247 research outputs found
Random sets and exact confidence regions
An important problem in statistics is the construction of confidence regions
for unknown parameters. In most cases, asymptotic distribution theory is used
to construct confidence regions, so any coverage probability claims only hold
approximately, for large samples. This paper describes a new approach, using
random sets, which allows users to construct exact confidence regions without
appeal to asymptotic theory. In particular, if the user-specified random set
satisfies a certain validity property, confidence regions obtained by
thresholding the induced data-dependent plausibility function are shown to have
the desired coverage probability.Comment: 14 pages, 2 figure
BPRS: Belief Propagation Based Iterative Recommender System
In this paper we introduce the first application of the Belief Propagation
(BP) algorithm in the design of recommender systems. We formulate the
recommendation problem as an inference problem and aim to compute the marginal
probability distributions of the variables which represent the ratings to be
predicted. However, computing these marginal probability functions is
computationally prohibitive for large-scale systems. Therefore, we utilize the
BP algorithm to efficiently compute these functions. Recommendations for each
active user are then iteratively computed by probabilistic message passing. As
opposed to the previous recommender algorithms, BPRS does not require solving
the recommendation problem for all the users if it wishes to update the
recommendations for only a single active. Further, BPRS computes the
recommendations for each user with linear complexity and without requiring a
training period. Via computer simulations (using the 100K MovieLens dataset),
we verify that BPRS iteratively reduces the error in the predicted ratings of
the users until it converges. Finally, we confirm that BPRS is comparable to
the state of art methods such as Correlation-based neighborhood model (CorNgbr)
and Singular Value Decomposition (SVD) in terms of rating and precision
accuracy. Therefore, we believe that the BP-based recommendation algorithm is a
new promising approach which offers a significant advantage on scalability
while providing competitive accuracy for the recommender systems
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