Related papers: Linear Independent Component Analysis over Finite …
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…
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude…
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…
Online blind source separation is essential for both speech communication and human-machine interaction. Among existing approaches, overdetermined independent vector analysis (OverIVA) delivers strong performance by exploiting the…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data (Spirtes et al. 2000; Pearl 2000). Such methods make various assumptions on the data generating process to facilitate its…
We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form $y = Ax + \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is a…
Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of…
Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Nonlinear independent component analysis (nICA) aims at recovering statistically independent latent components that are mixed by unknown nonlinear functions. Central to nICA is the identifiability of the latent components, which had been…
At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
Identifying the causal relations between interested variables plays a pivotal role in representation learning as it provides deep insights into the dataset. Identifiability, as the central theme of this approach, normally hinges on…
There is a gap between the theoretical foundations of disentanglement and the practice of modern representation learning. Existing theoretical frameworks, particularly Independent Component Analysis (ICA) and its nonlinear variants, assume…
In recent years, Independent Component Analysis (ICA) has successfully been applied to remove noise and artifacts in images obtained from Three-dimensional Polarized Light Imaging (3D-PLI) at the mesoscale (i.e., 64 $\mu$m). Here, we…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
We apply both distance-based (Jin and Matteson, 2017) and kernel-based (Pfister et al., 2016) mutual dependence measures to independent component analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA, minimizing…
In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA…
Independent component analysis is intended to recover the mutually independent components from their linear mixtures. This technique has been widely used in many fields, such as data analysis, signal processing, and machine learning. To…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…