7,651 research outputs found
Filtering Random Graph Processes Over Random Time-Varying Graphs
Graph filters play a key role in processing the graph spectra of signals
supported on the vertices of a graph. However, despite their widespread use,
graph filters have been analyzed only in the deterministic setting, ignoring
the impact of stochastic- ity in both the graph topology as well as the signal
itself. To bridge this gap, we examine the statistical behavior of the two key
filter types, finite impulse response (FIR) and autoregressive moving average
(ARMA) graph filters, when operating on random time- varying graph signals (or
random graph processes) over random time-varying graphs. Our analysis shows
that (i) in expectation, the filters behave as the same deterministic filters
operating on a deterministic graph, being the expected graph, having as input
signal a deterministic signal, being the expected signal, and (ii) there are
meaningful upper bounds for the variance of the filter output. We conclude the
paper by proposing two novel ways of exploiting randomness to improve (joint
graph-time) noise cancellation, as well as to reduce the computational
complexity of graph filtering. As demonstrated by numerical results, these
methods outperform the disjoint average and denoise algorithm, and yield a (up
to) four times complexity redution, with very little difference from the
optimal solution
Covariance estimation for multivariate conditionally Gaussian dynamic linear models
In multivariate time series, the estimation of the covariance matrix of the
observation innovations plays an important role in forecasting as it enables
the computation of the standardized forecast error vectors as well as it
enables the computation of confidence bounds of the forecasts. We develop an
on-line, non-iterative Bayesian algorithm for estimation and forecasting. It is
empirically found that, for a range of simulated time series, the proposed
covariance estimator has good performance converging to the true values of the
unknown observation covariance matrix. Over a simulated time series, the new
method approximates the correct estimates, produced by a non-sequential Monte
Carlo simulation procedure, which is used here as the gold standard. The
special, but important, vector autoregressive (VAR) and time-varying VAR models
are illustrated by considering London metal exchange data consisting of spot
prices of aluminium, copper, lead and zinc.Comment: 21 pages, 2 figures, 6 table
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