Related papers: Independent Component Analysis Over Galois Fields
Given independent samples generated from the joint distribution $p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional Independence (CI-Testing), i.e., whether the joint equals the CI distribution…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…
We present a Maximum A Posteriori (MAP) derivation of the Independent Vector Analysis (IVA) algorithm, a blind source separation algorithm, by incorporating a prior over the demixing matrices, relying on a free-field model. In this way, the…
Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called…
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…
I recall my first encounter with Professor Shun-ichi Amari who, once upon a time in Las Vegas, gave me a precious hint about connecting Independent Component Analysis (ICA) to Information Geometry. The paper sketches, rather informally,…
An analysis of the protein content of several crystal forms of proteins has been performed. We apply a new numerical technique, the Independent Component Analysis (ICA), to determine the volume fraction of the asymmetric unit occupied by…
We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current…
This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and…
Causal discovery aims to recover causal structures generating the observational data. Despite its success in certain problems, in many real-world scenarios the observed variables are not the target variables of interest, but the imperfect…
An important problem in network science is finding an optimal placement of sensors in nodes in order to uniquely detect failures in the network. This problem can be modelled as an identifying code set (ICS) problem, introduced by Karpovsky…
It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…
The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
This paper deals with a source separation strategy based on second-order statistics, namely, on data covariance matrices estimated at several lags. In general, ``blind'' approaches to source separation do not assume any knowledge on the…
The advancement in the field of data science especially in machine learning along with vast databases of variable star projects like the Optical Gravitational Lensing Experiment (OGLE) encourages researchers to analyse as well as classify…
Word embeddings represent words as multidimensional real vectors, facilitating data analysis and processing, but are often challenging to interpret. Independent Component Analysis (ICA) creates clearer semantic axes by identifying…