relations among them. Unlike many other domains, this approach has not achieved a desired performance in collaborative filtering problems, probably due to unavailability of appropriate textual data. In this paper we propose a new recommendation framework, called GEMRank that can be applied when the useritem matrix is the sole available souce of information. It uses the concept of profile co-occurrence for defining relations among entities and applies a factorization method for embedding the users and items. GEMRank then feeds the extracted representations to a neural network model to predict user-item like/dislike relations which the final recommendations are made based on. We evaluated GEMRank in an extensive set of experiments against state of the art recommendation methods. The results show that GEMRank significantly outperforms the baseline algorithms in a variety of data sets with different degrees of density. Recommendation Systems help users to find relevant items based on their preferences. Many prominent recommendation systems are using Collaborative Filtering (CF) for making recommendations ( [1]).

In this paper, we propose a listwise approach for constructing user-specific rankings in recommendation systems in a collaborative fashion. We contrast the listwise approach to previous pointwise and pairwise approaches, which are based on treating either each rating or each pairwise comparison as an independent instance respectively. By extending the work of (Cao et al., 2007), we cast listwise collaborative ranking as maximum likelihood under a permutation model which applies probability mass to permutations based on a low rank latent score matrix. We present a novel algorithm called SQL-Rank, which can accommodate ties and missing data and can run in linear time. We develop a theoretical framework for analyzing listwise ranking methods based on a novel representation theory for the permutation model. Applying this framework to collaborative ranking, we derive asymptotic statistical rates as the number of users and items grow together. We conclude by demonstrating that our SQL-Rank method often outperforms current state-of-the-art algorithms for implicit feedback such as Weighted-MF and BPR and achieve favorable results when compared to explicit feedback algorithms such as matrix factorization and collaborative ranking.

In personalized recommendation systems, it is important to predict preferences of a user on items that have not been seen by that user yet. Similarly, in revenue management, it is important to predict outcomes of comparisons among those items that have never been compared so far. The MultiNomial Logit model, a popular discrete choice model, captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

In applications such as recommendation systems and revenue management, it is important to predict preferences on items that have not been seen by a user or predict outcomes of comparisons among those that have never been compared. A popular discrete choice model of multinomial logit model captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single, relatively consistent ordering of those objects. However, in many cases, we might not want a single ranking and instead opt for individual rankings. We study a version of the problem known as collaborative ranking. In this problem we assume that individual users provide us with pairwise preferences (for example purchasing one item over another). From those preferences we wish to obtain rankings on items that the users have not had an opportunity to explore. The results here have a very interesting connection to the standard matrix completion problem. We provide a theoretical justification for a nuclear norm regularized optimization procedure, and provide high-dimensional scaling results that show how the error in estimating user preferences behaves as the number of observations increase.