9,404 research outputs found
Estimation of the complex frequency of a harmonic signal based on a linear least squares method
AbstractIn this study, we propose a simple linear least squares estimation method (LLS) based on a Fourier transform to estimate the complex frequency of a harmonic signal. We first use a synthetically-generated noisy time series to validate the accuracy and effectiveness of LLS by comparing it with the commonly used linear autoregressive method (AR). For an input frequency of 0.5Â mHz, the calculated deviations from the theoretical value were 0.004â° and 0.008â° for the LLS and AR methods respectively; and for an input 5Â ĂÂ 10â6 attenuation, the calculated deviations for the LLS and AR methods were 2.4% and 1.6%. Though the theory of the AR method is more complex than that of LLS, the results show LLS is a useful alternative method. Finally, we use LLS to estimate the complex frequencies of the five singlets of the 0S2 mode of the Earth's free oscillation. Not only are the results consistent with previous studies, the method has high estimation precisions, which may prove helpful in determining constraints on the Earth's interior structures
Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization
As a powerful statistical image modeling technique, sparse representation has
been successfully used in various image restoration applications. The success
of sparse representation owes to the development of l1-norm optimization
techniques, and the fact that natural images are intrinsically sparse in some
domain. The image restoration quality largely depends on whether the employed
sparse domain can represent well the underlying image. Considering that the
contents can vary significantly across different images or different patches in
a single image, we propose to learn various sets of bases from a pre-collected
dataset of example image patches, and then for a given patch to be processed,
one set of bases are adaptively selected to characterize the local sparse
domain. We further introduce two adaptive regularization terms into the sparse
representation framework. First, a set of autoregressive (AR) models are
learned from the dataset of example image patches. The best fitted AR models to
a given patch are adaptively selected to regularize the image local structures.
Second, the image non-local self-similarity is introduced as another
regularization term. In addition, the sparsity regularization parameter is
adaptively estimated for better image restoration performance. Extensive
experiments on image deblurring and super-resolution validate that by using
adaptive sparse domain selection and adaptive regularization, the proposed
method achieves much better results than many state-of-the-art algorithms in
terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI
Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes
We introduce GP-FNARX: a new model for nonlinear system identification based
on a nonlinear autoregressive exogenous model (NARX) with filtered regressors
(F) where the nonlinear regression problem is tackled using sparse Gaussian
processes (GP). We integrate data pre-processing with system identification
into a fully automated procedure that goes from raw data to an identified
model. Both pre-processing parameters and GP hyper-parameters are tuned by
maximizing the marginal likelihood of the probabilistic model. We obtain a
Bayesian model of the system's dynamics which is able to report its uncertainty
in regions where the data is scarce. The automated approach, the modeling of
uncertainty and its relatively low computational cost make of GP-FNARX a good
candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and
Control (CDC), Firenze, Italy, December 201
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
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 Wienerâs 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
Dollarization Persistence and Individual Heterogeneity
The most salient feature of financial dollarization, and the one that causes more concern to policy makers, is its persistence: even after successful macroeconomic stabilizations, dollarization ratios often remain high. In this paper we claim that this persistence is connected to the fact that the participants in the dollar deposit market are fairly heterogenous, and so is the way they form their optimal currency portfolio.We develop as simple model when agents differ in their ability to process information, which turns out to be enough to generate persistence up on aggregation. We find empirical support for this claim with data from three Latin American countries and Poland.Dollarization, individual heterogeneity, persistence, aggregation
Modeling sparse connectivity between underlying brain sources for EEG/MEG
We propose a novel technique to assess functional brain connectivity in
EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA),
can overcome the problem of volume conduction by modeling neural data
innovatively with the following ingredients: (a) the EEG is assumed to be a
linear mixture of correlated sources following a multivariate autoregressive
(MVAR) model, (b) the demixing is estimated jointly with the source MVAR
parameters, (c) overfitting is avoided by using the Group Lasso penalty. This
approach allows to extract the appropriate level cross-talk between the
extracted sources and in this manner we obtain a sparse data-driven model of
functional connectivity. We demonstrate the usefulness of SCSA with simulated
data, and compare to a number of existing algorithms with excellent results.Comment: 9 pages, 6 figure
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