Abstract not found

Data sparsity due to missing ratings is a major challenge for collaborative filtering (CF) techniques in recommender systems. This is especially true for CF domains where the ratings are expressed numerically. We observe that, while we may lack the information in numerical ratings, we may have more data in the form of binary ratings. This is especially true when users can easily express themselves with their likes and dislikes for certain items. In this paper, we explore how to use the binary preference data expressed in the form of like/dislike to help reduce the impact of data sparsity of more expressive numerical ratings. We do this by transferring the rating knowledge from some auxiliary data source in binary form (that is, likes or dislikes), to a target numerical rating matrix. Our solution is to model both numerical ratings and like/dislike in a principled way, using a novel framework of Transfer by Collective Factorization (TCF). In particular, we construct the shared latent space collectively and learn the data-dependent effect separately. A major advantage of the TCF approach over previous collective matrix factorization (or bifactorization) methods is that we are able to capture the data-dependent effect when sharing the dataindependent knowledge, so as to increase the overall quality of knowledge transfer. Experimental results demonstrate the effectiveness of TCF at various sparsity levels as compared to several state-ofthe-art methods. 1

We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted-trace norm might fail when the sampling distribution is not a product distribution (i.e. when row and column indexes are not selected independently), present a corrected variant for which we establish strong learning guarantees, and demonstrate that it works better in practice. We provide guarantees when weighting by either the true or empirical sampling distribution, and suggest that even if the true distribution is known (or is uniform), weighting by the empirical distribution may be beneficial. 1

We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-norm, and present reconstruction guarantees based on existing analysis on the Rademacher complexity of the unit balls of these norms. We show how these are superior in several ways to recently published guarantees based on specialized analysis.

We consider the problem of recovering a matrix M that is the sum of a low-rank matrix L and a sparse matrix S from a small set of linear measurements of the form y = A(M) =A(L + S). This model subsumes three important classes of signal recovery problems: compressive sensing, affine rank minimization, and robust principal component analysis. We propose a natural optimization problem for signal recovery under this model and develop a new greedy algorithm called SpaRCS to solve it. Empirically, SpaRCS inherits a number of desirable properties from the state-of-the-art CoSaMP and ADMiRA algorithms, including exponential convergence and efficient implementation. Simulation results with video compressive sensing, hyperspectral imaging, and robust matrix completion data sets demonstrate both the accuracy and efficacy of the algorithm. 1

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to highdimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixedrank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. 1.

Data sparsity is a major problem for collaborative filtering (CF) techniques in recommender systems, especially for new users and items. We observe that, while our target data are sparse for CF systems, related and relatively dense auxiliary data may already exist in some other more mature application domains. In this paper, we address the data sparsity problem in a target domain by transferring knowledge about both users and items from auxiliary data sources. We observe that in different domains the user feedbacks are often heterogeneous such as ratings vs. clicks. Our solution is to integrate both user and item knowledge in auxiliary data sources through a principled matrix-based transfer learning framework that takes into account the data heterogeneity. In particular, we discover the principle coordinates of both users and items in the auxiliary data matrices, and transfer them to the target domain in order to reduce the effect of data sparsity. We describe our method, which is known as coordinate system transfer or CST, and demonstrate its effectiveness in alleviating the data sparsity problem in collaborative filtering. We show that our proposed method can significantly outperform several state-of-the-art solutions for this problem.

Abstract. We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a minimal nuclear norm and an approximatively low-rank solution. Under the assumption that the linear measurements fulfill a suitable generalization of the Null Space Property known in the context of compressed sensing, the algorithm is guaranteed to recover iteratively any matrix with an error of the order of the best k-rank approximation. In certain relevant cases, for instance for the matrix completion problem, our version of this algorithm can take advantage of the Woodbury matrix identity, which allows to expedite the solution of the least squares problems required at each iteration. We present numerical experiments which confirm the robustness of the algorithm for the solution of matrix completion problems, and demonstrate its competitiveness with respect to other techniques proposed recently in the literature. AMS subject classification: 65J22, 65K10, 52A41, 49M30. Key Words: low-rank matrix recovery, iteratively reweighted least squares, matrix completion.

Abstract not found

Transfer learning addresses the problems that labeled training data are insufficient to produce a high-performance model. Typically, given a target learning task, most transfer learning approaches require to select one or more auxiliary tasks as sources by the designers. However, how to select the right source data to enable effective knowledge transfer automatically is still an unsolved problem, which limits the applicability of transfer learning. In this paper, we take one step ahead and propose a novel transfer learning framework, known as source-selection-free transfer learning (SSFTL), to free users from the need to select source domains. Instead of asking the users for source and target data pairs, as traditional transfer learning does, SS-FTL turns to some online information sources such as World Wide Web or the Wikipedia for help. The source data for transfer learning can be hidden somewhere within this large online information source, but the users do not know where they are. Based on the online information sources, we train a large number of classifiers. Then, given a target task, a bridge is built for labels of the potential source candidates and the target domain data in SSFTL via some large online social media with tag cloud as a label translator. An added advantage of SSFTL is that, unlike many previous transfer learning approaches, which are difficult to scale up to the Web scale, SSFTL is highly scalable and can offset much of the training work to offline stage. We demonstrate the effectiveness and efficiency of SS-FTL through extensive experiments on several realworld datasets in text classification. 1