28,296 research outputs found
Optimal design of an unsupervised adaptive classifier with unknown priors
An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained
Deterministic Mean-field Ensemble Kalman Filtering
The proof of convergence of the standard ensemble Kalman filter (EnKF) from
Legland etal. (2011) is extended to non-Gaussian state space models. A
density-based deterministic approximation of the mean-field limit EnKF
(DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given
a certain minimal order of convergence between the two, this extends
to the deterministic filter approximation, which is therefore asymptotically
superior to standard EnKF when the dimension . The fidelity of
approximation of the true distribution is also established using an extension
of total variation metric to random measures. This is limited by a Gaussian
bias term arising from non-linearity/non-Gaussianity of the model, which exists
for both DMFEnKF and standard EnKF. Numerical results support and extend the
theory
A Mean-field Approach for an Intercarrier Interference Canceller for OFDM
The similarity of the mathematical description of random-field spin systems
to orthogonal frequency-division multiplexing (OFDM) scheme for wireless
communication is exploited in an intercarrier-interference (ICI) canceller used
in the demodulation of OFDM. The translational symmetry in the Fourier domain
generically concentrates the major contribution of ICI from each subcarrier in
the subcarrier's neighborhood. This observation in conjunction with mean field
approach leads to a development of an ICI canceller whose necessary cost of
computation scales linearly with respect to the number of subcarriers. It is
also shown that the dynamics of the mean-field canceller are well captured by a
discrete map of a single macroscopic variable, without taking the spatial and
time correlations of estimated variables into account.Comment: 7pages, 3figure
Mean Estimation from One-Bit Measurements
We consider the problem of estimating the mean of a symmetric log-concave
distribution under the constraint that only a single bit per sample from this
distribution is available to the estimator. We study the mean squared error as
a function of the sample size (and hence the number of bits). We consider three
settings: first, a centralized setting, where an encoder may release bits
given a sample of size , and for which there is no asymptotic penalty for
quantization; second, an adaptive setting in which each bit is a function of
the current observation and previously recorded bits, where we show that the
optimal relative efficiency compared to the sample mean is precisely the
efficiency of the median; lastly, we show that in a distributed setting where
each bit is only a function of a local sample, no estimator can achieve optimal
efficiency uniformly over the parameter space. We additionally complement our
results in the adaptive setting by showing that \emph{one} round of adaptivity
is sufficient to achieve optimal mean-square error
Performance analysis and optimal selection of large mean-variance portfolios under estimation risk
We study the consistency of sample mean-variance portfolios of arbitrarily
high dimension that are based on Bayesian or shrinkage estimation of the input
parameters as well as weighted sampling. In an asymptotic setting where the
number of assets remains comparable in magnitude to the sample size, we provide
a characterization of the estimation risk by providing deterministic
equivalents of the portfolio out-of-sample performance in terms of the
underlying investment scenario. The previous estimates represent a means of
quantifying the amount of risk underestimation and return overestimation of
improved portfolio constructions beyond standard ones. Well-known for the
latter, if not corrected, these deviations lead to inaccurate and overly
optimistic Sharpe-based investment decisions. Our results are based on recent
contributions in the field of random matrix theory. Along with the asymptotic
analysis, the analytical framework allows us to find bias corrections improving
on the achieved out-of-sample performance of typical portfolio constructions.
Some numerical simulations validate our theoretical findings
"An Asymptotic Expansion Scheme for the Optimal Investment Problems"
We shall propose a new computational scheme for the evaluation of the optimal portfolio for investment.Our method is based on an extension of the asymptotic expansion approach which has been recently developed for pricing problems of the contingent claims' analysis by Kunitomo-Takahashi (1992, 1995, 1998, 2001), Yoshida (1992), Takahashi (1995, 1999),Takahashi and Yoshida (2001). In particular, we will explicitly derive a formula of the optimal portfolio associated with maximizing utility from terminal wealth in a nancial market with Markovian coe cients,and give a numerical example for a power utility function.
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