Related papers: Copula Component Analysis

Independent Mechanism Analysis (IMA) seeks to address non-identifiability in nonlinear Independent Component Analysis (ICA) by assuming that the Jacobian of the mixing function has orthogonal columns. As typical in ICA, previous work…

Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the…

Handling highly dependent data is crucial in clinical trials, particularly in fields related to ophthalmology. Incorrectly specifying the dependency structure can lead to biased inferences. Traditionally, models rely on three fixed…

Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear…

We describe a method for unmixing mixtures of freely independent random variables in a manner analogous to the independent component analysis (ICA) based method for unmixing independent random variables from their additive mixtures. Random…

This study utilizes Independent Component Analysis (ICA) to unveil a consistent semantic structure within embeddings of words or images. Our approach extracts independent semantic components from the embeddings of a pre-trained model by…

We consider independent component analysis of binary data. While fundamental in practice, this case has been much less developed than ICA for continuous data. We start by assuming a linear mixing model in a continuous-valued latent space,…

In this paper we derive a new framework for independent component analysis (ICA), called measure-transformed ICA (MTICA), that is based on applying a structured transform to the probability distribution of the observation vector, i.e.,…

We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a…

Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…

Independent component analysis (ICA) is a widespread data exploration technique, where observed signals are modeled as linear mixtures of independent components. From a machine learning point of view, it amounts to a matrix factorization…

In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…

Principal Component Analysis (PCA)-based techniques can separate data into different uncorrelated components and facilitate the statistical analysis as a pre-processing step. Independent Component Analysis (ICA) can separate statistically…

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear…

Independent Component Analysis (ICA) is an effective unsupervised tool to learn statistically independent representation. However, ICA is not only sensitive to whitening but also difficult to learn an over-complete basis. Consequently, ICA…

We develop a new neural network based independent component analysis (ICA) method by directly minimizing the dependence amongst all extracted components. Using the matrix-based R{\'e}nyi's $\alpha$-order entropy functional, our network can…

We present a new high performance Convex Cauchy Schwarz Divergence (CCS DIV) measure for Independent Component Analysis (ICA) and Blind Source Separation (BSS). The CCS DIV measure is developed by integrating convex functions into the…

Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits forms of sparsity and structure to reduce the memory and/or computational complexity of the learning task. In this…

Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory…