Bayesian models for multivariate count dataPirš, Gregor (Avtor) Štrumbelj, Erik (Mentor) latent structureconditional independencecopulanegative binomial distributionensemble learningMultivariate normal distribution offers a convenient approach to several multivariate problems due to its mathematical simplicity. However, often the data can not be modeled with the multivariate normal distribution well, and one such example are multivariate counts. Some approaches, which can be considered trivial for continuous, can be very difficult for count data. Due to that, some options are not explored well. For example, in factor analysis, it is relatively simple to alleviate the assumption of conditional independence for continuous data, but it is not that straight-forward for count data. By using suitable multivariate count distributions we are able to extend some established methods in a new direction of modeling the uncertainty. In this thesis, we focus on two such extensions: a) alleviating the conditional independence assumption in count factor analysis, and b) combining count predictions by fitting their structure with a suitable multivariate count distribution. At the beginning, we explored how the assumption of conditional independence in static count factor analysis methods affects their out-of-sample probabilistic predictions. We implemented several Bayesian factor analysis methods and paired them with a Gaussian copula in a two-stage fitting process. The copula serves to find the covariance not found by the latent structure of the model. We compared the methods on a toy and 5 real-world data sets in terms of out-of-sample probabilistic predictions. The results indicate that the assumption of conditional independence is very restrictive in terms of probabilistic prediction power. Additionally, we provide a normalization step for finding interpretable latent structure with count factor analysis. As the next step, we focused on problems that include continuous covariates, for example time. In this setting, the factor scores are not assumed static, but we enforce a smooth structure on their values, depending on the covariate – resulting in smooth latent trajectories. We developed a new Bayesian model for latent trajectory extraction and prediction for count data, without the assumption of conditional independence, based on Gaussian process factor analysis. We extended count-likelihood Gaussian process factor analysis by modeling the residual covariance with a Gaussian copula. Contrary to the two stage fitting process described in the previous paragraph, we incorporated both elements into a single model. We provide a fully Bayesian implementation of the model and use augmented likelihood for inference with Hamiltonian Monte Carlo. We compared the proposed method to other Gaussian process factor analysis models on 20 toy data sets, finding latent qualities of NBA teams, and forecasting disease counts. The results show that the proposed method is useful for latent structure extraction and out-of-sample prediction of multivariate counts. In the second part of this thesis we explored the use of multivariate count distributions in developing count ensembles based on modeling the structure of candidate predictions. Combining classifiers proved a rich source of models, which combine the knowledge of candidate models by learning the latent structure of their predictions. As such, they are especially useful for combining biased models, or models with systematic errors. Their performance is directly affected by how well we are able to model the structure of predictions. First, we developed a new method for combining classifiers, based on modeling the latent structure of predictions with multivariate normal mixtures, to alleviate some of the drawbacks of the state-of-the-art related methods. The method proved to be very flexible while remaining robust. As the next step, we extended the classifier combination method to combining counts, by truncating the response counts and using suitable multivariate count distributions to model the candidate predictions. Results suggest that using this extension provides better probabilistic predictions than the original classifier model, even though it is less flexible.20212021-07-02 14:50:01Doktorsko delo/naloga128112sl