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Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…

Non-Gaussian Component Analysis (NGCA) is the following distribution learning problem: Given i.i.d. samples from a distribution on $\mathbb{R}^d$ that is non-gaussian in a hidden direction $v$ and an independent standard Gaussian in the…

We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…

Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…

Objective: In some situations that exist both scalar and functional data, called mixed and hybrid data, the hybrid PCA (HPCA) was introduced. Among the regression models for the hybrid data, we can count covariate-adjusted HPCA, the…

We introduce a new analysis method to deal with stationary non-Gaussian noises in gravitational wave detectors in terms of the independent component analysis. First, we consider the simplest case where the detector outputs are linear…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

At the crossway of machine learning and data analysis, anomaly detection aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

The functional generalized additive model (FGAM) was recently proposed in McLean et al. (2013) as a more flexible alternative to the common functional linear model (FLM) for regressing a scalar on functional covariates. In this paper, we…

This paper aims to develop new techniques to describe joint behavior of stocks, beyond regression and correlation. For example, we want to identify the clusters of the stocks that move together. Our work is based on applying Kernel…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Recent studies demonstrate that trends in indicators extracted from measured time series can indicate approaching to an impending transition. Kendall's {\tau} coefficient is often used to study the trend of statistics related to the…

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components…