1,924 research outputs found
Recursive Compressed Sensing
We introduce a recursive algorithm for performing compressed sensing on
streaming data. The approach consists of a) recursive encoding, where we sample
the input stream via overlapping windowing and make use of the previous
measurement in obtaining the next one, and b) recursive decoding, where the
signal estimate from the previous window is utilized in order to achieve faster
convergence in an iterative optimization scheme applied to decode the new one.
To remove estimation bias, a two-step estimation procedure is proposed
comprising support set detection and signal amplitude estimation. Estimation
accuracy is enhanced by a non-linear voting method and averaging estimates over
multiple windows. We analyze the computational complexity and estimation error,
and show that the normalized error variance asymptotically goes to zero for
sublinear sparsity. Our simulation results show speed up of an order of
magnitude over traditional CS, while obtaining significantly lower
reconstruction error under mild conditions on the signal magnitudes and the
noise level.Comment: Submitted to IEEE Transactions on Information Theor
Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models
Recent studies on analyzing dynamic brain connectivity rely on sliding-window
analysis or time-varying coefficient models which are unable to capture both
smooth and abrupt changes simultaneously. Emerging evidence suggests
state-related changes in brain connectivity where dependence structure
alternates between a finite number of latent states or regimes. Another
challenge is inference of full-brain networks with large number of nodes. We
employ a Markov-switching dynamic factor model in which the state-driven
time-varying connectivity regimes of high-dimensional fMRI data are
characterized by lower-dimensional common latent factors, following a
regime-switching process. It enables a reliable, data-adaptive estimation of
change-points of connectivity regimes and the massive dependencies associated
with each regime. We consider the switching VAR to quantity the dynamic
effective connectivity. We propose a three-step estimation procedure: (1)
extracting the factors using principal component analysis (PCA) and (2)
identifying dynamic connectivity states using the factor-based switching vector
autoregressive (VAR) models in a state-space formulation using Kalman filter
and expectation-maximization (EM) algorithm, and (3) constructing the
high-dimensional connectivity metrics for each state based on subspace
estimates. Simulation results show that our proposed estimator outperforms the
K-means clustering of time-windowed coefficients, providing more accurate
estimation of regime dynamics and connectivity metrics in high-dimensional
settings. Applications to analyzing resting-state fMRI data identify dynamic
changes in brain states during rest, and reveal distinct directed connectivity
patterns and modular organization in resting-state networks across different
states.Comment: 21 page
Sliding window adaptive fast QR and QR-lattice algorithms
Published versio
Data-driven adaptive model-based predictive control with application in wastewater systems
This study is concerned with the development of a new data-driven adaptive model-based predictive controller (MBPC) with input constraints. The proposed methods employ subspace identification technique and a singular value decomposition (SVD)-based optimisation strategy to formulate the control algorithm and incorporate the input constraints. Both direct adaptive model-based predictive controller (DAMBPC) and indirect adaptive model-based predictive controller (IAMBPC) are considered. In DAMBPC, the direct identification of controller parameters is desired to reduce the design effort and computational load while the IAMBPC involves a two-stage process of model identification and controller design. The former method only requires a single QR decomposition for obtaining the controller parameters and uses a receding horizon approach to process input/output data for the identification. A suboptimal SVD-based optimisation technique is proposed to incorporate the input constraints. The proposed techniques are implemented and tested on a fourth order non-linear model of a wastewater system. Simulation results are presented to compare the direct and indirect adaptive methods and to demonstrate the performance of the proposed algorithms
A new recursive dynamic factor analysis for point and interval forecast of electricity price
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