8,617 research outputs found
Reducing statistical time-series problems to binary classification
We show how binary classification methods developed to work on i.i.d. data
can be used for solving statistical problems that are seemingly unrelated to
classification and concern highly-dependent time series. Specifically, the
problems of time-series clustering, homogeneity testing and the three-sample
problem are addressed. The algorithms that we construct for solving these
problems are based on a new metric between time-series distributions, which can
be evaluated using binary classification methods. Universal consistency of the
proposed algorithms is proven under most general assumptions. The theoretical
results are illustrated with experiments on synthetic and real-world data.Comment: In proceedings of NIPS 2012, pp. 2069-207
Rare event simulation for multiscale diffusions in random environments
We consider systems of stochastic differential equations with multiple scales
and small noise and assume that the coefficients of the equations are ergodic
and stationary random fields. Our goal is to construct provably-efficient
importance sampling Monte Carlo methods that allow efficient computation of
rare event probabilities or expectations of functionals that can be associated
with rare events. Standard Monte Carlo algorithms perform poorly in the small
noise limit and hence fast simulations algorithms become relevant. The presence
of multiple scales complicates the design and the analysis of efficient
importance sampling schemes. An additional complication is the randomness of
the environment. We construct explicit changes of measures that are proven to
be logarithmic asymptotically efficient with probability one with respect to
the random environment (i.e., in the quenched sense). Numerical simulations
support the theoretical results.Comment: Final version, paper to appear in SIAM Journal Multiscale Modelling
and Simulatio
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