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The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called…

In multimedia broadcasting, no-reference image quality assessment (NR-IQA) is used to indicate the user-perceived quality of experience (QoE) and to support intelligent data transmission while optimizing user experience. This paper proposes…

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…

Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…

Recent advances have sparked significant interest in the development of privacy-preserving Principal Component Analysis (PCA). However, many existing approaches rely on restrictive assumptions, such as assuming sub-Gaussian data or being…

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

We develop two methods for the following fundamental statistical task: given an $\epsilon$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our…

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than…

Methods for parameter estimation of gravitational-wave data assume that detector noise is stationary and Gaussian. Real data deviates from these assumptions, which causes bias in the inferred parameters and incorrect estimates of the…

Data processing constitutes a critical component of high-contrast exoplanet imaging. Its role is almost as important as the choice of a coronagraph or a wavefront control system, and it is intertwined with the chosen observing strategy.…

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Logan's graphical analysis (LGA) is a widely-used approach for quantification of biochemical and physiological processes from Positron emission tomography (PET) image data. A well-noted problem associated with the LGA method is the bias in…

Laser-induced breakdown spectroscopy is a preferred technique for fast and direct multi-elemental mapping of samples under ambient pressure, without any limitation on the targeted element. However, LIBS mapping data have two peculiarities:…

Searching for and charactering the non-Gaussianity (NG) of a given field has been a vital task in many fields of science, because we expect the consequences of different physical processes to carry different statistical properties. Here we…

In this paper, we introduce a general extension of linear sparse component analysis (SCA) approaches to postnonlinear (PNL) mixtures. In particular, and contrary to the state-of-art methods, our approaches use a weak sparsity source…