3,451 research outputs found
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
Many real world datasets subsume a linear or non-linear low-rank structure in
a very low-dimensional space. Unfortunately, one often has very little or no
information about the geometry of the space, resulting in a highly
under-determined recovery problem. Under certain circumstances,
state-of-the-art algorithms provide an exact recovery for linear low-rank
structures but at the expense of highly inscalable algorithms which use nuclear
norm. However, the case of non-linear structures remains unresolved. We revisit
the problem of low-rank recovery from a totally different perspective,
involving graphs which encode pairwise similarity between the data samples and
features. Surprisingly, our analysis confirms that it is possible to recover
many approximate linear and non-linear low-rank structures with recovery
guarantees with a set of highly scalable and efficient algorithms. We call such
data matrices as \textit{Low-Rank matrices on graphs} and show that many real
world datasets satisfy this assumption approximately due to underlying
stationarity. Our detailed theoretical and experimental analysis unveils the
power of the simple, yet very novel recovery framework \textit{Fast Robust PCA
on Graphs
Chiron: A Robust Recommendation System with Graph Regularizer
Recommendation systems have been widely used by commercial service providers
for giving suggestions to users. Collaborative filtering (CF) systems, one of
the most popular recommendation systems, utilize the history of behaviors of
the aggregate user-base to provide individual recommendations and are effective
when almost all users faithfully express their opinions. However, they are
vulnerable to malicious users biasing their inputs in order to change the
overall ratings of a specific group of items. CF systems largely fall into two
categories - neighborhood-based and (matrix) factorization-based - and the
presence of adversarial input can influence recommendations in both categories,
leading to instabilities in estimation and prediction. Although the robustness
of different collaborative filtering algorithms has been extensively studied,
designing an efficient system that is immune to manipulation remains a
significant challenge. In this work we propose a novel "hybrid" recommendation
system with an adaptive graph-based user/item similarity-regularization -
"Chiron". Chiron ties the performance benefits of dimensionality reduction
(through factorization) with the advantage of neighborhood clustering (through
regularization). We demonstrate, using extensive comparative experiments, that
Chiron is resistant to manipulation by large and lethal attacks
A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression
Many machine learning problems can be formulated as predicting labels for a
pair of objects. Problems of that kind are often referred to as pairwise
learning, dyadic prediction or network inference problems. During the last
decade kernel methods have played a dominant role in pairwise learning. They
still obtain a state-of-the-art predictive performance, but a theoretical
analysis of their behavior has been underexplored in the machine learning
literature.
In this work we review and unify existing kernel-based algorithms that are
commonly used in different pairwise learning settings, ranging from matrix
filtering to zero-shot learning. To this end, we focus on closed-form efficient
instantiations of Kronecker kernel ridge regression. We show that independent
task kernel ridge regression, two-step kernel ridge regression and a linear
matrix filter arise naturally as a special case of Kronecker kernel ridge
regression, implying that all these methods implicitly minimize a squared loss.
In addition, we analyze universality, consistency and spectral filtering
properties. Our theoretical results provide valuable insights in assessing the
advantages and limitations of existing pairwise learning methods.Comment: arXiv admin note: text overlap with arXiv:1606.0427
A Collective Variational Autoencoder for Top- Recommendation with Side Information
Recommender systems have been studied extensively due to their practical use
in many real-world scenarios. Despite this, generating effective
recommendations with sparse user ratings remains a challenge. Side information
associated with items has been widely utilized to address rating sparsity.
Existing recommendation models that use side information are linear and, hence,
have restricted expressiveness. Deep learning has been used to capture
non-linearities by learning deep item representations from side information but
as side information is high-dimensional existing deep models tend to have large
input dimensionality, which dominates their overall size. This makes them
difficult to train, especially with small numbers of inputs.
Rather than learning item representations, which is problematic with
high-dimensional side information, in this paper, we propose to learn feature
representation through deep learning from side information. Learning feature
representations, on the other hand, ensures a sufficient number of inputs to
train a deep network. To achieve this, we propose to simultaneously recover
user ratings and side information, by using a Variational Autoencoder (VAE).
Specifically, user ratings and side information are encoded and decoded
collectively through the same inference network and generation network. This is
possible as both user ratings and side information are data associated with
items. To account for the heterogeneity of user rating and side information,
the final layer of the generation network follows different distributions
depending on the type of information. The proposed model is easy to implement
and efficient to optimize and is shown to outperform state-of-the-art top-
recommendation methods that use side information.Comment: 7 pages, 3 figures, DLRS workshop 201
Extracting Implicit Social Relation for Social Recommendation Techniques in User Rating Prediction
Recommendation plays an increasingly important role in our daily lives.
Recommender systems automatically suggest items to users that might be
interesting for them. Recent studies illustrate that incorporating social trust
in Matrix Factorization methods demonstrably improves accuracy of rating
prediction. Such approaches mainly use the trust scores explicitly expressed by
users. However, it is often challenging to have users provide explicit trust
scores of each other. There exist quite a few works, which propose Trust
Metrics to compute and predict trust scores between users based on their
interactions. In this paper, first we present how social relation can be
extracted from users' ratings to items by describing Hellinger distance between
users in recommender systems. Then, we propose to incorporate the predicted
trust scores into social matrix factorization models. By analyzing social
relation extraction from three well-known real-world datasets, which both:
trust and recommendation data available, we conclude that using the implicit
social relation in social recommendation techniques has almost the same
performance compared to the actual trust scores explicitly expressed by users.
Hence, we build our method, called Hell-TrustSVD, on top of the
state-of-the-art social recommendation technique to incorporate both the
extracted implicit social relations and ratings given by users on the
prediction of items for an active user. To the best of our knowledge, this is
the first work to extend TrustSVD with extracted social trust information. The
experimental results support the idea of employing implicit trust into matrix
factorization whenever explicit trust is not available, can perform much better
than the state-of-the-art approaches in user rating prediction
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