Source separation in post-nonlinear mixtures

By Anisse Taleb, Christian Jutten. 1999

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

The Incomplete Rosetta Stone problem: Identifiability results for Multi-view Nonlinear ICA (2019, background): “Such assumptions may be grouped into two main categories: (i) those regarding properties of the sources (e.g. non-stationarity or time correlation in time series settings [6, 37]); and (ii) those restricting the functional form of the mixing functions (e.g., post-nonlinear mixing [40]).”
Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning (2018, background): “However, very few results are available in that direction, and usually based on very restrictive conditions, such as adding scalar nonlinearities to a linear mixing (Taleb and Jutten, 1999).”
A Survey of Inductive Biases for Factorial Representation-Learning (2016, methodology): “ICA models, like PCA , generally assume a linear relationship between observation and representation, but there has been some research into developing non-linear ICA -like methods [50].”
Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays (2006, methodology): “Remark 1: The assumption (11) on the stochastic disturbance term, (cid:27)(t;x(t); x(t (cid:0) h)) , has been used in recent papers dealing with stochastic neural networks, see [12] and references therein.”
Extensions of ICA for Causality Discovery in the Hong Kong Stock Market (2006, methodology): “We further adopt the algorithm in [ 12 ] to do PNL ICA, but to reduce the model complexity and to achieve a reliable result, all gi are modeled by the same MLP.”
Learning Independent Features with Adversarial Nets for Non-linear ICA (2017, background): “However, under certain circumstances, some speciﬁc types of non-linear mixtures like post non-linear mixtures (PNL) can still be separated (Taleb & Jutten, 1999).”
Some extensions of score matching (2007, methodology): “The proof is a simple variant of the partial integration trick used in basic score matching [3] based on earlier work by [7,8].”
Kernel-Based Nonlinear Blind Source Separation (2003, unknown): “…1992;Valpola,Giannakopoulos,Honkela,&Karhunen,2000;Lee,Koehler, &Orglmeister,1997;Lin,Grier,&Cowan,1997;Yang,Amari,&Cichocki, 1998;Marques&Almeida,1999;Pajunen,Hyv¨arinen,&Karhunen,1996; Pajunen&Karhunen,1997;Fyfe&Lai,2000;Taleb&Jutten,1999;Hyvari-nen,Karhunen,&Oja,2001).”
Blind source separation based vibration mode identification (2007, background): “Depending upon the type of mixing, BSS can be classified as linear [15,16] or nonlinear [17], where the mixtures are linear or nonlinear combinations, respectively, of the sources.”
Advances in Nonlinear Blind Source Separation (2003, methodology): “Taleb and Jutten have considered separability of nonlinear mixtures in [24], [5].”
On Estimation of Functional Causal Models (2015, methodology): “As in post-nonlinear independent component analysis (ICA) [Taleb and Jutten 1999; Zhang and Chan 2005], the post-nonlinear transformation f 2 represents the sensor or measurement distortion, which is frequently encountered in practice.”