Abstract
Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era.
Highlights
Rodrıguez et al./Sparse covariance estimation in heterogeneous samples graphical models
As in [59], the hidden Markov models we discuss allow for the graph encoding the conditional independence structure of the data to change over time, an important feature that has been missing in other multivariate time series models employing graphical models [10, 60]
In the case when inference is restricted to decomposable graphs, the slice sampler avoids the need to compute the normalizing constants associated with the graphs, which can potentially lead to speedups
Summary
If G is assumed to be decomposable, the posterior normalizing constant IG(δ0 + n, D0 + U + A) can be calculated directly using a formula similar to equation (2.5), p(x(n+1) | G) and p(x(n+1) | x(n), G) can be calculated directly without any numerical approximation techniques. We assume that the observed variables are independent apriori
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