19,493 research outputs found
Data-driven satisficing measure and ranking
We propose an computational framework for real-time risk assessment and
prioritizing for random outcomes without prior information on probability
distributions. The basic model is built based on satisficing measure (SM) which
yields a single index for risk comparison. Since SM is a dual representation
for a family of risk measures, we consider problems constrained by general
convex risk measures and specifically by Conditional value-at-risk. Starting
from offline optimization, we apply sample average approximation technique and
argue the convergence rate and validation of optimal solutions. In online
stochastic optimization case, we develop primal-dual stochastic approximation
algorithms respectively for general risk constrained problems, and derive their
regret bounds. For both offline and online cases, we illustrate the
relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure
Top-N Recommender System via Matrix Completion
Top-N recommender systems have been investigated widely both in industry and
academia. However, the recommendation quality is far from satisfactory. In this
paper, we propose a simple yet promising algorithm. We fill the user-item
matrix based on a low-rank assumption and simultaneously keep the original
information. To do that, a nonconvex rank relaxation rather than the nuclear
norm is adopted to provide a better rank approximation and an efficient
optimization strategy is designed. A comprehensive set of experiments on real
datasets demonstrates that our method pushes the accuracy of Top-N
recommendation to a new level.Comment: AAAI 201
Bayesian inference for bivariate ranks
A recommender system based on ranks is proposed, where an expert's ranking of
a set of objects and a user's ranking of a subset of those objects are combined
to make a prediction of the user's ranking of all objects. The rankings are
assumed to be induced by latent continuous variables corresponding to the
grades assigned by the expert and the user to the objects. The dependence
between the expert and user grades is modelled by a copula in some parametric
family. Given a prior distribution on the copula parameter, the user's complete
ranking is predicted by the mode of the posterior predictive distribution of
the user's complete ranking conditional on the expert's complete and the user's
incomplete rankings. Various Markov chain Monte-Carlo algorithms are proposed
to approximate the predictive distribution or only its mode. The predictive
distribution can be obtained exactly for the Farlie-Gumbel-Morgenstern copula
family, providing a benchmark for the approximation accuracy of the algorithms.
The method is applied to the MovieLens 100k dataset with a Gaussian copula
modelling dependence between the expert's and user's grades.Comment: 21 page
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