Semi-parametric Gaussian copula models for machine learning

The aim of machine learning and statistics is to learn and predict from data. With the introduction of copulas, probabilistic models and algorithms can benefit from the separation of dependency and marginals. The additional flexibility allows to generalise better and increase the prediction accuracy. Based on this observation, this work enlightens different models within the framework of a semi-parametric Gaussian copula model.
The first model we consider is archetypal analysis. We show that the Gaussian copula approximates the dependency structure of the generative model we consider. With copula archetypal analysis, we present a new model, which extends the applicability of the original model. Our second contribution refers to the semi-parametric Gaussian copula extension of principal component analysis. We consider the model in the context of parametric appearance models for facial appearance. We show, that the copula relaxation leads ultimately to a higher specificity and provide a unifying way of combining different data. The third contribution is Bayesian sub-network estimation within the framework of Gaussian graphical models. We show that the Markov blanket of a set of query variables has analytical form and can be efficiently estimated. Our last contribution is the motivation of time-resolved information flows in the context of directed information and Pearlian graphs. We show, how to discover information flows in non-stationary time series and give a convenient estimator.
At the core of these models lies the semi-parametric Gaussian copula model. In this work we show how it allows to relax certain assumptions in the aforementioned models. Ultimately, this leads to non-Gaussian and latent linear models, which better apply to real-world data sets.