Unbiased Mechanism Analysis and the Manifold Hypothesis
Authors: Shubhangi Ghosh, Luigi Gresele, Julius von Kügelgen, Michel Besserve, Bernhard Schölkopf
Abstract: Unbiased Mechanism Analysis (IMA) seeks to take care of non-identifiability in nonlinear Unbiased Ingredient Analysis (ICA) by assuming that the Jacobian of the mixing carry out has orthogonal columns. As typical in ICA, earlier work focused on the case with an equal number of latent elements and observed mixtures. Proper right here, we lengthen IMA to settings with an even bigger number of mixtures that reside on a manifold embedded in a higher-dimensional than the latent space — in response to the manifold hypothesis in illustration learning. For this setting, we current that IMA nonetheless circumvents numerous non-identifiability factors, suggesting that it may be a helpful principle for higher-dimensional observations when the manifold hypothesis holds. Extra, we present that the IMA principle is roughly glad with extreme probability (rising with the number of observed mixtures) when the directions alongside which the latent elements have an effect on the observations are chosen independently at random. This provides a model new and rigorous statistical interpretation of IMA.
