New Approximations of Differential Entropy for Independent Component Analysis and Projection Pursuit

By Aapo Hyvärinen. 1997

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, neutral): “, 2009; Gray, 2006) (Grenander and Szego, 1958) EdE ITE: Shannon Edgeworth (van Hulle, 2005) Gau based on (9) ME1 ITE: Shannon MaxEnt1 (Hyvärinen, 1997) ME2 ITE: Shannon MaxEnt2 (Hyvärinen, 1997)”
Edgeworth Approximation of Multivariate Differential Entropy (2005, background): “The more sophisticated approximation of one-dimensional entropy, based on the maximum entropy principle (Hyv¨arinen, 1998), cannot be readily extended to the multidimensional case.”
Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models (2013, methodology): “(23) We can approximate R using the same maximum entropy approximations (Hyvärinen, 1998) as in the linear case in Section 2.3.”
Dependence, Correlation and Gaussianity in Independent Component Analysis (2003, methodology): “This is essentially the rhetoric of projection pursuit, initiated by Friedman and Tukey (1974) and whose connections to ICA have long been noticed and put to good use for justifying sequential extraction of sources as in the fastICA algorithm (see Hyvärinen, 1998).”
Nonlinear independent component analysis: Existence and uniqueness results (1999, background): “1 = g 0 (9) Now, denote by ^ s i (); i = 1; 2 the components obtained by ^ s = g (x) (10) Take some measure of the dependence of the obtained components, for example mutual information I (Comon, 1994; Hyvrinen, 1998 ).”
Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, unknown): “, 2009; Gray, 2006) (Grenander and Szego, 1958) EdE ITE: Shannon Edgeworth (van Hulle, 2005) Gau based on (10) ME1 ITE: Shannon MaxEnt1 (Hyvärinen, 1997) ME2 ITE: Shannon MaxEnt2 (Hyvärinen, 1997)”
Independent component analysis: algorithms and applications (2000, methodology): “In many applications, it would be more realistic to assume that there is some noise in the measurements (Hyvärinen, 1998a; Hyvärinen, 1999c), which would mean adding a noise term in the model.”
Approach and applications of constrained ICA (2005, background): “Hence, the contrast function for the less-complete ICA is defined as (9) where is estimated by a flexible and reliable approximation given in [32] (10) where is a positive constant, is a nonquadratic function, and is a Gaussian variable having zero mean and unit variance .”
Review of methods for functional brain connectivity detection using fMRI (2008, methodology): “…components (ICs) simply by: (10) As for the solution of ICA, there are two commonly used algorithms: the Infomax [37] and the Fixed-Point [38], both of which are through the minimization of mutual information of components C i Informax achieved this goal by adaptively maximizing the…”
Fast and robust fixed-point algorithms for independent component analysis (1999, methodology): “In [19] it was shown that these approximations are often considerably more accurate than the conventional, cumulant-based approximations in [1], [7], and [26].”
Non-linear Causal Inference using Gaussianity Measures (2014, methodology): “Furthermore, by extending the results of Hyvärinen and Smith (2013) based on information theory, we have shown that this Gaussianization effect is also present when the two random variables are multivariate due to an increment of the”