128 Conclusion and Future Work due to a failing decoder. Thus, there are some limitations to assessing the OOD generalisation of these models based on likelihood. 6.3 Future Work As discussed in the previous section, there are already various research directions that aim to overcome some of the challenges around anomaly detection with likelihood-based models. While these works already suggest some solutions to the problems they highlight, there still remains work to be done to obtain reliable anomaly scores for complicated real-world data sets. In particular, if likelihood according to a generative model is not the right quantity to assess the normality of a data point, a clear question to be answered by future work is what the right quantity can be. Another area of future work is dealing with the constraint that training requires access to a normal dataset without anomalies. Chalapathy and Chawla (2019) refer to this scenario as unsupervised anomaly detection, whereas they use the term semi-supervised anomaly detection for our setting where a dataset of known normal data is available. They list a number of deep learning approaches that address such unsupervised anomaly detection, but none of these are based on the VAE framework. Thus, training a VAE that is suitable for anomaly detection for a dataset that includes unlabelled anomalies remains an open problem. Further future work could focus on learning better models that can represent well what we consider normal, without being so flexible that they can represent anomalous behaviour as well. We have investigated one specific approach in the context of LSBD for OOD generalisation, but there are many other methods that aim to learn better likelihood estimations of the data, which may be useful for anomaly detection. The limitations described in the previous section about the applicability of LSBD, and in particular our DLSBD metric and LSBD-VAE method, also highlight clear directions for future work. In our work we make some explicit assumptions, and formalise the quantification of LSBD. This also allows us to pinpoint specific challenges to be addressed, by figuring out how to relax the assumptions and limitations in our work. Future work can e.g. focus on investigating how to computeDLSBDand how to formulate LSBD-VAE for different types of subgroups. Another next step is trying to relax the assumption of a regular group action on the data space, such that methods can deal with situations such as occlusion. Furthermore, more practical follow-ups are identifying settings where transfor-
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