1.2 Research Questions 7 However, this definition only describes what perfect LSBD should look like— it does not supply a metric to quantify how well LSBD is achieved for given representations. Moreover, it does not provide any method to actually obtain LSBD representations. It is crucial to have a metric that quantifies LSBD, to be able to evaluate methods that aim to obtain LSBD representations and to compare LSBD to previous understandings of disentanglement. Since the proposal of LSBD, several methods have been proposed to learn LSBD representations (Caselles-Dupré et al., 2019; Quessard et al., 2020; Painter et al., 2020). Although some of these works do propose metrics that measure some aspect of LSBD, none of them provide a general metric that fully quantifies LSBD according to its formal definition and for any learned representation. A quantification of LSBD can furthermore be helpful to develop methods to learn LSBD representations. Typically, evaluation metrics of traditional disentanglement assume access to the underlying factors that should be disentangled, whereas methods to learn disentangled representations have limited access to these factors. But even partial information can be beneficial, as demonstrated by weakly-supervised methods (Locatello et al., 2020; Träuble et al., 2021). Similarly, a quantification metric for LSBD may be useful for learning LSBD representations, even if this metric can only be computed under certain assumptions and in a weakly-supervised fashion. Given the lack of a general quantification metric for LSBD, as well as the need for methods that can obtain LSBD representations, we pose the following research questions: Q: How, and under which assumptions, canLinear Symmetry-Based Disentanglement (LSBD) be quantified according to its formal definition? Q: How, and under which assumptions, can such a quantification help with learning LSBD representations? 1.2.3 Out-of-Distribution Generalisation with Linear SymmetryBased Disentangled Representations We previously focused on the suitability of probabilistic latent variable models, in particular Variational Autoencoders (VAEs), for anomaly detection. Since the latent space Z ideally shares desirable properties with the real world W, it should form a reliable model to describe what is normal and what is anomalous.
RkJQdWJsaXNoZXIy MjY0ODMw