163 research outputs found
Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions
We consider the problem of adaptive stratified sampling for Monte Carlo
integration of a differentiable function given a finite number of evaluations
to the function. We construct a sampling scheme that samples more often in
regions where the function oscillates more, while allocating the samples such
that they are well spread on the domain (this notion shares similitude with low
discrepancy). We prove that the estimate returned by the algorithm is almost
similarly accurate as the estimate that an optimal oracle strategy (that would
know the variations of the function everywhere) would return, and provide a
finite-sample analysis.Comment: 23 pages, 3 figures, to appear in NIPS 2012 conference proceeding
Simple regret for infinitely many armed bandits
We consider a stochastic bandit problem with infinitely many arms. In this
setting, the learner has no chance of trying all the arms even once and has to
dedicate its limited number of samples only to a certain number of arms. All
previous algorithms for this setting were designed for minimizing the
cumulative regret of the learner. In this paper, we propose an algorithm aiming
at minimizing the simple regret. As in the cumulative regret setting of
infinitely many armed bandits, the rate of the simple regret will depend on a
parameter characterizing the distribution of the near-optimal arms. We
prove that depending on , our algorithm is minimax optimal either up to
a multiplicative constant or up to a factor. We also provide
extensions to several important cases: when is unknown, in a natural
setting where the near-optimal arms have a small variance, and in the case of
unknown time horizon.Comment: in 32th International Conference on Machine Learning (ICML 2015
Bandit Theory meets Compressed Sensing for high dimensional Stochastic Linear Bandit
We consider a linear stochastic bandit problem where the dimension of the
unknown parameter is larger than the sampling budget . In such
cases, it is in general impossible to derive sub-linear regret bounds since
usual linear bandit algorithms have a regret in . In this paper
we assume that is sparse, i.e. has at most non-zero
components, and that the space of arms is the unit ball for the norm.
We combine ideas from Compressed Sensing and Bandit Theory and derive
algorithms with regret bounds in
On the informativeness of dominant and co-dominant genetic markers for Bayesian supervised clustering
We study the accuracy of Bayesian supervised method used to cluster
individuals into genetically homogeneous groups on the basis of dominant or
codominant molecular markers. We provide a formula relating an error criterion
the number of loci used and the number of clusters. This formula is exact and
holds for arbitrary number of clusters and markers. Our work suggests that
dominant markers studies can achieve an accuracy similar to that of codominant
markers studies if the number of markers used in the former is about 1.7 times
larger than in the latter
- …