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In recent years, longitudinal neuroimaging study has become increasingly popular in neuroscience research to investigate disease-related changes in brain functions. In current neuroscience literature, one of the most commonly used tools to…
Self-supervised learning aims to learn a embedding space where semantically similar samples are close. Contrastive learning methods pull views of samples together and push different samples away, which utilizes semantic invariance of…
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 coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
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…
Independent Component Analysis (ICA) recently has attracted attention in the statistical literature as an alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however,…
Representation learning models exhibit a surprising stability in their internal representations. Whereas most prior work treats this stability as a single property, we formalize it as two distinct concepts: statistical identifiability…
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…
Inference and inverse problems are closely related concepts, both fundamentally involving the deduction of unknown causes or parameters from observed data. Bayesian inference, a powerful class of methods, is often employed to solve a…
Independent component analysis (ICA) is now a widely used solution for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Independent vector analysis (IVA) generalizes ICA to multiple datasets, i.e., to…
Independent Component Analysis (ICA) plays a central role in modern machine learning as a flexible framework for feature extraction. We introduce a horseshoe-type prior with a latent Polya-Gamma scale mixture representation, yielding…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data.…
Although approaches to Independent Component Analysis (ICA) based on characteristic function seem theoretically elegant, they may suffer from implementational challenges because of numerical integration steps or selection of tuning…
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 study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA). We consider both the the problem constrained to white signals and the unconstrained problem. The Hessian of the objective…
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…
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in…
We consider the framework of Independent Component Analysis (ICA) for the case where the independent sources and their linear mixtures all reside in a Galois field of prime order P. Similarities and differences from the classical ICA…
The Independent Component Analysis (ICA) algorithm is implemented as a neural network for separating signals of different origin in astrophysical sky maps. Due to its self-organizing capability, it works without prior assumptions on the…
Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or…