17,618 research outputs found
Concentration inequalities of the cross-validation estimate for stable predictors
In this article, we derive concentration inequalities for the
cross-validation estimate of the generalization error for stable predictors in
the context of risk assessment. The notion of stability has been first
introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and
\cite{KUNIY02} to characterize class of predictors with infinite VC dimension.
In particular, this covers -nearest neighbors rules, bayesian algorithm
(\cite{KEA95}), boosting,... General loss functions and class of predictors are
considered. We use the formalism introduced by \cite{DUD03} to cover a large
variety of cross-validation procedures including leave-one-out
cross-validation, -fold cross-validation, hold-out cross-validation (or
split sample), and the leave--out cross-validation.
In particular, we give a simple rule on how to choose the cross-validation,
depending on the stability of the class of predictors. In the special case of
uniform stability, an interesting consequence is that the number of elements in
the test set is not required to grow to infinity for the consistency of the
cross-validation procedure. In this special case, the particular interest of
leave-one-out cross-validation is emphasized
Ranking algorithms for implicit feedback
This report presents novel algorithms to use eye movements as an implicit relevance feedback in order to improve the performance of the searches. The algorithms are evaluated on "Transport Rank Five" Dataset which were previously collected in Task 8.3. We demonstrated that simple linear combination or tensor product of eye movement and image features can improve the retrieval accuracy
Kernel Mean Shrinkage Estimators
A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel
mean, is central to kernel methods in that it is used by many classical
algorithms such as kernel principal component analysis, and it also forms the
core inference step of modern kernel methods that rely on embedding probability
distributions in RKHSs. Given a finite sample, an empirical average has been
used commonly as a standard estimator of the true kernel mean. Despite a
widespread use of this estimator, we show that it can be improved thanks to the
well-known Stein phenomenon. We propose a new family of estimators called
kernel mean shrinkage estimators (KMSEs), which benefit from both theoretical
justifications and good empirical performance. The results demonstrate that the
proposed estimators outperform the standard one, especially in a "large d,
small n" paradigm.Comment: 41 page
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