Related papers: Sparse Gaussian ICA
Modeling non Gaussian and non stationary signals and images has always been one of the most important part of signal and image processing methods. In this paper, first we propose a few new models, all based on using hidden variables for…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA works only for two datasets, i.e., there are only two views or two distinct objects. To…
Independent component analysis is an unsupervised learning approach for computing the independent components (ICs) from the multivariate signals or data matrix. The ICs are evaluated based on the multiplication of the weight matrix with the…
Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the…
This work introduces a novel principle we call disentanglement via mechanism sparsity regularization, which can be applied when the latent factors of interest depend sparsely on past latent factors and/or observed auxiliary variables. We…
Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the observation that the first-layer filters learnt by deep…
Linear Independent Component Analysis (ICA) is a blind source separation technique that has been used in various domains to identify independent latent sources from observed signals. In order to obtain a higher signal-to-noise ratio, the…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…
Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving a series of…
For statistical analysis of functional Magnetic Resonance Imaging (fMRI) data sets, we propose a data-driven approach based on Independent Component Analysis (ICA) implemented in a new version of the AnalyzeFMRI R package. For fMRI data…
The interpretability of generative models is considered a key factor in demonstrating their effectiveness and controllability. The generated data are believed to be determined by latent variables that are not directly observable. Therefore,…
We consider shared response modeling, a multi-view learning problem where one wants to identify common components from multiple datasets or views. We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear…
We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
The brain effortlessly solves blind source separation (BSS) problems, but the algorithm it uses remains elusive. In signal processing, linear BSS problems are often solved by Independent Component Analysis (ICA). To serve as a model of a…
Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…
We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models…
Spatial Independent Component Analysis (ICA) decomposes the time by space functional MRI (fMRI) matrix into a set of 1-D basis time courses and their associated 3-D spatial maps that are optimized for mutual independence. When applied to…
Independent component analysis (ICA) has often been used as a tool to model natural image statistics by separating multivariate signals in the image into components that are assumed to be independent. However, these estimated components…