Given a default distribution$P$and a set of test data$x^{M}=\{x_{1},\ x_{2},\ \ldots,\ x_{M}\}$this paper seeks to answer the question if it was likely that$x^{M}$was generated by$P$. For discrete distributions, the definitive answer is in principle given by Kolmogorov-Martin-Lof randomness. In this paper we seek to generalize this to continuous distributions. We consider a set of statistics$T_{1}(x^{M}), T_{2}(x^{M}),\cdots$. To each statistic we associate its maximum entropy distribution and with this a universal source coder. The maximum entropy distributions are subsequently combined to give a total codelength, which is compared with$-\log P(x^{M})$. We show that this approach satisfied a number of theoretical properties. For real world data$P$usually is unknown. We transform data into a standard distribution in the latent space using a bidirectional generate network and use maximum entropy coding there. We compare the resulting method to other methods that also used generative neural networks to detect anomalies. In most cases, our results show better performance.

A classic application of description length is for model selection with the minimum description length (MDL) principle. The focus of this paper is to extend description length for data analysis beyond simple model selection and sequences of scalars. More specifically, we extend the description length for data analysis in Gaussian graphical models. These are powerful tools to model interactions among variables in a sequence of i.i.d Gaussian data in the form of a graph. Our method uses universal graph coding methods to accurately account for model complexity, and therefore provide a more rigorous approach for graph model selection. The developed method is tested with synthetic and electrocardiogram (ECG) data to find the graph model and anomaly in Gaussian graphical models. The experiments show that our method gives better performance compared to commonly used methods.