5,980 research outputs found
Large-Scale Distributed Bayesian Matrix Factorization using Stochastic Gradient MCMC
Despite having various attractive qualities such as high prediction accuracy
and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix
Factorization has not been widely adopted because of the prohibitive cost of
inference. In this paper, we propose a scalable distributed Bayesian matrix
factorization algorithm using stochastic gradient MCMC. Our algorithm, based on
Distributed Stochastic Gradient Langevin Dynamics, can not only match the
prediction accuracy of standard MCMC methods like Gibbs sampling, but at the
same time is as fast and simple as stochastic gradient descent. In our
experiments, we show that our algorithm can achieve the same level of
prediction accuracy as Gibbs sampling an order of magnitude faster. We also
show that our method reduces the prediction error as fast as distributed
stochastic gradient descent, achieving a 4.1% improvement in RMSE for the
Netflix dataset and an 1.8% for the Yahoo music dataset
Fast Differentially Private Matrix Factorization
Differentially private collaborative filtering is a challenging task, both in
terms of accuracy and speed. We present a simple algorithm that is provably
differentially private, while offering good performance, using a novel
connection of differential privacy to Bayesian posterior sampling via
Stochastic Gradient Langevin Dynamics. Due to its simplicity the algorithm
lends itself to efficient implementation. By careful systems design and by
exploiting the power law behavior of the data to maximize CPU cache bandwidth
we are able to generate 1024 dimensional models at a rate of 8.5 million
recommendations per second on a single PC
Dynamic Matrix Factorization with Priors on Unknown Values
Advanced and effective collaborative filtering methods based on explicit
feedback assume that unknown ratings do not follow the same model as the
observed ones (\emph{not missing at random}). In this work, we build on this
assumption, and introduce a novel dynamic matrix factorization framework that
allows to set an explicit prior on unknown values. When new ratings, users, or
items enter the system, we can update the factorization in time independent of
the size of data (number of users, items and ratings). Hence, we can quickly
recommend items even to very recent users. We test our methods on three large
datasets, including two very sparse ones, in static and dynamic conditions. In
each case, we outrank state-of-the-art matrix factorization methods that do not
use a prior on unknown ratings.Comment: in the Proceedings of 21st ACM SIGKDD Conference on Knowledge
Discovery and Data Mining 201
DMFSGD: A Decentralized Matrix Factorization Algorithm for Network Distance Prediction
The knowledge of end-to-end network distances is essential to many Internet
applications. As active probing of all pairwise distances is infeasible in
large-scale networks, a natural idea is to measure a few pairs and to predict
the other ones without actually measuring them. This paper formulates the
distance prediction problem as matrix completion where unknown entries of an
incomplete matrix of pairwise distances are to be predicted. The problem is
solvable because strong correlations among network distances exist and cause
the constructed distance matrix to be low rank. The new formulation circumvents
the well-known drawbacks of existing approaches based on Euclidean embedding.
A new algorithm, so-called Decentralized Matrix Factorization by Stochastic
Gradient Descent (DMFSGD), is proposed to solve the network distance prediction
problem. By letting network nodes exchange messages with each other, the
algorithm is fully decentralized and only requires each node to collect and to
process local measurements, with neither explicit matrix constructions nor
special nodes such as landmarks and central servers. In addition, we compared
comprehensively matrix factorization and Euclidean embedding to demonstrate the
suitability of the former on network distance prediction. We further studied
the incorporation of a robust loss function and of non-negativity constraints.
Extensive experiments on various publicly-available datasets of network delays
show not only the scalability and the accuracy of our approach but also its
usability in real Internet applications.Comment: submitted to IEEE/ACM Transactions on Networking on Nov. 201
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