132 research outputs found
Efficient Variational Bayesian Structure Learning of Dynamic Graphical Models
Estimating time-varying graphical models are of paramount importance in
various social, financial, biological, and engineering systems, since the
evolution of such networks can be utilized for example to spot trends, detect
anomalies, predict vulnerability, and evaluate the impact of interventions.
Existing methods require extensive tuning of parameters that control the graph
sparsity and temporal smoothness. Furthermore, these methods are
computationally burdensome with time complexity O(NP^3) for P variables and N
time points. As a remedy, we propose a low-complexity tuning-free Bayesian
approach, named BADGE. Specifically, we impose temporally-dependent
spike-and-slab priors on the graphs such that they are sparse and varying
smoothly across time. A variational inference algorithm is then derived to
learn the graph structures from the data automatically. Owning to the
pseudo-likelihood and the mean-field approximation, the time complexity of
BADGE is only O(NP^2). Additionally, by identifying the frequency-domain
resemblance to the time-varying graphical models, we show that BADGE can be
extended to learning frequency-varying inverse spectral density matrices, and
yields graphical models for multivariate stationary time series. Numerical
results on both synthetic and real data show that that BADGE can better recover
the underlying true graphs, while being more efficient than the existing
methods, especially for high-dimensional cases
Sparse Approximate Inference for Spatio-Temporal Point Process Models
Spatio-temporal point process models play a central role in the analysis of
spatially distributed systems in several disciplines. Yet, scalable inference
remains computa- tionally challenging both due to the high resolution modelling
generally required and the analytically intractable likelihood function. Here,
we exploit the sparsity structure typical of (spatially) discretised
log-Gaussian Cox process models by using approximate message-passing
algorithms. The proposed algorithms scale well with the state dimension and the
length of the temporal horizon with moderate loss in distributional accuracy.
They hence provide a flexible and faster alternative to both non-linear
filtering-smoothing type algorithms and to approaches that implement the
Laplace method or expectation propagation on (block) sparse latent Gaussian
models. We infer the parameters of the latent Gaussian model using a structured
variational Bayes approach. We demonstrate the proposed framework on simulation
studies with both Gaussian and point-process observations and use it to
reconstruct the conflict intensity and dynamics in Afghanistan from the
WikiLeaks Afghan War Diary
Accelerating proximal Markov chain Monte Carlo by using an explicit stabilised method
We present a highly efficient proximal Markov chain Monte Carlo methodology
to perform Bayesian computation in imaging problems. Similarly to previous
proximal Monte Carlo approaches, the proposed method is derived from an
approximation of the Langevin diffusion. However, instead of the conventional
Euler-Maruyama approximation that underpins existing proximal Monte Carlo
methods, here we use a state-of-the-art orthogonal Runge-Kutta-Chebyshev
stochastic approximation that combines several gradient evaluations to
significantly accelerate its convergence speed, similarly to accelerated
gradient optimisation methods. The proposed methodology is demonstrated via a
range of numerical experiments, including non-blind image deconvolution,
hyperspectral unmixing, and tomographic reconstruction, with total-variation
and -type priors. Comparisons with Euler-type proximal Monte Carlo
methods confirm that the Markov chains generated with our method exhibit
significantly faster convergence speeds, achieve larger effective sample sizes,
and produce lower mean square estimation errors at equal computational budget.Comment: 28 pages, 13 figures. Accepted for publication in SIAM Journal on
Imaging Sciences (SIIMS
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