298 research outputs found
An Incidence Geometry approach to Dictionary Learning
We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a
sparse representation of data points, by learning \emph{dictionary vectors}
upon which the data points can be written as sparse linear combinations. We
view this problem from a geometry perspective as the spanning set of a subspace
arrangement, and focus on understanding the case when the underlying hypergraph
of the subspace arrangement is specified. For this Fitted Dictionary Learning
problem, we completely characterize the combinatorics of the associated
subspace arrangements (i.e.\ their underlying hypergraphs). Specifically, a
combinatorial rigidity-type theorem is proven for a type of geometric incidence
system. The theorem characterizes the hypergraphs of subspace arrangements that
generically yield (a) at least one dictionary (b) a locally unique dictionary
(i.e.\ at most a finite number of isolated dictionaries) of the specified size.
We are unaware of prior application of combinatorial rigidity techniques in the
setting of Dictionary Learning, or even in machine learning. We also provide a
systematic classification of problems related to Dictionary Learning together
with various algorithms, their assumptions and performance
Collaborative Filtering with Social Exposure: A Modular Approach to Social Recommendation
This paper is concerned with how to make efficient use of social information
to improve recommendations. Most existing social recommender systems assume
people share similar preferences with their social friends. Which, however, may
not hold true due to various motivations of making online friends and dynamics
of online social networks. Inspired by recent causal process based
recommendations that first model user exposures towards items and then use
these exposures to guide rating prediction, we utilize social information to
capture user exposures rather than user preferences. We assume that people get
information of products from their online friends and they do not have to share
similar preferences, which is less restrictive and seems closer to reality.
Under this new assumption, in this paper, we present a novel recommendation
approach (named SERec) to integrate social exposure into collaborative
filtering. We propose two methods to implement SERec, namely social
regularization and social boosting, each with different ways to construct
social exposures. Experiments on four real-world datasets demonstrate that our
methods outperform the state-of-the-art methods on top-N recommendations.
Further study compares the robustness and scalability of the two proposed
methods.Comment: Accepted for publication at the 32nd Conference on Artificial
Intelligence (AAAI 2018), New Orleans, Louisian
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