Learning low-dimensional representations that disentangle the underlying
factors of variation in data has been posited as an important step towards
interpretable machine learning with good generalization. To address the fact
that there is no consensus on what disentanglement entails, Higgins et al.
(2018) propose a formal definition for Linear Symmetry-Based Disentanglement,
or LSBD, arguing that underlying real-world transformations give exploitable
structure to data.
Although several works focus on learning LSBD representations, such methods
require supervision on the underlying transformations for the entire dataset,
and cannot deal with unlabeled data. Moreover, none of these works provide a
metric to quantify LSBD.
We propose a metric to quantify LSBD representations that is easy to compute
under certain well-defined assumptions. Furthermore, we present a method that
can leverage unlabeled data, such that LSBD representations can be learned with
limited supervision on transformations. Using our LSBD metric, our results show
that limited supervision is indeed sufficient to learn LSBD representations