Multivariate Bernoulli distribution
By Bin Dai, Shilin Ding, Grace Wahba. 2012
189 citations recorded by the source corpus.
In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can estimate not only the main effects and pairwise interactions among the nodes but also is capable of modeling higher order interactions, allowing for the existence of complex clique effects. We compare the multivariate Bernoulli model with existing graphical inference models - the Ising model and the multivariate Gaussian model, where only the pairwise interactions are considered. On the other hand, the multivariate Bernoulli distribution has an interesting property in that independence and uncorrelatedness of the component random variables are equivalent. Both the marginal and conditional distributions of a subset of variables in the multivariate Bernoulli distribution still follow the multivariate Bernoulli distribution. Furthermore, the multivariate Bernoulli logistic model is developed under generalized linear model theory by utilizing the canonical link function in order to include covariate information on the nodes, edges and cliques. We also consider variable selection techniques such as LASSO in the logistic model to impose sparsity structure on the graph. Finally, we discuss extending the smoothing spline ANOVA approach to the multivariate Bernoulli logistic model to enable estimation of non-linear effects of the predictor variables.
Subfields: Artificial Intelligence, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a6f4a4e3de754cb0e29485925c1cf47ba2ee8456
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In Artificial Intelligence
In Statistical and Nonlinear Physics
Citations in the corpus
- Probabilistic forecasting in day-ahead electricity markets: Simulating peak and off-peak prices (2018, methodology): “For the bivariate Bernoulli setting we follow Dai et al. (2013). Assuming a bivariate jump process.”