Identifiability, separability, and uniqueness of linear ICA models

By Jan Eriksson, Visa Koivunen. 2004

197 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Artificial Intelligence, Signal Processing

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Citations in the corpus

Causal Discovery from Temporally Aggregated Time Series (2017, methodology): “According to the Uniqueness Theorem in Eriksson & Koivunen (2004), we know that under condition A2, for each i, there exists one and only one j such that the distribution of e(l)i , l = 0, ..., 2k − 2 (which have the same distribution), is the same as the distribution of e′(l)j , l = 0, ..., 2k −…”
Measure Transformed Independent Component Analysis (2013, background): “Under the model (5) it has been shown that the mixing matrix A can be uniquely identified, up to permutation and scaling of its columns, if and only if at most one of the sources is Gaussian (Kagan et al., 1973; Common, 1994; Hyvärinen et al., 2001; Errikson and Koivunen, 2004).”
Estimation of linear non-Gaussian acyclic models for latent factors (2009, methodology): “independent, this is an ICA model with additive errors (Noisy ICA), which is identifiable up to an arbitrary permutation and scaling of columns of A [2, 3 ].”
Recent Progress in Log-Concave Density Estimation (2017, background): “Eriksson and Koivunen (2004) proved that the pair of conditions that none of P1, .”
Estimation of causal effects using linear non-Gaussian causal models with hidden variables (2008, background): “For Gaussian data, the causal inference problem is restricted by the degree to which these covariance matrices are distinguishable from each other.”
Specific and Shared Causal Relation Modeling and Mechanism-Based Clustering (2019, methodology): “Next, thanks to the identifiability of independent component analysis-based models [7, 32], we can show that in each group, instantaneous causal relations bij and lagged causal relations aij,p are identifiable [21].”
Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures (2007, background): “This is no longer possible in the case of underdetermined mixtures: for each sample , the corresponding source sample that satisfies is only known to belong to an affine variety of dimension —hence the term “underdetermined.” However, the mixing matrix and the source densities are still unique under”
Identifiability and estimation of structural vector autoregressive models for subsampled and mixed-frequency time series. (2017, background): “This line of work applies techniques originally developed for both structural equation modeling with non-Gaussian errors and independent component analysis (ICA) [20] to the SVAR context.”
Independent component analysis: recent advances (2013, unknown): “Under these three conditions, the model is essentially identiﬁable (Comon, 1994; Eriksson and Koivunen, 2004).”
Causal Discovery with Linear Non-Gaussian Models under Measurement Error: Structural Identifiability Results (2018, methodology): “This lemma is implied by Theorem 10.3.1 in (Kagan et al., 1973) or Theorem 1 in (Eriksson & Koivunen, 2004).”
DirectLiNGAM: A Direct Method for Learning a Linear Non-Gaussian Structural Equation Model (2011, background): “, 2001), which is known to be identifiable (Comon, 1994; Eriksson and Koivunen, 2004).”