The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA

By Luigi Gresele, Paul K. Rubenstein, Arash Mehrjou, Francesco Locatello, Bernhard Schölkopf. 2019

118 citations recorded by the source corpus.

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.

Subfields: Artificial Intelligence, Electrochemistry, Statistics and Probability, Representation & Self-Supervised Learning, Signal Processing

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Citations in the corpus

A Sober Look at the Unsupervised Learning of Disentangled Representations and their Evaluation (2020, background): “…recently shifted to non-iid data types exploiting time dependent or grouped observations (Hyvarinen and Morioka, 2016; Hyvarinen et al., 2019; Gresele et al., 2019) We focus our study on the setting where factors of variations are not observable at all, that is, we only observe samples from…”
Toward Causal Representation Learning (2021, background): “These contexts can come from interventions [187], [191], [220], nonstationary time series [101], [116], [192], or multiple views [90], [114].”
Towards Causal Representation Learning (2021, background): “These contexts can come from interventions [218, 189, 192], non-stationary time series [117, 100, 193] or multiple views [89, 115].”
On the Transfer of Disentangled Representations in Realistic Settings (2020, background): “Ideas related to disentangling the factors of variation date back to the non-linear ICA literature (Comon, 1994; Hyv¨arinen and Pajunen, 1999; Bach and Jordan, 2002; Jutten and Karhunen, 2003; Hyvarinen and Morioka, 2016; Hyvarinen et al., 2019; Gresele et al., 2019).”
Weakly-Supervised Disentanglement Without Compromises (2020, background): “Recently, the ICA community has considered weak forms of supervision such as temporal consistency (Hyvarinen & Morioka, 2016; 2017), auxiliary supervised information (Hyvarinen et al., 2019; Khemakhem et al., 2019), and multiple views (Gresele et al., 2019).”
Weakly Supervised Disentanglement with Guarantees (2019, neutral): “Because we do not assume the factors of variation are statistically independent, our theoretical analysis is also distinct from the closely-related match pairing analysis in Gresele et al. (2019).”
On the Fairness of Disentangled Representations (2019, background): “Ideas related to disentangling the factors of variations have a long tradition in machine learning, dating back to the non-linear ICA literature [17, 3, 46, 42, 43, 44, 32].”
Are Disentangled Representations Helpful for Abstract Visual Reasoning? (2019, background): “…prior, using λ 1 = 0 and λ 2 ≥ 1 with R 2 ( q φ ( z ) Other related works Learning disentangled representations is similar in spirit to non-linear ICA, although it relies primarily on (architectural) inductive biases and different degrees of supervision [13, 2, 39, 36, 37, 38, 25, 33, 32].”
Disentangling Factors of Variation Using Few Labels (2019, background): “This problem has already been studied extensively in the non-linear ICA literature (Comon, 1994; Bach & Jordan, 2002; Jutten & Karhunen, 2003; Hyvarinen & Morioka, 2016; Hyvärinen & Pajunen, 1999; Hyvarinen et al., 2019; Gresele et al., 2019).”
Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style (2021, background): “Since it is impossible to identify the true latent factors without any supervisory signal in the general nonlinear case [57, 82], recent work has turned to weakly- or self-supervised approaches which leverage additional information in the form of multiple views [39, 83, 108, 129], auxiliary variable”
Disentangling Factors of Variations Using Few Labels (2020, background): “This problem has already been studied extensively in the non-linear ICA literature (Comon, 1994; Bach & Jordan, 2002; Jutten & Karhunen, 2003; Hyvarinen & Morioka, 2016; Hyvärinen & Pajunen, 1999; Hyvarinen et al., 2019; Gresele et al., 2019).”