Preserving correlations: A statistical method for generating synthetic data

We propose a method to generate statistically representative synthetic data from a given dataset. The main goal of our method is for the created data set to mimic the between feature correlations present in the original data, while also offering a tunable parameter to influence the privacy level. In particular, our method constructs a statistical map by using the empirical conditional distributions between the features of the original dataset. We describe in detail our algorithms used both in the construction of a statistical map and how to use this map to generate synthetic observations. This approach is tested in three different ways: with a hand calculated example; a manufactured dataset; and a real world energy-related dataset of consumption/production of households in Madeira Island. We test our method's performance by comparing the datasets using the on Pearson correlation matrix. The proposed methodology is general in the sense that it does not rely on the used test dataset. We expect it to be applicable in a much broader context than indicated here.