11,864 research outputs found
Graph Convolutional Matrix Completion
We consider matrix completion for recommender systems from the point of view
of link prediction on graphs. Interaction data such as movie ratings can be
represented by a bipartite user-item graph with labeled edges denoting observed
ratings. Building on recent progress in deep learning on graph-structured data,
we propose a graph auto-encoder framework based on differentiable message
passing on the bipartite interaction graph. Our model shows competitive
performance on standard collaborative filtering benchmarks. In settings where
complimentary feature information or structured data such as a social network
is available, our framework outperforms recent state-of-the-art methods.Comment: 9 pages, 3 figures, updated with additional experimental evaluatio
Matrix Completion on Graphs
The problem of finding the missing values of a matrix given a few of its
entries, called matrix completion, has gathered a lot of attention in the
recent years. Although the problem under the standard low rank assumption is
NP-hard, Cand\`es and Recht showed that it can be exactly relaxed if the number
of observed entries is sufficiently large. In this work, we introduce a novel
matrix completion model that makes use of proximity information about rows and
columns by assuming they form communities. This assumption makes sense in
several real-world problems like in recommender systems, where there are
communities of people sharing preferences, while products form clusters that
receive similar ratings. Our main goal is thus to find a low-rank solution that
is structured by the proximities of rows and columns encoded by graphs. We
borrow ideas from manifold learning to constrain our solution to be smooth on
these graphs, in order to implicitly force row and column proximities. Our
matrix recovery model is formulated as a convex non-smooth optimization
problem, for which a well-posed iterative scheme is provided. We study and
evaluate the proposed matrix completion on synthetic and real data, showing
that the proposed structured low-rank recovery model outperforms the standard
matrix completion model in many situations.Comment: Version of NIPS 2014 workshop "Out of the Box: Robustness in High
Dimension
Exact and efficient top-K inference for multi-target prediction by querying separable linear relational models
Many complex multi-target prediction problems that concern large target
spaces are characterised by a need for efficient prediction strategies that
avoid the computation of predictions for all targets explicitly. Examples of
such problems emerge in several subfields of machine learning, such as
collaborative filtering, multi-label classification, dyadic prediction and
biological network inference. In this article we analyse efficient and exact
algorithms for computing the top- predictions in the above problem settings,
using a general class of models that we refer to as separable linear relational
models. We show how to use those inference algorithms, which are modifications
of well-known information retrieval methods, in a variety of machine learning
settings. Furthermore, we study the possibility of scoring items incompletely,
while still retaining an exact top-K retrieval. Experimental results in several
application domains reveal that the so-called threshold algorithm is very
scalable, performing often many orders of magnitude more efficiently than the
naive approach
- …