Robust Causal Analysis of Linear Cyclic Systems With Hidden Confounders

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.

Comparative Study of Causal Discovery Methods for Cyclic Models with Hidden Confounders

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.

Anomaly Detection With Partitioning Overfitting Autoencoder Ensembles

In this paper, we propose POTATOES (Partitioning OverfiTting AuTOencoder EnSemble) a new type of autoencoder ensembles for unsupervised outlier detection. Autoencoders are a popular method for this type of problem, especially if the data is located near a submanifold of smaller dimension than that of the ambient space. The standard approach is to approximate the data with the decoder submanifold of the autoencoder and to use the reconstruction error as anomaly score. However, one of the main problems is often to find the right amount of regularization. If the regularization is too strong, the data is underfitted and we obtain many false positives. If the regularization is too weak, the data is overfitted which results in false negatives. The remedy we propose 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 realistic data and show that it often outperforms current outlier detection methods.

Anomaly Detection with HMM Gauge Likelihood Analysis

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.