15,654 research outputs found
Tracking Stopping Times Through Noisy Observations
A novel quickest detection setting is proposed which is a generalization of
the well-known Bayesian change-point detection model. Suppose
\{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S
is a stopping time with respect to \{X_i\}_{i\geq 1}. The problem is to find a
stopping time T with respect to \{Y_i\}_{i\geq 1} that optimally tracks S, in
the sense that T minimizes the expected reaction delay E(T-S)^+, while keeping
the false-alarm probability P(T<S) below a given threshold \alpha \in [0,1].
This problem formulation applies in several areas, such as in communication,
detection, forecasting, and quality control.
Our results relate to the situation where the X_i's and Y_i's take values in
finite alphabets and where S is bounded by some positive integer \kappa. By
using elementary methods based on the analysis of the tree structure of
stopping times, we exhibit an algorithm that computes the optimal average
reaction delays for all \alpha \in [0,1], and constructs the associated optimal
stopping times T. Under certain conditions on \{(X_i,Y_i)\}_{i\geq 1} and S,
the algorithm running time is polynomial in \kappa.Comment: 19 pages, 4 figures, to appear in IEEE Transactions on Information
Theor
Reconstruction of Causal Networks by Set Covering
We present a method for the reconstruction of networks, based on the order of
nodes visited by a stochastic branching process. Our algorithm reconstructs a
network of minimal size that ensures consistency with the data. Crucially, we
show that global consistency with the data can be achieved through purely local
considerations, inferring the neighbourhood of each node in turn. The
optimisation problem solved for each individual node can be reduced to a Set
Covering Problem, which is known to be NP-hard but can be approximated well in
practice. We then extend our approach to account for noisy data, based on the
Minimum Description Length principle. We demonstrate our algorithms on
synthetic data, generated by an SIR-like epidemiological model.Comment: Under consideration for the ECML PKDD 2010 conferenc
Sequential Design for Ranking Response Surfaces
We propose and analyze sequential design methods for the problem of ranking
several response surfaces. Namely, given response surfaces over a
continuous input space , the aim is to efficiently find the index of
the minimal response across the entire . The response surfaces are not
known and have to be noisily sampled one-at-a-time. This setting is motivated
by stochastic control applications and requires joint experimental design both
in space and response-index dimensions. To generate sequential design
heuristics we investigate stepwise uncertainty reduction approaches, as well as
sampling based on posterior classification complexity. We also make connections
between our continuous-input formulation and the discrete framework of pure
regret in multi-armed bandits. To model the response surfaces we utilize
kriging surrogates. Several numerical examples using both synthetic data and an
epidemics control problem are provided to illustrate our approach and the
efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures
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