Boris Lorbeer

Boris Lorbeer, Mustafa Mohsen

Nowadays, the need for causal discovery is ubiquitous. A better understanding of not just the stochastic dependencies between parts of a system, but also the actual cause-effect relations, is essential for all parts of science. Thus, the need for reliable methods to detect causal directions is growing constantly. In the last 50 years, many causal discovery algorithms have emerged, but most of them are applicable only under the assumption that the systems have no feedback loops and that they are causally sufficient, i.e. that there are no unmeasured subsystems that can affect multiple measured variables. This is unfortunate since those restrictions can often not be presumed in practice. Feedback is an integral feature of many processes, and real-world systems are rarely completely isolated and fully measured. Fortunately, in recent years, several techniques, that can cope with cyclic, causally insufficient systems, have been developed. And with multiple methods available, a practical application of those algorithms now requires knowledge of the respective strengths and weaknesses. Here, we focus on the problem of causal discovery for sparse linear models which are allowed to have cycles and hidden confounders. We have prepared a comprehensive and thorough comparative study of four causal discovery techniques: two versions of the LLC method [10] and two variants of the ASP-based algorithm [11]. The evaluation investigates the performance of those techniques for various experiments with multiple interventional setups and different dataset sizes.

Boris Lorbeer, Axel Küpper

We live in a world full of complex systems which we need to improve our understanding of. To accomplish this, purely probabilistic investigations are often not enough. They are only the first step and must be followed by learning the system's underlying mechanisms. This is what the discipline of causality is concerned with. Many of those complex systems contain feedback loops which means that our methods have to allow for cyclic causal relations. Furthermore, systems are rarely sufficiently isolated, which means that there are usually hidden confounders, i.e., unmeasured variables that each causally affects more than one measured variable. Finally, data is often distorted by contaminating processes, and we need to apply methods that are robust against such distortions. That's why we consider the robustness of LLC, see \cite{llc}, one of the few causal analysis methods that can deal with cyclic models with hidden confounders. Following a theoretical analysis of LLC's robustness properties, we also provide robust extensions of LLC. To facilitate reproducibility and further research in this field, we make the source code publicly available.

Boris Lorbeer, Max Botler

In this paper, we propose POTATOES (Partitioning OverfiTting AuTOencoder EnSemble), a new method for unsupervised outlier detection (UOD). More precisely, given any autoencoder for UOD, this technique can be used to improve its accuracy while at the same time removing the burden of tuning its regularization. The idea is to not regularize at all, but to rather randomly partition the data into sufficiently many equally sized parts, overfit each part with its own autoencoder, and to use the maximum over all autoencoder reconstruction errors as the anomaly score. We apply our model to various realistic datasets and show that if the set of inliers is dense enough, our method indeed improves the UOD performance of a given autoencoder significantly. For reproducibility, the code is made available on github so the reader can recreate the results in this paper as well as apply the method to other autoencoders and datasets.

Boris Lorbeer, Tanja Deutsch, Peter Ruppel et al.

This paper describes a new method, HMM gauge likelihood analysis, or GLA, of detecting anomalies in discrete time series using Hidden Markov Models and clustering. At the center of the method lies the comparison of subsequences. To achieve this, they first get assigned to their Hidden Markov Models using the Baum-Welch algorithm. Next, those models are described by an approximating representation of the probability distributions they define. Finally, this representation is then analyzed with the help of some clustering technique or other outlier detection tool and anomalies are detected. Clearly, HMMs could be substituted by some other appropriate model, e.g. some other dynamic Bayesian network. Our learning algorithm is unsupervised, so it does not require the labeling of large amounts of data. The usability of this method is demonstrated by applying it to synthetic and real-world syslog data.