8,481 research outputs found
A Separation Theorem for Expected Value and Feared Value Discrete Time Control
We show how the use of a parallel between the ordinary and the algebras, Maslov measures that exploit this parallel, and more specifically their specialization to probabilities and the corresponding {\em cost measures} of Quadrat, offer a completely parallel treatment of stochastic and minimax control of disturbed nonlinear discrete time systems with partial information. This paper is based upon, and improves, the discrete time part of the earlier paper \cite{ber95}
A non-autonomous stochastic discrete time system with uniform disturbances
The main objective of this article is to present Bayesian optimal control
over a class of non-autonomous linear stochastic discrete time systems with
disturbances belonging to a family of the one parameter uniform distributions.
It is proved that the Bayes control for the Pareto priors is the solution of a
linear system of algebraic equations. For the case that this linear system is
singular, we apply optimization techniques to gain the Bayesian optimal
control. These results are extended to generalized linear stochastic systems of
difference equations and provide the Bayesian optimal control for the case
where the coefficients of these type of systems are non-square matrices. The
paper extends the results of the authors developed for system with disturbances
belonging to the exponential family
Diffusion Approximations for Online Principal Component Estimation and Global Convergence
In this paper, we propose to adopt the diffusion approximation tools to study
the dynamics of Oja's iteration which is an online stochastic gradient descent
method for the principal component analysis. Oja's iteration maintains a
running estimate of the true principal component from streaming data and enjoys
less temporal and spatial complexities. We show that the Oja's iteration for
the top eigenvector generates a continuous-state discrete-time Markov chain
over the unit sphere. We characterize the Oja's iteration in three phases using
diffusion approximation and weak convergence tools. Our three-phase analysis
further provides a finite-sample error bound for the running estimate, which
matches the minimax information lower bound for principal component analysis
under the additional assumption of bounded samples.Comment: Appeared in NIPS 201
A detectability criterion and data assimilation for non-linear differential equations
In this paper we propose a new sequential data assimilation method for
non-linear ordinary differential equations with compact state space. The method
is designed so that the Lyapunov exponents of the corresponding estimation
error dynamics are negative, i.e. the estimation error decays exponentially
fast. The latter is shown to be the case for generic regular flow maps if and
only if the observation matrix H satisfies detectability conditions: the rank
of H must be at least as great as the number of nonnegative Lyapunov exponents
of the underlying attractor. Numerical experiments illustrate the exponential
convergence of the method and the sharpness of the theory for the case of
Lorenz96 and Burgers equations with incomplete and noisy observations
Efficient pointwise estimation based on discrete data in ergodic nonparametric diffusions
A truncated sequential procedure is constructed for estimating the drift
coefficient at a given state point based on discrete data of ergodic diffusion
process. A nonasymptotic upper bound is obtained for a pointwise absolute error
risk. The optimal convergence rate and a sharp constant in the bounds are found
for the asymptotic pointwise minimax risk. As a consequence, the efficiency is
obtained of the proposed sequential procedure.Comment: Published at http://dx.doi.org/10.3150/14-BEJ655 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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