Personalized recommendation systems are used in a wide variety of applications such as electronic commerce, social networks, web search, and more. Collaborative filtering approaches to recommendation systems typically assume that the rating matrix (e.g., movie ratings by viewers) is lowrank. In this paper, we examine an alternative approach in which the rating matrix is locally low-rank. Concretely, we assume that the rating matrix is low-rank within certain neighborhoods of the metric space defined by (user, item) pairs. We combine a recent approach for local low-rank approximation based on the Frobenius norm with a general empirical risk minimization for ranking losses. Our experiments indicate that the combination of a mixture of local low-rank matrices each of which was trained to minimize a ranking loss outperforms many of the currently used stateof-the-art recommendation systems. Moreover, our method is easy to parallelize, making it a viable approach for large scale real-world rank-based recommendation systems.

Many algorithms in machine learning rely on being given a good distance metric over the input space. Rather than using a default metric such as the Euclidean metric, it is desirable to obtain a metric based on the provided data. We consider the problem of learning a Riemannian metric associated with a given differentiable manifold and a set of points. Our approach to the problem involves choosing a metric from a parametric family that is based on maximizing the inverse volume of a given data set of points. From a statistical perspective, it is related to maximum likelihood under a model that assigns probabilities inversely proportional to the Riemannian volume element. We discuss in detail learning a metric on the multinomial simplex where the metric candidates are pull-back metrics of the Fisher information under a Lie group of transformations. When applied to text document classification the resulting geodesic distance resemble, but outperform, the tfidf cosine similarity measure.

For cold-start recommendation, it is important to rapidly profile new users and generate a good initial set of recommendations through an interview process -users should be queried adaptively in a sequential fashion, and multiple items should be offered for opinion solicitation at each trial. In this work, we propose a novel algorithm that learns to conduct the interview process guided by a decision tree with multiple questions at each split. The splits, represented as sparse weight vectors, are learned through an L1-constrained optimization framework. The users are directed to child nodes according to the inner product of their responses and the corresponding weight vector. More importantly, to account for the variety of responses coming to a node, a linear regressor is learned within each node using all the previously obtained answers as input to predict item ratings. A user study, preliminary but first in its kind in cold-start recommendation, is conducted to explore the efficient number and format of questions being asked in a recommendation survey to minimize user cognitive efforts. Quantitative experimental validations also show that the proposed algorithm outperforms state-of-the-art approaches in terms of both the prediction accuracy and user cognitive efforts.

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In this paper we present an inference procedure for the semantic segmentation of images. Different from many CRF approaches that rely on dependencies modeled with unary and pairwise pixel or superpixel potentials, our method is entirely based on estimates of the overlap between each of a set of mid-level object segmentation proposals and the objects present in the image. We define continuous latent variables on superpixels obtained by multiple intersections of segments, then output the optimal segments from the inferred superpixel statistics. The algorithm is capable of recombine and refine initial mid-level proposals, as well as handle multiple interacting objects, even from the same class, all in a consistent joint inference framework by maximizing the composite likelihood of the underlying statistical model using an EM algorithm. In the PASCAL VOC segmentation challenge, the proposed approach obtains high accuracy and successfully handles images of complex object interactions.