Related papers: Large Dimensional Independent Component Analysis: …
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
Identifying the causal relations between interested variables plays a pivotal role in representation learning as it provides deep insights into the dataset. Identifiability, as the central theme of this approach, normally hinges on…
Independent Component Analysis (ICA) is an algorithm originally developed for finding separate sources in a mixed signal, such as a recording of multiple people in the same room speaking at the same time. Unlike Principal Component Analysis…
Stochastic algorithms are well-known for their performance in the era of big data. In convex optimization, stochastic algorithms have been studied in depth and breadth. However, the current body of research on stochastic algorithms for…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together…
Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper…
The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…
Modern data workflows are inherently adaptive, repeatedly querying the same dataset to refine and validate sequential decisions, but such adaptivity can lead to overfitting and invalid statistical inference. Adaptive Data Analysis (ADA)…
Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully…
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
Here, we address the problem of Independent Subspace Analysis (ISA). We develop a technique that (i) builds upon joint decorrelation for a set of functions, (ii) can be related to kernel based techniques, (iii) can be interpreted as a…
We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to…
Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…