23,499 research outputs found
An Efficient Approach for Computing Optimal Low-Rank Regularized Inverse Matrices
Standard regularization methods that are used to compute solutions to
ill-posed inverse problems require knowledge of the forward model. In many
real-life applications, the forward model is not known, but training data is
readily available. In this paper, we develop a new framework that uses training
data, as a substitute for knowledge of the forward model, to compute an optimal
low-rank regularized inverse matrix directly, allowing for very fast
computation of a regularized solution. We consider a statistical framework
based on Bayes and empirical Bayes risk minimization to analyze theoretical
properties of the problem. We propose an efficient rank update approach for
computing an optimal low-rank regularized inverse matrix for various error
measures. Numerical experiments demonstrate the benefits and potential
applications of our approach to problems in signal and image processing.Comment: 24 pages, 11 figure
Hybrid Collaborative Filtering with Autoencoders
Collaborative Filtering aims at exploiting the feedback of users to provide
personalised recommendations. Such algorithms look for latent variables in a
large sparse matrix of ratings. They can be enhanced by adding side information
to tackle the well-known cold start problem. While Neu-ral Networks have
tremendous success in image and speech recognition, they have received less
attention in Collaborative Filtering. This is all the more surprising that
Neural Networks are able to discover latent variables in large and
heterogeneous datasets. In this paper, we introduce a Collaborative Filtering
Neural network architecture aka CFN which computes a non-linear Matrix
Factorization from sparse rating inputs and side information. We show
experimentally on the MovieLens and Douban dataset that CFN outper-forms the
state of the art and benefits from side information. We provide an
implementation of the algorithm as a reusable plugin for Torch, a popular
Neural Network framework
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