2,259 research outputs found
Dual optimal filters for parameter estimation of a multivariate autoregressive process from noisy observations
This study deals with the estimation of a vector process disturbed by an additive white noise. When this process is
modelled by a multivariate autoregressive (M-AR) process, optimal filters such as Kalman or H1 filter can be used for
prediction or estimation from noisy observations. However, the estimation of the M-AR parameters from noisy observations is
a key issue to be addressed. Off-line or iterative approaches have been proposed recently, but their computational costs can be
a drawback. Using on-line methods such as extended Kalman filter and sigma-point Kalman filter are of interest, but the size
of the state vector to be estimated is quite high. In order to reduce this size and the resulting computational cost, the authors
suggest using dual optimal filters. In this study, the authors propose to extend to the multi-channel case the so-called dual
Kalman or H1 filters-based scheme initially proposed for single-channel applications. The proposed methods are first tested
with a synthetic M-AR process and then with an M-AR process corresponding to a mobile fading channel. The comparative
simulation study the authors carried out with existing techniques confirms the effectiveness of the proposed methods
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates
Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation
Multichannel Deconvolution with Long-Range Dependence: A Minimax Study
We consider the problem of estimating the unknown response function in the
multichannel deconvolution model with long-range dependent Gaussian errors. We
do not limit our consideration to a specific type of long-range dependence
rather we assume that the errors should satisfy a general assumption in terms
of the smallest and larger eigenvalues of their covariance matrices. We derive
minimax lower bounds for the quadratic risk in the proposed multichannel
deconvolution model when the response function is assumed to belong to a Besov
ball and the blurring function is assumed to possess some smoothness
properties, including both regular-smooth and super-smooth convolutions.
Furthermore, we propose an adaptive wavelet estimator of the response function
that is asymptotically optimal (in the minimax sense), or near-optimal within a
logarithmic factor, in a wide range of Besov balls. It is shown that the
optimal convergence rates depend on the balance between the smoothness
parameter of the response function, the kernel parameters of the blurring
function, the long memory parameters of the errors, and how the total number of
observations is distributed among the total number of channels. Some examples
of inverse problems in mathematical physics where one needs to recover initial
or boundary conditions on the basis of observations from a noisy solution of a
partial differential equation are used to illustrate the application of the
theory we developed. The optimal convergence rates and the adaptive estimators
we consider extend the ones studied by Pensky and Sapatinas (2009, 2010) for
independent and identically distributed Gaussian errors to the case of
long-range dependent Gaussian errors
Measuring information-transfer delays
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics
Communication Theoretic Data Analytics
Widespread use of the Internet and social networks invokes the generation of
big data, which is proving to be useful in a number of applications. To deal
with explosively growing amounts of data, data analytics has emerged as a
critical technology related to computing, signal processing, and information
networking. In this paper, a formalism is considered in which data is modeled
as a generalized social network and communication theory and information theory
are thereby extended to data analytics. First, the creation of an equalizer to
optimize information transfer between two data variables is considered, and
financial data is used to demonstrate the advantages. Then, an information
coupling approach based on information geometry is applied for dimensionality
reduction, with a pattern recognition example to illustrate the effectiveness.
These initial trials suggest the potential of communication theoretic data
analytics for a wide range of applications.Comment: Published in IEEE Journal on Selected Areas in Communications, Jan.
201
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